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Fabio Petri - Advanced Microeconomics - provisional textbook
CHAPTER 1
THE CLASSICAL OR SURPLUS APPROACH
1.1. A VERY BRIEF HISTORICAL INTRODUCTION
Microeconomics is the branch of economic theory where, from the study of the decisions of
individuals and of their effects, one tries to answer the question: what is produced, how, and for
whom. Historically, this question used to be studied under a different name: ‘theory of value and of
income distribution’. The theory of value narrowly understood studies what determines the relative
prices (or values) of the goods and services sold in a market economy; but from the inception of
economic theory as a systematic enquiry, it was found that this study is intimately connected with
the study of what determines wages, land rents, profits, interest, in other words, income distribution;
hence an impossibility to separate the study of value from the study of income distribution; and the
study of the latter was found necessarily to involve also the study of the forces determining the
quantities produced, and the utilization of resources, in a market economy.
In the history of economic analysis it is possible, albeit at the cost of drastic simplification,
to distinguish two main, successive approaches to this theory.
The earlier approach, the one of the Physiocrats, Adam Smith, David Ricardo, was called
classical by Karl Marx. In order to avoid confusion with other current usages of the term ‘classical’,
nowadays it is also called surplus approach, because centrally based on the notion of social surplus,
the production in excess of what (inclusive of the necessary consumption of workers) must be put
back into the production process in order to allow the repetition of production on an unchanged
scale. The focus was on what determined the size, the distribution among the different social
classes, and the growth, of the social surplus. This approach was born in a clear form in the third
quarter of the 18th century with François Quesnay; it was developed by Adam Smith (his magnum
opus, The Wealth of Nations, was published in 1776), and then by David Ricardo (who wrote
between 1810 and 1823); when already a majority of economists was moving in another direction it
was resumed and further developed by Karl Marx (the first volume of Das Kapital, the sole one not
posthumously published, came out in 1867).
After a fairly confused and eclectic interregnum in the period 1830-1870, in the last quarter
of the 19th century whatever was left of the influence of the classical approach was reduced to a
decidedly minoritarian position by a new approach, centered on the notion of a tendency toward an
equilibrium between supply and demand for the ‘factors of production’ labour, land, and capital, a
tendency due to technical and psychological substitution processes induced by changes in relative
‘factor prices’. Anticipations of this approach are found, around the middle of the 19th century, in
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the German author Von Thunen; but the founders of the approach are generally considered to be
Stanley Jevons in England, Carl Menger in Austria, and Léon Walras in France, who with striking
near-simultaneity all published little before or after 1870. Alfred Marshall (who was to become the
most influential economist for decades) published later but had autonomously reached essentially
the same approach at about the same time. Because of the central role in it of the notions of
marginal utility and marginal product (cf. ch. 3 below), this approach was called marginal or
marginalist, but it is nowadays more often referred to as neoclassical (a potentially misleading
name, because, as chapter 3 will show, it is rather anti-classical[1]). With the second generation of
marginalist economists (Edgeworth, Wicksteed in Great Britain; Wieser, Böhm-Bawerk in Austria;
J B Clark, Irving Fisher in USA; Pareto, Barone, Pantaleoni in Italy; Wicksell, Cassel in Sweden;
etc.) this approach came to dominate economic science nearly completely, and is still largely
The approach is even sometimes called ‘classical’. Thus the terms 'classical' and 'neoclassical' are
susceptible of generating confusions, and some clarification is now necessary, albeit at the risk of mentioning
notions still unfamiliar to some readers. Karl Marx had called 'classical' the body of economic theories from
Petty through the Physiocrats and Adam Smith to David Ricardo, but John Maynard Keynes, in his
influential General Theory of Employment, Interest and Money (1936), extended the term 'classical' to cover
also the marginal approach. He wrote:
“The classical economists” was a name invented by Marx to cover Ricardo and James Mill and their
predecessors, that is to say the founders of the theory which culminated in the Ricardian economics. I have
been accustomed, perhaps perpetrating a solecism, to include in “the classical school” the followers of
Ricardo, those, that is to say, who adopted and perfected the theory of the Ricardian economics, including
(for example) J. S. Mill, Marshall, Edgeworth and Prof. Pigou. (Keynes, p. 3, fn. 1, of the edition of the
General Theory in The Collected Works of J.M.Keynes, ed. Moggridge, vol. VII, italics in original).
As this passage makes clear, Keynes based his use of the term ‘classical’ on Marshall's interpretation
(the dominant one at the time) of marginalism as, not a radical rejection, but instead a development of and
improvement upon Ricardo’s approach; the phrase ‘perhaps perpetrating a solecism’ [Oxford Dictionary:
“solecism: 1. A violation of conventional usage and grammar. 2. A violation of etiquette. 3. An impropriety,
mistake, or incongruity.”] shows that Keynes was not sure of his right thus to extend the meaning of
‘classical school’; but, further helped by Ricardo's acceptance of Say's Law (the issue that concerned him
most), Keynes appears to have considered there to be little difference, for his purposes, between Ricardo and
the theories of employment he was intent on criticizing, i.e. the marginal theories of Marshall, Pigou, and the
generality of economists at the time. Keynes' usage, which essentially identifies ‘classical’ with
‘marginalist’, made it possible for Samuelson to call 'a grand neo-classical synthesis' the subsequent
synthesis of Keynes' ideas with the marginal approach operated by Hicks, Modigliani, Tobin, etc.;
afterwards, in the debates of the 1950s and 1960s on the validity of the ‘neoclassical synthesis’ argument that
persistent unemployment was ultimately due to the downward rigidity of money wages, the term
'neoclassical' came more and more to indicate the 'real' forces that in the 'neoclassical synthesis' would push
toward a marginalist full-employment equilibrium if they did not meet the Keynesian obstacles (cf. ch. 14??
below); thus 'neoclassical' nowadays stands essentially for 'marginalist'. Keynes' usage of the term ‘classical’
occasionally reappears in macroeconomics, e.g. in the term ‘New Classical Macroeconomics’. Since the
1950s, however, further research stimulated above all by the Italian economist Piero Sraffa’s critical edition
of the Collected Works of David Ricardo and in particular by his editorial Introduction to Vol. I of that
edition (1951), has radically questioned Marshall’s claim of an analytical continuity between Ricardo and
marginal theory, and the majority view is now that Marshall and Pigou did not adopt and perfect Ricardian
economics, they replaced it with the marginal approach which was, if anything, anti-Ricardian. Thus, since
Keynes did perpetrate a solecism, in this book 'classical' is used in Marx's sense, and the term ‘marginalist’
or ‘marginal’ has been generally preferred to 'neoclassical'.
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dominant.
But, among value theory specialists, doubts about the validity of the marginal approach have
considerably increased since the 1960s. The rigorous formulation of the approach – the theory of
general equilibrium – is increasingly accused of having to rely on exceedingly implausible
assumptions; furthermore, many economists have come to believe that a satisfactory treatment of
capital in this approach is impossible[2]. Also, the approach is not easily reconciled with the
empirical evidence: it forecasts a spontaneous tendency of market economies toward the full
employment of all resources, a forecast which according to many economists is blatantly
contradicted by the historical evidence. Thus, for both theoretical and empirical reasons, a number
of dissident schools of thought have sprung up in recent decades, arguing in favour of alternative
approaches. Nowadays the teaching of microeconomics must recognize that the situation is one of a
plurality of approaches, and of sharp disagreements among economists. The disagreements have
profound implications on the characterization of the society in which we live; there is a very wide
spectrum of positions, from theories that view the market economy we live in – modern capitalism
– as quite close to the best of all possible worlds, to theories that characterize it as more similar to a
society based on slavery than one would tend to think on the basis of appearances. And these
difference do not rest on different ethical judgements, but on different descriptions of the basic
mechanisms and forces operating in our market economy, i.e. on scientific disagreements.
In this situation of uncertainty and debate about the very foundations of economic theory, a
consistent group of economists argues that it was a mistake to abandon the classical or surplus
approach in favour of the marginal/neoclassical approach, because the deficiencies of the analyses
of the classical authors can be surmounted while remaining within their approach, while on the
contrary the marginal/neoclassical approach has come out to suffer from insurmountable
difficulties; the result of a resumption of the classical approach, these economists argue, is greater
logical consistency and a great improvement in the correspondence between the predictions of
economic theory and empirical observation. For example a combination of the classical approach to
value and distribution with the Keynesian approach to the determinants of employment and growth
is argued to avoid the problems that the marginal/neoclassical approach encounters in the treatment
of capital and of dynamics, and to permit more convincing explanations of unemployment and
crises than the explanations compatible with the marginal/neoclassical approach. There already
exists a considerable body of economic analyses belonging to the modern classical revival; and a
resumption of one or other aspect of classical analyses can be found in a majority of the non2
This development is again largely due to the contributions of Piero Sraffa, who ranks therefore
together with Keynes as one of the two most important economic theorists of the XX century. Cf. chapter 7.
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neoclassical schools of thought. Classical influences can be detected even in the notion of NAIRU,
the Non-Accelerating-Inflation Rate of Unemployment, so popular in macroeconomics. A good
grasp of the classical approach, of its method, and of its basic differences from the marginal
approach appears indispensable for an understanding of the state of contemporary economic theory,
but requires surmounting widespread misinterpretations and confusions. The first chapter of this
textbook addresses this task.
The present chapter introduces to the classical approach assuming no prior acquaintance
with it, and privileges the presentation of the classical perspective in simple terms, leaving more
advanced analytical details for chapters 2 and 10. It has seemed best to present the approach in its
historical evolution, letting the classical authors speak for themselves more often than in usual
textbook practice, and allowing the differences among classical authors to bring out the structure
and evolution of the approach and its central problems; this will allow a better understanding of the
approach, avoiding widespread confusions and misunderstandings that make a recuperation of the
potential contributions of the approach more difficult[3]. Readers particularly interested in
understanding the differences between classical and marginal approach may skip chapter 2 on a first
reading and proceed directly to chapter 3, which, after a clarification of the essential structure of the
marginal approach to value and distribution, contrasts it with the classical approach.
1.2. SOCIAL SURPLUS AND INCOME DISTRIBUTION
The surplus approach progressed considerably from the Physiocrats to Karl Marx. With
hindsight, however, we can discern a nucleus of common analytical structure in the analyses of
classical economists. All these authors concentrate first of all on the conditions that must be
satisfied in order for the productive processes of the economy to be repeatable on the same scale
period after period. To such an end, they distinguish the ensemble of the goods produced in an
economy in a year in two parts:
a) the necessary consumption, i.e. the part that must be employed again in the productive
process in order to repeat it; in this part they include both the replacement of all means of
production consumed in the productive process, and what must go to the workers (the subsistence of
3
An understanding of the evolution of a theory is generally necessary in order fully to understand its
logic, the form it has taken, its open problems. In particular, a direct study of the authors who first propose
an approach is usually enormously enlightening because in their writings one finds cautions, doubts,
motivations, justifications, that disappear in the subsequent textbook canonization and simplification of the
approach, but are fundamental for an appraisal of the approach and of its potential. In our presentation of the
neoclassical approach too, an explanation of its evolution will be important.
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workers[4]);
b) the remainder, which we can call ‘social surplus’, whose value constitutes the income of
the social classes other than the workers[5]; this surplus can be employed by society as it likes,
without impairing the continuation of productive activity on at least the same scale.
The centrality of the notion of surplus and its connection with the theory of income
distribution derives in the classical authors from their interest in the causes, and in the ways to
increase, the “wealth of nations”. The utilization of the surplus determines the evolution of the
economy, the speed of its growth or decline; and this utilization is seen as essentially depending on
how the surplus gets distributed among the different social classes. Ricardo, for example, sees the
surplus as constituting the income of capitalists and of landlords, and is in favour of giving as great
as possible a portion of the surplus to the capitalists rather than to the landlords (that is to say, he is
in favour of raising the profits on capital to the detriment of land rents), because according to him
the capitalists re-invest the greater part of their income, thus favouring the growth of production,
while the landlords consume their income in luxuries; however, Ricardo concludes that the
expansion of production tends to increase the share of land rents in the surplus, and he concludes
that economic growth will inexorably tend to slow down, and to come finally to a halt (unless this
tendency is contrasted by technical progress in agriculture). Here we have an example of how the
determination of the surplus and of its evolution over time (growth theory, we would call it
nowadays) is intimately connected, in the classical approach, with the study of the determinants of
the division of the social product among the social classes.
We can grasp many of the central aspects of the classical approach through description of a
simple economy, where the sole product is corn, produced in yearly cycles by labour and corn (used
as seed, and as food for the labourers) over lands of different, or even of uniform, quality.
Suppose that in a certain year 1000 tons of corn are produced by 1000 labourers who in the
process have used up 300 tons as seed and 500 tons as subsistence. Then the net product of that year
(total product minus produced means of production used up as inputs) is 1000-300=700; the surplus
product is the net product minus the labourers’ subsistence, 700-500=200. The necessary
consumption has been 300+500=800 tons.
If production is to be repeated on the same scale the following year, then 800 tons of the
corn produced must be set aside to be used as seed and subsistence for the next production cycle;
Actually in this definition ‘workers’ should be interpreted to mean ‘productive workers’ only, cf.
footnote 86?? below.
5
Sometimes workers too can obtain a part of the surplus by raising their wages above subsistence,
and this can change the subsistence itself; we will discuss these issues at several points in the chapter.
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society is only free to use as it prefers the 200 tons of surplus, for example for consumption of
landlords or warriors, or to maintain poets or musicians, or for reinvestment. This last use means
that part of the surplus is destined to increase the seed and the subsistence necessary for the
production of corn. If for example the entire surplus is reinvested, then seed and subsistence
employed in the next production cycle become 1000 tons i.e. increase by 25%; if there is sufficient
extra labour and extra land of the same quality as the land utilized up to then, and neglecting
irregularities of agricultural yield, then in the subsequent production cycle production will be 1250
tons, obtained through the use of 1250 workers (who have consumed a total subsistence of 625 tons
of corn) and 375 tons of seed.
So far the description might apply also to a society based on slavery, where the agricultural
workers are slaves. Let us see how the classical analysis of income distribution in capitalist society
would apply to this simple economy.
Their own concrete experience suggested to classical authors that population was divided
into three fundamental social classes: the landowners (generally aristocrats), whose income derived
from the property of land; the bourgeois (ethimologically, inhabitants of towns) who were either
professionals (lawyers, doctors, teachers etc.) or businessmen (tradesmen, shopkeepers,
industrialists, bankers, etc.); and the labourers or workers (mostly wage labourers, both agricultural,
commercial and industrial). Dress, manners, values, everything sharply distinguished the members
of these three classes. Slaves and serfs were given much less attention because, after the French
Revolution, slavery was mostly abolished in the Western world (it survived in the USA, a sad
record) and serfdom only survived in Russia and some other backward countries.
By the time of Adam Smith it became evident that the drive to economic development and
change was coming above all from the capitalists, that is from that part of the bourgeoisie directly
engaged as entrepreneurs-owners into obtaining an income from the employment of money sums
(monetary capitals) in productive or commercial activities capable of yielding a revenue in excess
of costs, i.e. a profit. This profit was in large part destined to enlarge the invested capital, i.e. it was
reinvested into the creation of further factories, shops, farms, ships, etc., in an endless expansion
process accompanied by an incessant search for technological innovations and entailing profound
social transformations. This process is vividly portrayed by Karl Marx and Friedrich Engels in some
deservedly famous pages of their Manifesto of the Communist Party (1848), that are worth quoting
at length:
From the serfs of the Middle Ages sprang the chartered burghers of the earliest towns.
From these burgesses the first elements of the bourgeoisie were developed.
The discovery of America, the rounding of the Cape, opened up fresh ground for the rising
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bourgeoisie. The East-Indian and Chinese markets, the colonization of America, trade with
the colonies, the increase in the means of exchange and in commodities generally, gave to
commerce, to navigation, to industry an impulse never known before, and thereby to the
revolutionary element in the tottering feudal society a rapid development.
The feudal system of industry, in which industrial production was monopolized by closed
guilds, now no longer sufficed for the growing wants of the new markets. The
manufacturing system took its place. The guild-masters were pushed aside by the
manufacturing middle class; division of labour between the different corporate guilds
vanished in the face of division of labour in each single workshop.
Meantime the markets kept ever growing, the demand ever rising. Even manufacture no
longer sufficed. Thereupon, steam and machinery revolutionized industrial production. The
place of manufacture was taken by the giant modern industry, the place of the industrial
middle class by industrial millionaires − the leaders of whole industrial armies, the modern
bourgeois.
Modern industry has established the world market, for which the discovery of America
paved the way. This market has given an immense development to commerce, to
navigation, to communication by land. This development has in turn reacted on the
extension of industry; and in proportion as industry, commerce, navigation, railways
extended, in the same proportion the bourgeoisie developed, increased its capital, and
pushed into the background every class handed down from the Middle Ages.
....................................
Each step in the development of the bourgeoisie was accompanied by a corresponding
political advance of that class. An oppressed class under the sway of the feudal nobility, it
became an armed and self-governing association in the medieval commune; here
independent urban republic (as in Italy and Germany), there taxable ‘third estate’ of the
monarchy (as in France). Afterwards, in the period of manufacture proper, serving either
the semi-feudal or the absolute monarchy as a counterpoise against the nobility, and in fact
cornerstone of the great monarchies in general – the bourgeoisie since the establishment of
modern industry and of the world market, has at last conquered for itself, in the modern
representative state, exclusive political sway. The executive of the modern state is but a
committee for managing the common affairs of the whole bourgeoisie.
The bourgeoisie has played a most revolutionary rôle in history. Wherever it has got the
upper hand it has put an end to all feudal, patriarchial, idyllic relations. It has pitilessly torn
asunder the motley feudal ties that bound man to his ‘natural superiors’, and has left no
other bond between man and man than naked self-interest, than callous ‘cash payment’. It
has drowned the most heavenly ecstacies of religious fervour, of chivalrous enthusiasm, of
philistine sentimentalism, in the icy water of egoistical calculation. It has resolved personal
worth into exchange-value, and in place of the numberless indefeasible chartered
freedoms, has set up that single unconscionable freedom − Free Trade. In one word, for
exploitation veiled by religious and political illusions, it has substituted naked, shameless,
direct, brutal exploitation.
..................................
The bourgeoisie cannot exist without constantly revolutionizing the instruments of
production and thereby the relations of production, and with them the whole relations of
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society. Conservation of the old modes of production in unaltered form was, on the
contrary, the first condition of existence for all earlier industrial classes. Constant
revolutionizing of production, uninterrupted disturbance of all social conditions,
everlasting uncertainty and agitation distinguish the bourgeois epoch from all earlier ones.
All fixed fast-frozen relations, with their train of ancient and venerable prejudices become
antiquated before they can ossify. All that is solid melts into air, all that is holy is profaned,
and man is at last compelled to face with sober senses his real conditions of life and his
relations with his kind.
The need of a constantly expanding market for its products chases the bourgeoisie over the
whole surface of the globe. It must nestle everywhere, settle everywhere, establish
connexions everywhere. The bourgeoisie has through its exploitation of the world market
given a cosmopolitan character to production and consumption in every country. To the
great chagrin of reactionaries, it has drawn from under the feet of industry the national
ground on which it stood. All old-established national industries have been destroyed or
are daily being destroyed. They are dislodged by new industries, whose introduction
becomes a life and death question for all civilized nations, by industries that no longer
work an indigenous raw material, but raw material drawn from the remotest zones;
industries whose products are consumed not only at home, but in every quarter of the
globe. In place of the old wants satisfied by the production of the country we find new
wants requiring for their satisfaction the products of distant lands and climes. In place of
the old local and national seclusion and self-sufficiency, we have intercourse in every
direction, universal interdependence of nations.
.....................................
The bourgeoisie, by the rapid improvement of all instruments of production, by the
immensely facilitated means of communication, draws all nations, even the most barbarian,
into civilization. The cheap prices of its commodities are the heavy artillery with which it
batters down all Chinese walls, with which it forces the barbarians’ intensely obstinate
hatred of foreigners to capitulate. It compels all nations, on pain of extinction, to adopt the
bourgeois mode of production; it compels them to introduce what it calls civilization into
their midst, i.e., to become bourgeois themselves. In a word, it creates a world after its own
image.
.......................................
The bourgeoisie, during its rule of scarce one hundred years, has created more massive and
more colossal productive forces than have all preceding generations together. Subjection of
nature’s forces to man, machinery, application of chemistry to industry and agriculture,
steam-navigation, railways, electric telegraphs, clearing of whole continents for
cultivation, canalization of rivers, whole populations conjured out of the ground − what
earlier century had even a presentiment that such productive forces slumbered in the lap of
social labour?
We see then that the means of production and of exchange, which served as the foundation
for the growth of the bourgeoisie, were generated in feudal society. At a certain stage in the
development of these means of production and of exchange, the conditions under which
feudal society produced and exchanged, the feudal organization of agriculture and
manufacturing industry, in a word, the feudal relations of property became no longer
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compatible with the already developed productive forces, they became so many fetters.
They had to be burst asunder; they were burst asunder.
Into their place stepped free competition, accompanied by a social and political
constitution adapted to it, and by the economic and political sway of the bourgeois class.[6]
The aristocrats, owing to their cultural formation of feudal origin (that stressed the
inferiority of money matters relative to courage and honour), did not like to become capitalists
actively engaged in entrepreneurial activities and therefore generally rented out their lands to
agricultural capitalists who created agricultural farms run for profits; the income of the aristocrats
derived therefore from the rent of the land they owned. The bankers, who lent money to the
capitalists, were able to obtain an interest on their loans which depended on the profits of the
capitalists; as Adam Smith explains, if an entrepreneur counts on earning a rate of return (rate of
profits) of, say, 10% on an investment, he will be ready, considering the personal risk and fatigue,
to borrow the capital necessary for the investment at a rate of interest perhaps of 5%, perhaps of
7%, depending on the riskiness etc. of the investment; if the expected rate of return is only 6%, then
he will seldom accept to pay a rate of interest above 3%; in either case, interest is only a portion of
his profit, interest therefore determines a subdivision of profits between lenders and entrepreneurs,
but it can only be positive because profits are positive.
On this basis, classical economists concentrated on the forces determining three basic
incomes: wages, profits, and land rents, respectively the incomes of wage labourers, capitalists, and
landlords. The theorists’ interest being in the share of the product appropriated by each of these
incomes, what was mainly relevant for them was not the money (or nominal) value of these
incomes, but rather their real value, i.e. their purchasing power in terms of commodities and
services; in other words, their relative value in terms of some commodity or basket of commodities
chosen as measure of value (in more modern terminology deriving from Walras, as numéraire) and
therefore of real value 1. (When we will speak of value of something without further specification,
it will mean the real value, i.e. the relative value in terms of the chosen numéraire.) In the corn
economy of our numerical example, the obvious numéraire is corn itself and what must be
determined is the real rate of wages (the amount of corn earned by workers per unit of labour time),
the real rate of rent on each type of land (the amount of corn paid on a unit of land for its utilization
for one time period), and the (real) rate of profits (the excess of the corn produced over costs, per
unit of corn capital anticipated)[7].
6
Reproduced from Freeman (??), pp. ??
For the rate of profits, which is a ratio, the difference between ‘real’ and ‘nominal’ is not the same
as for the rate of wages or the rate of rents, and it corresponds instead to the difference between ‘real’ and
7
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A numerical example may be useful to fix these notions. Suppose that in the example
previously formulated, where 1000 tons of corn are produced by 1000 identical workers with the aid
of 300 tons of seed-corn, production is organized capitalistically: landlords rent out the land to
capitalist farmers who hire wage labourers and pay a land rent, and sell the corn produced against
money. There are many capitalists and landlords, and free competition tends to ensure a uniform
price for corn and a uniform rate of remuneration for labourers with the same skills, and for lands of
the same quality (but now for simplicity we assume that labourers are only of one type, and land too
is of uniform fertility). Let us assume that the money price of one ton of corn is 10 pounds. We have
assumed that the workers receive 500 tons as their aggregate real income; this means a real wage
rate of ½ ton of corn per man-year, corresponding to a money or nominal yearly wage rate of 5
pounds. Suppose now that the land surface utilized is 100 acres, all of the same quality and earning
a total rent of 1200 pounds, equivalent to 120 tons of corn; this means a real yearly rate of land rent
of 1.2 tons per acre. Suppose lastly that the capitalist farmers at the beginning of the year must both
purchase the seed to be employed, and pay in advance the wage to the workers, to allow them to
subsist during the year; land rent on the contrary is paid at the end of the year, after the sale of the
product.
Owing to the assumption of competition and of a uniform quality of land, we can suppose a
tendency toward a situation in which technology is the same in all farms, because inefficient
entrepreneurs tend to be replaced by more efficient ones. Assuming such a situation to be more or
less realized, we have that all capitalists advance 0.3 tons of seed, and employ 1 labourer, i.e.
advance 0.5 tons of corn as wages, per ton produced. Thus the advanced capital is 0.8 tons of corn
per ton produced. After reconstituting the capital advanced, each capitalist is left with 0.2 tons per
ton produced. But out of these he must pay land rent; he needs 0.1 acres of land per ton produced,
so he pays 0.12 tons in land rent per ton produced. Thus an advance of 0.8 yields him a profit of
0.08, i.e. a real rate of profits (profit divided by capital advanced) of 10%[8].
‘nominal’ rate of interest. As long as money prices do not change as between the moment when money
capital is anticipated and the moment when profits are obtained, the nominal and the real rate of profits
coincide, and are not altered by changes in the price level that affect capital advances and earnings in the
same proportion (on the contrary, for a given real rate of wages or of rents, a change in the price level alters
the nominal rate). Cf. the next footnote.
8
We can now illustrate the difference between real and nominal rate of profits. Suppose that in the
example in the text the money price of corn is 10 when capital is advanced at the beginning of the year, and
15 when the product is obtained and sold at the end of the year; then the nominal rate of profits is 65%,
because one unit of product has money value 15 and after paying rents − physically unaltered, we assume,
and therefore of value 1.8 – the entrepreneur is left with a gross money revenue of 13.2 which yields a
money rate of return of 65% over the money capital advance of 8. Thus the entrepreneur is able to repay a
debt contracted with a nominal rate of interest of up to 65%. Now real and nominal rates of profit do not
coincide, because money prices have changed as between the moment when capital is advanced, and the

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In this example the technology (the seed corn, the labour, and the land surface needed per
unit of corn produced), the real wage rate, and the real land rate were given. Profits could then be
calculated as a residual, and the rate of profits could be determined as the ratio of corn profits to the
corn capital advanced. We must now inquire into how these magnitudes, taken as given when
determining the rate of profits, were determined by classical authors.
1.3. INCOME DISTRIBUTION: WAGES
1.3.1. The general wage level
In the classical approach the level of the real wage rate[9] is determined by a complex of
social, demographic and economic circumstances, which allow its determination before the
determination of the other incomes, and make it possible to take it as given (or as an independently
varying parameter) when determining the land rents and the rate of profits.
These circumstances can be classified in two groups.
A first group comprises those institutional and conventional elements that establish the level
of the real wage considered normal in the period and in the society under discussion. This wage
level, that the classical economists call “natural” or “subsistence wage”, is conceived as the value of
the ensemble of commodities necessary to the worker in the given historical situation:
“necessaries”, as these commodities were called, not because indispensable to his/her physical
survival, capacity to work and reproduction (they would normally exceed such a level), but because
indispensable in the common opinion of society for one’s social role and membership in the social
structure. Historically specific customs are seen as part of the notion of subsistence; and the
subsistence level is susceptible of changes, albeit slow, through time.
A quotation from Adam Smith illustrates this perspective:
By necessaries I understand not only the commodities which are indispensably necessary
for the support of life, but whatever the custom of the country renders it indecent for
creditable people, even of the lowest order, to be without. A linen shirt, for example, is,
moment when earnings accrue. If r is the real rate of profits, ρ the nominal rate of profits, and π the rate of
inflation, it is (1+r)(1+π)=(1+ρ). But if the price of corn, after rising to 15, stays constant at 15, the following
year the nominal rate of profits goes back to equality with the real rate, at 10%.
9
The classical numéraire is often corn, at the time the main constituent of food, which absorbed most
of the workers’ income; sometimes it is gold, considered a produced good whose price is determined by cost
of production in the same way as for other products.
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strictly speaking, not a necessary of life. The Greeks and Romans lived, I suppose, very
comfortably though they had no linen. But in the present times, through the greater part of
Europe, a creditable day-labourer would be ashamed to appear in public without a linen
shirt, the want of which would be supposed to denote that disgraceful degree of poverty
which, it is presumed, nobody can well fall into without extreme bad conduct. Custom, in
the same manner, has rendered leather shoes a necessary of life in England. The poorest
creditable person of either sex would be ashamed to appear in public without them. In
Scotland, custom has rendered them a necessary of life to the lowest order of men; but not
to the same order of women, who may, without any discredit, walk about barefooted. In
France they are necessaries neither to men nor to women, the lowest rank of both sexes
appearing there publicly, without any discredit, sometimes in wooden shoes, and
sometimes barefooted. Under necessaries, therefore, I comprehend not only those things
which nature, but those things which the established rules of decency have rendered
necessary to the lowest rank of people. (Wealth of Nations, Bk V, Ch. II, Part II, Article
IV, Section “Taxes upon Consumable Commodities”; Dent and Dutton ed., Everyman’s
Library, vol. II, 1971 (1910), pp. 351-2)
Notice the importance assigned by Smith to custom and to certain aspects of consumption
and lifestyle as signals of one’s personality, essential for status and for acceptance by society (the
importance of being ‘creditable’ is repeatedly stressed; ‘day-labourers’ must show that they are
‘creditable’ by showing that they are not so poor as to make it probable that they are untrustworthy).
This idea makes lots of sense and can be generalized. Acceptance by the others in social life
requires, in modern times, not only being reasonably clean and not smelly, but also sharing with
one’s reference group a sufficient set of informations and interests and activities; for example,
nowadays not having a mobile phone may mean for adolescents to be intolerably cut off from social
life; not watching television may mean difficulties of social relationships because of inability to
share in conversations; wearing clothes of outmoded fashion can entail being ridiculed. Except in
rare instances, a car is necessary for a normal life, and often it is absolutely indispensable to go to
work or for shopping. More and more, schools take it for granted that students have a computer at
home with an Internet connection. Thus a mobile phone, a television set, fashionable clothes, a car,
a computer must be considered necessaries, part of modern subsistence.
An important implication of this perspective is that, if wages rise above subsistence for a
considerable period, subsistence tends to rise too; the new level of real wages tends to become the
new subsistence, because of internalization of new consumption habits which become both a habit
and part of what is socially expected. Historical experience suggests that another reason is that, with
rises in average income, the low-quality goods that might permit living with a very low income tend
to disappear from shops because too few people ask for them, and then the minimum necessary
expense for an acceptable life rises.
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The second group of factors affecting the real wage consists of the various elements
influencing what can be called the relative bargaining strength of wage earners vis-à-vis employers,
and determining whether the actual wage level is above or below the normal, customary
subsistence. To start to grasp these elements we can quote again Adam Smith (in this passage
‘stock’ means capital):
What are the common wages of labour, depends everywhere upon the contract usually
made between those two parties, whose interests are by no means the same. The workmen
desire to get as much, the masters to give as little as possible. The former are disposed to
combine in order to raise, the latter in order to lower the wages of labour.
It is not, however, difficult to foresee which of the two parties must, upon all ordinary
occasions, have the advantage in the dispute, and force the other into a compliance with
their terms. The masters, being fewer in number, can combine much more easily; and the
law, besides, authorises, or at least does not prohibit their combinations, while it prohibits
those of the workmen. We have no acts of parliament against combining to lower the price
of work; but many against combining to raise it. In all such disputes the masters can hold
out much longer. A landlord, a farmer, a master manufacturer, a merchant, though they did
not employ a single workman, could generally live a year or two upon the stocks which
they have already acquired. Many workmen could not subsist a week, few could subsist a
month, and scarce any a year without employment. In the long-run the workman may be as
necessary to his master as his master is to him; but the necessity is not so immediate.
We rarely hear, it has been said, of the combinations of masters, though frequently of those
of workmen. But whoever imagines, upon this account, that masters rarely combine, is as
ignorant of the world as of the subject. Masters are always and everywhere in a sort of
tacit, but constant and uniform combination, not to raise the wages of labour above their
actual rate. To violate this combination is everywhere a most unpopular action, and a sort
of reproach to a master among his neighbours and equals. We seldom, indeed hear of this
combination, because it is the usual, and one may say, the natural state of things, which
nobody ever hears of. Masters, too, sometimes enter into particular combinations to sink
the wages of labour even below this rate. These are always conducted with the utmost
silence and secrecy, till the moment of execution, and when the workmen yield, as they
sometimes do, without resistance, though severely felt by them, they are never heard of by
other people. Such combinations, however, are frequently resisted by a contrary defensive
combination of the workmen; who sometimes too, without any provocation of this kind,
combine of their own accord to raise the price of their labour. Their usual pretences are,
sometimes the high price of provisions; sometimes the great profit which their masters
make by their work. But whether their combinations be offensive or defensive, they are
always abundantly heard of. In order to bring the point to a speedy decision, they have
always recourse to the loudest clamour, and sometimes to the most shocking violence and
outrage. They are desperate, and act with the folly and extravagance of desperate men, who
must either starve, or frighten their masters into an immediate compliance with their
demands. The masters upon these occasions are just as clamorous upon the other side, and
never cease to call aloud for the assistance of the civil magistrate, and the rigorous
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execution of those laws which have been enacted with so much severity against the
combinations of servants, labourers, and journeymen. The workmen, accordingly, very
seldom derive any advantage from the violence of those tumultuous combinations, which,
partly from the interposition of the civil magistrate, partly from the superior steadiness of
the masters, partly from the necessity which the greater part of the workmen are under of
submitting for the sake of present subsistence, generally end in nothing but the punishment
or ruin of the ringleaders. (WN, cit., Bk. I, Ch. VIII, Dent and Dutton, Everyman’s Library,
vol. I, 1975 (1910), pp. 58-60)
Thus according to Smith the employers (the ‘masters’) are able normally to win in the wage
disputes because of their capacity to resist longer in case of conflict, supplemented by the active
support of the state in case of outbursts of revolt and violence. The members of each class are
united, in their relations with the opposing class, by a widespread consciousness of a common class
interest: thus on the issue of the attitude toward workers there is a “tacit, but constant and uniform
combination” among the capitalists, maintained by social mechanisms of contact, disapproval,
ostracism, etc. inside their class. It is a natural consequence that the capitalists are always very
reluctant to raise wages, and even when in situations of scarcity of labour supply they try to subtract
workers one from the other, they can be expected to do it with moderation, always careful not to
endanger their class domination. Similar social mechanisms connected with a consciousness of a
common class interest are active on the workers’ side, and this tacit or sometimes vociferous
alliance among workers can be expected, even in the absence of trade unions or other explicit
“defensive combinations”, to render the real wage rate fairly resistant to downward pressures, even
in the presence of considerable unemployment. Indeed, historical experience shows a great
reluctance of workers to accept to work for a wage inferior to the one that, in the given historical
situation, is the usual and generally considered ‘fair’ for their type of labour.
However for Smith and the other classical authors the capitalists remain the stronger class;
but then, one might ask, why don’t they compress the wage rate even more?
Smith continues:
When in any country the demand for those who live by wages ... is continually increasing
... the workmen have no occasion to combine in order to raise their wages. The scarcity of
hands occasions a competition among masters, who bid against one another, in order to get
workmen, and thus voluntarily break through the natural combination of masters not to
raise wages;
conversely,
where the funds destined for the maintenance of labour were sensibly decaying ... the
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competition for employment would be so great ... , as to reduce the wages of labour to the
most miserable and scanty subsistence of the labourer. Many would not be able to find
employment even upon these hard terms, but would either starve, or be driven to seek a
subsistence either by begging, or by the perpetration perhaps of the greatest enormities.
Want, famine, and mortality would immediately prevail in that class, ... till the number of
inhabitants in the country was reduced to what could easily be maintained by the revenue
and stock which remained in it” (WN, cit., vol. I p. 61, 64-5).
One might derive from these observations a simple theory based on a population
mechanism, and this theory was indeed derived by Thomas Malthus: if the real wage decreases
below subsistence, then population decreases, labour supply decreases relative to labour demand,
sooner or later a “scarcity of hands” arises and competition among capitalists raises the real wage
above subsistence; but then workers – Malthus argued – give birth to so many children and so many
of these survive to working age that an excess of labour supply develops, which pushes the wage
down, eventually below the subsistence level, causing a decrease of population and thus of labour
supply; thus the real wage always tends to return to the subsistence level owing to its effect on
population and hence on labour supply. The conclusion is very pessimistic, or if you like, very
conservative: it is useless to try to raise wages, the labouring classes are condemned to remain poor
by their tendency to have too many children as soon as the wage is raised above subsistence.
Smith, on the contrary, admits a possible very-long-run influence of the real wage on the
rate of growth of labour supply but sees the sign of this influence as not always certain; he admits
that wage increases need not always favour increases in population: the newly available comforts
may induce workers to have fewer children, so as better to defend their higher standards of
living[10]. Thus persistent rises of real wages are perfectly possible, owing to the influence of the
real wage itself on subsistence. This is an example of the openness of classical economics to
different possibilities depending on specific social and political conditions. Also very interesting
(especially in view of the comparison with the marginal/neoclassical approach to come in ch. 3) is
that Smith does not say that wages keep decreasing as long as labour supply is greater than the
demand for labour[11], as modern supply-and-demand analysis would suggest. He classifies Great
Britain as a country where the demand for labour has been growing and wages have therefore
And Ricardo agrees: “population may be so little stimulated by ample wages as to increase at the
slowest rate – or it may even go in a retrograde direction” (Collected Works, vol. VIII, p. 168-69). The
correctness of the usual attribution to Ricardo of a wholehearted endorsement of Malthusian wage theory can
therefore be doubted, because, like Smith, Ricardo admits a cultural-customary element in subsistence,
susceptible of being modified by experienced levels of consumption.
11
In Smith ‘supply’ and 'demand' are always quantities, not functions; accordingly the 'demand for
labour' is the quantity of labour demanded (i.e., labour employment) in the given period.
10
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tended to increase; and yet unemployment (beggars, and people on public relief or confined to
workhouses) did exist in Great Britain in Adam Smith’s time[12]. Some unemployment is evidently
considered by Smith to be a normal component of market economies, and not necessarily capable of
preventing wage increases. Extensive and durable unemployment certainly tends to reduce wages,
but not below the “lowest rate which is consistent with common humanity”, that is, the one
“sufficient to maintain the labourer, and to enable him to bring up a family” (WN bk.I ch. 8 p. 63),
which, let us not forget, includes a historical customary element above strict biological subsistence.
But, if unemployment is generally present, why don’t capitalists use their greater bargaining
power to compress wages to the bare biological minimum that allows workers to have the energy to
work, or even below that level[13]? what is it that allows workers generally to defend the historical
and customary excess of wages above bare biological subsistence? why does Smith speak of a
“lowest rate [of wages] which is consistent with common humanity”, below which even capitalists
do not find it convenient to push wages?
The answer would appear to lie in Smith’s description quoted above of the bargaining
process between workers and “masters”, with the workers described as “They are desperate, and act
with the folly and extravagance of desperate men”, and with a hint of possible interventions “of the
civil magistrate” i.e. of the police (and perhaps even the army) against their protests. “Desperate”
and “extravagant” acts need not be caused by inability physically to survive; the same social habits,
conventions and pressures that turn certain commodities into “necessaries” can and will make it
unbearable to go without them; thus, it would seem, Smith is implicitly admitting that it is the
danger of ruptures of social peace and consequent disruptions of economic activity (both in the firm
- e.g. sabotage -, and in society at large), that makes it not convenient for the dominant class to try
and depress the real wage below the historical subsistence level, i.e. below the level considered
indispensable to a tolerable living by a majority of workers.
Actually, some such view of wages as considerably ‘sticky’ downwards is also implicit in
the Malthusian wage theory based on the population mechanism. Variations of population are very
slow; when a greater than usual excess of labour supply over labour demand causes a decrease of
12
An esteemed historian of economic thought has indeed written with reference to classical
economists that “in an era when the number of individuals on public relief hovered steadily around ... 10 per
cent of population ... the existence of a hard core of surplus labour must have been taken for granted” (Blaug,
Ricardian Economics, 1958, p. 75); “Ricardo assumed the existence of Marxian unemployment” (ibid., p.
179). Also cf. Stirati “Wages” in Elgar Companion, p. 531; and Smith’s “constant scarcity of employment”
in WN, Bk I ch. 8 p. 63. This shows that the frequent identification of Adam Smith’s methaphor of the
‘invisible hand’ with the neoclassical thesis of a spontaneous tendency of market economies toward a Paretooptimal state of full employment of resources is deeply mistaken.
13
As long as there are desperate workers available, the ones that die can be replaced – this is not
historically unknown.
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real wages, the influence of this decrease on population (and possibly, by raising profits, on capital
accumulation) cannot but take many years to cause a significant decrease of unemployment[14]; if
one were to admit that as long as there is excess labour supply wages keep decreasing indefinitely,
one would have to conclude that the continuing fall in real wages during all those years would bring
real wages to implausibly low levels if not to zero, against the empirical evidence; thus it is
necessarily implicit even in the Malthusian population mechanism that real wages only change very
slowly, and that a high unemployment will cause decreases in real wages, but only very slowly, and
not indefinitely; and the reason must ultimately be the same as in Smith.
It appears therefore legitimate to say that in the classical approach real wages result from a
continuous open or latent conflict, and oscillate around a 'natural', or customary, real wage, which
labourers expect to earn (and consider therefore a 'fair' wage[15]) because it reflects the average
balance of bargaining power between capitalists and wage labourers over the recent past; this
customary 'subsistence' wage, which guarantees a standard of living which through habit has come
to be regarded as indispensable to decent living, is the starting point of further bargaining. The
latter, if conditioned by a changed balance of bargaining power, may result in a lasting divergence
of wages from their customary level, with a resulting slow change of the customary or 'natural' or
‘fair’ real wage itself. Unemployment does not necessarily exert a downward pressure on wages,
except when it becomes very severe, and then it is still a slow and not indefinite downward pressure,
which will generally reduce real wages by a limited amount only; more rapid and drastic decreases
of real wages will only be observed in exceptional situations involving considerable political
change (e.g. - to make a more modern example - after a right-wing military coup).
14
As we will better see later, the classical authors do not entertain the marginalist notion that lower
wages increase the demand for labour by inducing the adoption of lower capital-labour ratios; in classical
analyses increases in employment can only come about owing to capital accumulation.
15
. Historical evidence confirms the great importance, in the concrete behaviour of workers, of
notions of “a fair day’s wage for a fair day’s labour” (quote from Marshall??)(for recent evidence cf. the
writings of Truman Bewley: Bewley T. F. (1999), Why Wages Don't Fall During a Recession, Cambridge,
Mass., Harvard University Press; Bewley, T., 2005, “Fairness, Reciprocity and Wage Rigidity”, in H. Gintis,
S. Bowles, R. Boyd, E. Fehr, Moral Sentiments and Material Interests. The Foundations of Cooperation in
Economic Life, MIT Press.). The role and meaning of these notions is best appreciated, I would suggest, by
viewing the normal real wage level as reflecting, in every period, an explicit or implicit armistice or truce in
the continual latent or open conflict between wage labourers and employers. An armistice is a pact which
saves losses and suffering to both parties to the conflict by suspending active fighting; pacts must be
honoured; honouring a pact is ‘fair’ i.e. correct behaviour (remember that ‘fair’, in its basic meaning, does
not mean ethically just, it means respectful of the rules, and giving each one its due, as in ‘fair play’ or ‘fair
decision’); a fair wage is then simply the wage that workers must get if they work correctly, according to the
truce implicitly or explicitly signed by both parties; paying less would mean reneging on the armistice, and
then workers too would not be bound to abide by their side of the pact. So, I would suggest, fair wages are
fair, not in the sense of reflecting some perceived social justice of the resulting income distribution, but only
in the sense that they correspond to the current truce, and must be paid if capitalists do not want a resumption
of active conflict.
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Such a perspective makes it natural to consider the average real wage as something hardly
susceptible of rapid change, and to consider it an expense of production as inevitable as fodder for
cattle. Hence the treatment of the real wage as given when attempting the determination of the rate
of profits and of land rents, and the conception of the incomes other than wages as a surplus over
the necessities of reproduction[16]: given, not in the sense of exogenous with respect to economic
analysis, but in the sense of explained by forces which allow one to consider wages as determined
before profits and rents. Of course the forces affecting changes of real wages over time are not left
unanalyzed: we have seen how Smith discusses both the evolution of custom over time, and the
influence of economic growth; later we will see Marx’s views.
1.3.2. Relative wages
So far we have spoken of labour as if homogeneous[17], with a single wage rate. Classical
authors of course know that there are different kinds of labour, with differences in wage rates, and
do discuss what determines these differences. Here too, the main reference is Adam Smith. He
argues that wage differences: 1) tend to compensate differences in the advantages and
disadvantages of different types of work, much like persisting differences in rates of profit
compensate differences in the riskiness and fatigue of different types of investments of capital[18];
2) are also influenced by the relative ease with which different types of activities can be entered: if
long and difficult education is necessary, or if guilds or other barriers make entrance into a trade or
a profession more difficult, wages will be correspondingly higher. These elements appear to be
capable of maintaining the ratios between wages essentially unchanged when for some reason the
general level of wages is altered (possible changes of the differences can be analyzed, if it is
. Cf. P. Garegnani, “Sraffa: Classical versus Marginalist Analysis” in K. Bharadwaj, B. Schefold
eds., Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory, London: Routledge,
1992 (1st. ed. Unwin and Hyman, 1990).
17
May I be allowed to point out that this is the correct spelling, not ‘homogenous’. The point that
seems to escape many writers in economics is that ‘endogenous’ means ‘internally generated’, from the
Greek verbal root ‘gen’ (to produce, to generate) while ‘homogeneous’ means ‘of the same family or gender’
from the different root ‘genos’ (family, lineage). The same goes for ‘heterogeneous’ and ‘exogenous’.
18
The following quotation is still useful to-day: “The five following are the principal circumstances
which, so far as I have been able to observe, make up for a small pecuniary gain in some employments, and
counter-balance a great one in others: first, the agreeableness or disagreeableness of the employments
themselves; secondly, the easiness and cheapness, or the difficulty and expense of learning them; thirdly, the
constancy or inconstancy of employment in them; fourthly, the small or great trust which must be reposed in
those who exercise them; and, fifthly, the probability or improbability of success in them” (Smith, WN,
I.x.b.1). Particularly interesting is the fourth kind of circumstances, on which Smith adds: “We trust our
health to the physician, our fortune and sometimes our life and reputation to the lawyer and attorney. Such
confidence could not safely be reposed in people of a very mean and low condition. Their reward must be
such, therefore, as may give them that rank in the society which so important a trust requires” (WN, I.x.b.
19).
16
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deemed relevant, in a second approximation), Smith argues, and similarly for rates of profit:
The proportion between the different rates both of wages and profit in the different
employments of labour and stock[19], seems not to be much affected ... by the riches or
poverty, the advancing, stationary, or declining state of the society. Such revolutions in the
public welfare, though they affect the general rates both of wages and profit, must in the
end affect them equally in all different employments. The proportion between them,
therefore, must remain the same, and cannot well be altered, at least for any considerable
time, by any such revolution. (Wealth of Nations, Bk I, Ch X, cit., p. 130)
Thus it is possible, according to Smith, to treat relative wage rates (the ‘proportion’ between
wage rates) as given when attempting the determination of the other incomes and also when
analyzing the effects of forces that influence the general level of wages; analogous considerations
apply to relative rates of profit (this will be important later, cf. chapter 11).
Then it becomes possible to treat the wage costs of firms as if caused by homogeneous
labour, by ‘reducing’ quantities of heterogeneous labour to quantities of a single type of labour on
the basis of relative wage rates. For example if there are two types of labour, and if labour A has a
wage rate twice the wage rate of labour B, then in the determination both of the aggregate wage bill,
and of the wage expenses of each firm, nothing will change if one replaces each unit of labour A
with two units of labour B. Thus whenever classical authors speak of labour as if homogeneous and
of ‘the’ wage rate as if there were only a single wage rate, they are implicitly reducing quantities of
heterogeneous labour to different quantities of homogeneous labour on the basis of given relative
wages, generally reducing all labour to quantities of common, unskilled labour. In conclusion, the
existence of heterogeneous labour and of different wage rates does not impede the treatment of
wage costs as given when attempting the determination of land rents and of the average rate of
profits.
This procedure of taking relative wages as given (as well as the analogous one of taking the
average real wage as given) when determining the other distributive variables does not mean to
leave them unexplained; their determination is of course part of what economic theory must
explain, but the forces that determine them are such, that relative wages do not seem to be
relevantly affected (if not very slowly) by, for example, technical progress, or changes in the
general level of wages, or the extension of cultivation to less fertile lands.
19
Remember that Smith calls ‘stock’ the capital advances.
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1.4. THE OTHER DATA IN THE DETERMINATION OF THE SURPLUS
1.4.1. Quantities
In the corn-economy example, the determination of profits required taking as given, besides
the real wage, also the quantity produced, the technology adopted, and the land rent rate. We must
briefly illustrate the views that made it legitimate for the classical authors to treat these magnitudes
as given, when the problem was the determination of profits.
We start with the quantities produced. Briefly, the composition of production (an issue that
obviously does not arise in the corn economy example) was explained, for the part relative to the
composition of consumption, as dependent on the historical development of consumption habits; the
share, and the composition, of the production of capital goods were explained on the basis of the
technical needs for reintegration and expansion of the capital stock, and of the society’s propensity
to accumulate; both the development of consumption habits, and the propensity to accumulate, were
considered to be historically variable and depending on the specific circumstances of the period.
The aggregate level of production was considered to depend on the stage reached by the
accumulation of capital, that is, on the past destination of the surplus to savings rather than to
consumption; and also (in the classical authors not accepting Say’s Law − see below) on the factors
determining fluctuations and crises, on which we will say more later.
The main difference of these views from the later marginal approach is that one does not
find in the classical authors the idea of a univocal connection between income distribution and
composition or aggregate level of production, capable of deductively allowing a simultaneous
determination of changes in income distribution, and changes in the quantities produced. The
effects of, for example, a change of the real wage rate on the composition of consumption, or on
savings, were considered sufficiently historically variable as to suggest a different method of
analysis: in a first stage of analysis the effects of a change of the real wage on prices, on land rents
and on profits were studied by taking the quantities produced as unchanged; as we will better see
later, this study was strictly analytical-deductive; the results of this study could then be used in a
second, more inductive stage of the analysis to try and estimate the probable effects on the
quantities produced according to the specificities of the case. Thus for example in Marx a rise of
real wages would definitely reduce the average rate of profits (the deductive, certain conclusion),
but its effects on the quantities produced were to be determined according to historical
circumstances, because sometimes a moderate increase in wages could result in a stimulus to
production owing to the greater consumption of workers, some other times it could result in a
discouragement to investment if perceived by capitalists as signaling a dangerous social strength of
workers, capable of endangering the continuation of the capitalists’ class domination.
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1.4.2. Technology
The production technology adopted is explained by the classical authors as dependent on the
real wage, on the stage reached by technical progress, and on the extent of use of natural resources,
which depends on the quantities produced, as we will see when we come to the determination of
land rent. Initially for simplicity we neglect land rent. The stage reached by technical progress
determines the known alternative production methods for the same product. The real wage, by
determining costs, determines the relative convenience of these alternative methods, and this
relative convenience determines the choice of production method on the basis of cost minimization;
the available methods are seen to depend on the advances of scientific and technological
knowledge, and on the stage reached by the division of labour, which is considered to depend on the
extent of the market. This last point deserves some additional explanation. According to Adam
Smith
This great increase of the quantity of work which, in consequence of the division of labour,
the same number of people are capable of performing, is owing to three different
circumstances; first, to the increase of dexterity in every particular workman; secondly, to
the saving of the time which is commonly lost in passing from one species of work to
another; and lastly, to the invention of a great number of machines which facilitate and
abridge labour, and enable one man to do the work of many. (WN Bk. I, Ch. I, vol 1 p. 7)
Note how, according to Smith, the size of the demand to be satisfied stimulates also what we
nowadays call technical progress: the increase in the quantities to be produced allows a
specialization of work, such that each worker tends more and more repetitively to perform always
the same simple operations, and this makes it easier to grasp the potential for mechanical substitutes
of human labour; and the increased size of the market makes it possible to sell the increased
production that is necessary (owing to indivisibilities) in order for mechanization to be convenient.
This shows that Smith’s conception of a favourable effect of market expansion on
productive efficiency does not correspond to the modern notion of increasing returns to scale[20].
The increase in the division of labour is conceived as a dynamical process that entails the gradual
discovery of new ways to organize the production process, discovery stimulated and favoured by
the increase in the scale of production; this conception is applied by Smith to the study of the
20
The reader has certainly met this notion in her first economics course. It refers to the possibility to
increase production with a less than proportional increase in total costs, owing to the utilization of costsaving machinery or processes all well-known to the entrepreneur but that, owing to indivisibilities, are only
convenient at larger scales of production. A more rigorous discussion is in chapter 5.
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connection between capital accumulation and evolution of average labour productivity over time,
not to the study of the set of production possibilities open to a firm in a given period. In each given
period, average labour productivity is taken as given.
As to the choice of the most convenient method, this is very simple in the corn example if
land is free: if there are alternative methods for the production of corn, the method will be chosen
that permits the highest rate of profits. This choice may depend on the real wage. Let us see why.
We introduce here the first bit of formalization.
If land is free, a production method in the corn economy is defined by aL, the technical
coefficient of labour (i.e. the quantity of labour needed per unit of corn produced), and by ac, the
technical coefficient of corn input i.e. the quantity of seed-corn per unit of corn produced. The
technical coefficients are assumed independent of the quantity produced[21]. Let z indicate the real
wage rate, a quantity of corn, paid in advance as the classical authors assume; then the capital
advanced at the beginning of the year to obtain one unit of corn at the end of the year is (ac+zaL)
and the rate of profits is given by
r = (1–ac–zaL)/(ac+zaL) .
This equation establishes a functional relationship between z and r. We can study how r
changes depending on changes in z, or vice-versa. If z is zero the rate of profits is
rMax = (1–ac)/ac
which we assume to be positive (i.e. ac<1). An economy satisfying the condition rMax>0 is called
viable, and clearly this is an indispensable condition for the economy to be able to exist: an
economy incapable of producing a surplus even when labour is free cannot exist. Since a c<1, the
wage rate associated with r=0, i.e.
zMax =(1–ac)/aL
is also positive. Furthermore it is easy to check that
dr/dz = – aL/(ac+zaL)2 < 0,
hence r(z) is monotonically decreasing as long as z is different from –ac/aL and therefore, in
particular, r(z) is invertible for z non-negative. Following the usual practice in the literature we
draw this function with the rate of profits in abscissa and the wage rate in ordinate i.e. we draw z(r),
which is legitimate since we will concentrate on the portion of z(r) in the non-negative orthant.
Actually the rate of profits can become negative, but we will leave aside this possibility which
cannot be more than temporary, otherwise capitalism could not continue to function.
We have shown that the curve z(r) is a downward-sloping curve with positive intercepts.
21
When only one method is known then one says that there are fixed technical coefficients.
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The study of its curvature in the positive orthant is easy. The derivative
dz/dr = – (ac+zaL)2 /aL< 0
increases in absolute value with z, hence z(r) is convex[22]. It is also interesting to compare z(r) with
the curve obtaining if wages are paid at the end of the year, i.e. in arrears. Then the capital advanced
does not include the subsistence of workers, and the relationship between rate of profits and wage
rate – indicating now with w the real wage rate paid in arrears – is:
r = (1–ac–waL)/ac = (1/ac) – 1 – w(aL/ac)
or w = (1/aL) – (1+r)ac/aL.
Thus w(r) is a straight line with slope –ac/aL. The intercepts are the same as with advanced
wages. Let us now compare the equations establishing “price of corn = cost of production of corn
inclusive of profits” in the two cases, remembering that corn is the numéraire i.e. the price of corn is
1. The “cost of production inclusive of profits” of one unit of corn is the cost of seed-corn plus
wages plus the rate of profits r on the capital advanced. We obtain respectively:
1 = (1+r)(ac+zaL)
1 = (1+r)ac + waL.
Hence
z(r)(1+r)=w(r).
We see that to pass from the advanced wage rate to the wage rate paid in arrears
corresponding to the same rate of profits, it suffices to multiply the advanced wage rate by (1+r).
This means that in the positive orthant it is z(r)<w(r), while at the intercepts with the axes the two
curves coincide, cf. Fig. 1.1.
We can now compare the z(r) or the w(r) curves of two different methods, characterized by
different technical coefficients ac and aL. The study of the determinants of rMax and of zMax shows
that it is perfectly possible for a method to have a higher maximum rate of profits, and a lower
maximum rate of wages, than a second method: it suffices that the first method has a lower ac and a
sufficiently greater aL than the second method. Then their z(r) curves intersect in the positive
quadrant, i.e. which method yields the higher rate of profits (and therefore imposes itself in the
economy) depends on the level of z.
[interlinea minima 18pt]
z, w
I
A function f(x) is convex if, with t a scalar, 0≤t≤1, it is f(tx+(1−t)x’)≤tf(x)+(1−t)f(x’); in words, if
any segment connecting two points of the graph of the function does not lie below the graph.
22
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w(r’)
z(r’)
II
r’
r
Fig. 1.1. Intersecting wage curves of two alternative methods in the corn economy. The dotted lines
are the z(r) curves, the straight lines are the w(r) curves. The intersection of the z(r) curves is vertically
aligned with the intersection of the w(r) curves.
From the fact that for each method it is z(r)(1+r)=w(r), it follows that if the z(r) curves of
two different methods intersect at a certain level r’ of the rate of profits, then also the w(r) curves of
the two methods intersect at the same rate of profits r’, cf. Fig. 1.1. It follows that the order of
profitability of two methods, i.e. which one yields the higher r, may depend on whether the given
wage rate is advanced or not. In Fig. 1.1, for a real wage rate above z(r’) but below w(r’) the more
profitable method is I if the given wage rate is advanced, it is II if the same given wage rate is paid
in arrears; outside this range, the order of profitability is the same.
Since both the real wage rate, and the institutional circumstances that determine whether the
wage is advanced or paid in arrears, can be taken as given in the surplus approach, the result will be
a well-determined choice of production technology[23]. We will extend the study of choice of
techniques to more complex cases in chapter 2 and chapter 10. We now introduce land rent.
1.5. RENT
1.5.1. Extensive differential rent. In the corn economy example we assumed a uniform rate
of rent per acre of land; this will be the case if rent is determined as intensive differential rent,
which requires that land quality is uniform and land is fully employed, as will be explained later.
But land quality is generally not uniform, and the classical analysis of the case of heterogeneous
lands − the analysis of extensive differential rent − is simpler than, and a good preparation to, the
analysis of intensive differential rent. So we start from the case of different qualities of land. The
theory we present is Ricardo’s (who derived it from Malthus, West and Anderson).
Land is hired by capitalists who pay a yearly rent per acre to landlords for its use. We
assume that the real wage rate is the same for all labourers, and given. The real wage is advanced,
and therefore included in the advanced capital together with the seed-corn. For simplicity we
assume that only one production method is known for each type of land. Now the production
method on land of type α is specified by three technical coefficients: the quantity acα of seed-corn
per unit of output, the quantity aLα of labour per unit of output, and the acres tα of land of type α per
23
Except when the real wage is exactly at a level at which two methods are equally profitable.
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unit of output. From these technical coefficients one can also obtain an alternative representation of
the method, consisting of the quantities of seed-corn, of labour, and of output, per acre of land;
these are given by, respectively, acα/tα, aLα/tα, and 1/tα (if half an acre of land is required to produce
one ton of corn, then one acre of land produces two tons of corn). The latter is the representation we
adopt in the numerical examples below.
These assumptions imply that the surplus produced per unit of capital advanced, as well as
the surplus produced per acre, can be determined for each type of land[24].
Let us suppose that there are two types of land, a more fertile one, type A, and a less fertile
one, type B. We assume that the landowners have no other employment for their lands except
renting them to capitalists for cultivation, and that they prefer to rent them at a positive rent
however low, rather than leave them unused. Thus the entire quantity both of land A and of land B
is offered for rent even when the rate of rent is so low that for practical purposes we can take it as
equal to zero. Furthermore, landowners offer their lands at a lower rate of rent than the going rate
when they are unable to rent them, in order to induce capitalists to hire their lands rather than the
lands of other landowners; thus competition lowers the rate of rent on each type of land until either
the rate of rent becomes practically zero[25], or that type of land is fully employed.
If the rate of rent is zero on both types of land, then capitalists will only demand the land
that yields the higher rate of profits i.e. the higher surplus per unit of capital advanced. Let A be this
land. Then if initially the production of corn is so small that the quantity of land A is overabundant,
only land A is demanded, but not the whole of it, and the competition among landowners causes the
rate of rent on it to tend to zero.
Let us now imagine that, from such an initial situation, corn production grows because of
capital accumulation, and a point is reached when land A is no longer sufficient, and it is necessary
to employ also part of the supply of land B. As long as some part of land B is unemployed,
competition will cause the rate of rent on it to tend to zero. But if no rent is paid on land A, the
capitalists who use land B obtain a lower rate of profits than on land A. Therefore they will be ready
to pay a positive rate of rent for the use of land A, as long as this rate of rent allows them to obtain a
24
If the advanced corn wage rate is z, the surplus per unit of capital advanced is obtained by dividing
the surplus per unit of output by the capital advanced per unit of output, hence it is (1–acα–zaLα)/(acα+zaLα) i.e.
it is the rate of profits if no rent is paid. The surplus produced per acre is the surplus per unit of output times
the output per acre, hence it is (1–acα–zaLα)/tα.
25
When the rate of rent is truly zero, plausibly land will not be offered for rent (unless it loses its
fertility if left idle). So we should interpret the cases of zero rent as in fact meaning a very low rate of rent,
not quite zero but very close to zero, below which landowners refuse to rent their land because some minimal
rent is necessary to compensate them for the risk and trouble of signing the contract, checking that the
farmers do not ruin the land, etc. By ‘practically zero’ we mean precisely a rate of rent positive but so low
that it can be neglected; this being understood, from now on we drop ‘practically’.
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rate of profits higher than on no-rent land B. In order not to be displaced, the capitalists using land
A will have to accept themselves to pay that rate of rent. If competition works well, the tendency
will be for the rate of rent on land A to rise up to the point where the rate of profits on land A
becomes equal to the rate of profits on no-rent land B.
A numerical example can illustrate. Assume that the yearly quantity of capital advanced
per acre (seed-corn plus corn wages per acre[26]), and the yearly quantity produced per acre, are as
follows (the arrow stands for ‘produce’):
A: 5 → 9
B: 12 → 18.
If rent is zero, production yields a rate of profits of 80% on land A, of 50% on land B. Land
A is therefore the first one put to cultivation. (Notice that the order of profitability, i.e. of fertility
per unit of capital employed, need not correspond to the order of fertility per acre: here land B is
the one that produces the greater surplus per acre.). When the expansion of production brings land B
into cultivation, competition causes a rent to appear on land A, such as will cause the rate of profits
on land A to become 50% too. This means that profits per acre on land A must be 2.5, and the rate
of rent per acre on land A (paid, we assume, at the end of the yearly production cycle and requiring
therefore no advance of capital) is 1.5.
Let us now suppose that further expansion of production brings to the full employment of
land B too and requires in addition to utilize part of a third type of land, C, which when paying no
rent yields a rate of profits less than 50%, for example:
C: 10 → 12.
The rate of profits on no-rent land C is 20%. Competition will then bring down the rate of
profits to 20% on both lands A and B. The reader can check that the rates of rent per acre that
achieve such a result are, 3 on land A, and 3.6 on land B. (Note the higher rate of rent per acre on
land B: the order of profitability, although coinciding with the order of rent per unit of capital, does
not necessarily coincide with the order of rent per acre, or order of rentability, which also depends
on the fertility per acre.)
The existence of positive rates of rent derives from differences in the rates of profit
obtainable on different lands when there is no rent: this is why these rents are called differential
rents. And because they arise as cultivation is extended to less and less fertile lands, the rents thus
arising are called extensive differential rents.
Note an important consequence of this theory. Apart from the transitional periods when the
26
In this example it does not matter which portion of advanced capital is seed-corn and which
portion is advanced wages.
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last land put into cultivation has just become fully utilized and rents have not yet risen enough to
make it convenient to start producing on the next inferior land, there is always a type of land (the
last one put into cultivation) which is not fully utilized and whose rate of rent is therefore zero[ 27].
On this land the supply price (cost of production plus profits) of the product does not include rent;
as classical economists used to put it, rent does not enter price. The residual determination of the
rate of profits, achieved in the corn-economy example without rent, remains possible: the rate of
profits is determined by the technology on the no-rent land, and by the wage rate. And as long as
the no-rent land does not change, one can study the effects of changes in the real wage rate, or of
technical progress, on the rate of profits without considering rent.
1.5.2. Intensive differential rent. Differential rent can arise also for another reason. Let us
again suppose that a type of land becomes fully utilized and the rate of rent on it starts to rise. It
may be the case that a second productive process is available for that land, which was not utilized
up to then because it would have yielded a lower rate of profits when rent was zero, but which is
more productive per acre than the first process, so that, when the rate of rent rises, this causes a
slower decrease of the rate of profits for the second process than for the first. If so, it may happen
that a rate of rent is reached, at which the two processes are equally profitable; then they can be
used side by side, and since the second process is more productive than the first, a gradual extension
of the part of land using this process and corresponding contraction of the part using the first
process will assure a gradual increase in the amount of corn produced. In this case, rent arises
owing to the introduction of a second process (that utilizes land more intensively, i.e. produces
more on the same land surface) simultaneously with the old process; it is therefore called intensive
differential rent.
Let us illustrate with an example. Now we assume that there is only one type of land, and A
and B stand for two different productive methods on it. As before, wages are assumed advanced,
given and summed up with seed so as to obtain the total capital advanced per acre, and the
corresponding quantities produced per acre are:
A:
5 →
9
B : 12 → 18.
27
In the gradual process of expansion of production, there will be periods when the last land put into
cultivation becomes fully utlized but the next land in the profitability order has not started being utilized yet;
but these periods will be transitional, analogous to the periods of transition to a new long-period price of a
product, associated with the introduction of a newly discovered technology. Economic theory cannot aim at
describing the details of these transitions, which depend on a myriad of accidental elements, but it can
indicate the important things: the direction of change and the situation toward which the economy tends.
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The numbers are the same as in the previous example, but now they refer to two different
methods of production per acre on the same land. When rent is zero, the rate of profits is 80% with
method A, and 50% with method B, so capitalists adopt method A. Suppose that an increase in the
demand for corn renders the demand for land (derived from method A) greater than the supply of
land, and a rent starts to arise. The rise in the rate of rent causes the rate of profits to decrease faster
for the method that uses more land per unit of product, i.e. method A.
Let rA and rB be the rates of profit obtainable with the two methods, and let  stand for the
rate of rent per acre, paid at the end of the year. If β is given, the rates of profit are determined by:
[1.1]
5(1+rA) + β = 9
[1.2]
12(1+rB) + β = 18
Thus for example if  = 1 , it is rA  3 5  60% , rB  5 12  42% ; if  = 2 , it is
rA  2 5  40% , rB  1 3  33% . The two methods become equally profitable for the value of β
that solves the system of two equations obtained by putting rA  rB ; the solution is:
β=18/7, rA=rB=2/7≅28.6% .
If  becomes greater than 18/7, rB becomes greater than rA , method B is more profitable
and starts replacing A; the opposite happens if β is less than 18/7. This means that competition will
ensure a gravitation of β toward 18/7, as we illustrate now.
This gravitation will operate, although differently, both if corn is the sole product, and if it is
only one of the products in a larger economy. Let us initially assume the latter situation. Then the
demand for corn derives from the larger economy, so it can be taken as given from the viewpoint of
the corn industry. Assume for simplicity that no other production competes with corn for the use of
land. Suppose initially that β=18/7 and corn production equals demand; then corn demand rises.
This stimulates an increase in the price of corn and hence in the rate of profits in corn production at
the initially unchanged rent rate, thus investment in corn production rises, this enhances the
competition for land, and β rises; the result is that method B becomes more convenient than A and
is extended at the expense of A, and corn production increases until it equals demand – or perhaps
exceeds demand, but then β decreases, and the process is reversed: thus the oscillations of β cause
the production of corn to tend toward the demand for corn and β to tend back to 18/7.
If corn is the sole product, the process establishing the rent of land will function differently
because all capital goes to the production of corn anyway, and all income goes to demand corn; but
then what can be taken as given is the supply of corn-capital, gradually increased by net savings.
Method B uses more capital per acre than method A; initially only A is adopted; when capital
accumulation causes the supply of capital to exceed the amount needed to employ all land with
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method A, then competition for land causes rent to arise and to rise until method B becomes
convenient and starts to replace A and to absorb more capital per acre than A; there will be only one
allocation of land between the two methods that uses the entire given supply of capital; if B is used
on less land than required for the full absorption of the capital supply, demand for land exceeds land
supply, β rises, and B is extended; and vice-versa if B is overextended. Thus the oscillations of β
above or below 18/7 will cause the allocation of land between the two methods to become the one
that absorbs the supply of capital, and as capital accumulation proceeds, method B gradually
replaces A while β remains at 18/7.
In this last description of how the rate of rent is established, we have described the demand
for land as deriving from the amount of capital seeking employment; implicitly, we have assumed
that there is no problem in selling the entire product; this, since corn production is the sole product,
means that we have followed Ricardo in implicitly assuming Say’s Law, i.e. that aggregate demand
always equals the aggregate value of production. According to Ricardo all income is always spent
again: whatever is not spent on consumption is invested; savings automatically translate into
investment, so there never is a problem of insufficient aggregate demand. Say’s Law implies that
there is no obstacle to the full utilization of all capital; then, if corn is the sole product, the demand
for land depends on the amount of capital resulting from past accumulation. If on the contrary corn
production is only one part of a larger economy, or if (as in Keynes) Say’s Law does not hold and
aggregate demand is autonomously determined, then corn production will depend on the demand
for corn. But we have seen that the tendency of β toward the level that renders the two methods
equally profitable will work in both cases.
As capital accumulation, or the expansion of the demand for corn, proceeds, method B
gradually replaces method A, with an unchanged rate of rent and rate of profits. When method B
totally replaces method A, then corn production cannot be further increased, unless there is a third
method which is not profitable when β=18/7 and r=2/7, but is sufficiently more productive per acre
such that a rise in the rate of rent makes it equally profitable with method B while the rate of profits
is still positive. For example:
C : 16 → 23.
The reader can check that B and C are equally profitable for  = 3, r = 25%, while for
=18/7 the rate of profits obtainable with method C is less than 2/7.
The same process that caused B to become equally profitable with A will now cause a
decrease of r to 25% , and a rise of β to 3, rendering B and C equally profitable and thus allowing
a further expansion of production by gradual extension of the use of C and contraction of B. Method
A is no longer present: with intensive differential rent, only two processes co-exist at each time.
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Intensive differential rent is the possible justification of the assumption, made in our first
presentation of the corn economy, of a uniform rate of rent on land of uniform quality: this land
must be fully utilized.
Of course, the simultaneous presence of extensive and intensive rent is possible. The gradual
extension of corn production will use new lands, or new methods on already fully utilized lands,
depending on which way allows a higher rate of profits (i.e. a smaller decrease in the rate of profits
from its previous level). But since on each land the rates of profit at which two processes can coexist are well determined (they are isolated values, not intervals), except for flukes[ 28] or
transitional periods there will never be more than one land on which intensive differential rent is
present.
Is it possible to argue that intensive rent too does not enter price? It might seem not, since all
producers pay a rent. But in fact it is still possible to argue that rent does not enter the “cost of
production inclusive of profits” of the last unit of corn produced, if one reasons as follows. Take the
case when there is a single type of land, on which methods B and C are used. Consider the
“differential method” that represents the increase in capital (seed plus wages) producing the
increase in output if, on one acre, method C replaces B. This is
D: 4 → 5.
Notice that if this were an autonomous per-acre method paying no rent, it would yield a rate
of profits rD=25%, precisely the ruling rate of profits. Now, a producer who switches from method
B to C on one acre pays the same rent as before, so it is as if he were still using method B on that
acre and in addition he were using method D on an acre of another, no-rent, land. Thus production
using method B on x acres and method C on the remaining y acres and yielding an intensive rate of
rent β on the x+y acres can also be visualized as using method B on all the x+y acres of available
land, on which an extensive differential rate of rent β is paid, and using method D on y acres of an
(imaginary) no-rent land of total surface of x+y acres too, but x acres of which are still unused. For
example if the total land surface is 12 acres, and B is used on 10 acres and C on the other 2 acres,
then total production is 180+46=226 tons, the same as if B were used on all 12 acres (216 tons) and
the differential method D were used on 2 acres of a no-rent land, producing 10 tons.
With this visualization, all rent is extensive differential rent, with method B representing the
conditions of production on the fully-utilized land which, because fully utilized, earns a positive
rent, and method D representing the conditions of production on the hypothetical no-rent land
which, being only partially utilized, earns zero rent. Method D can be seen as representing the
28
I.e. cases in which the co-existence of two processes requires exactly the same rate of profits on
two different types of fully utilized land.
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conditions of production of that part of corn production that pays no rent. Thus it is possible, with
intensive rent too, to arrive at a method of production that pays no rent: the differential method.
An implication of this theory of extensive and intensive differential rent is that it may well
be the case that moderate changes in the quantities to be produced do not alter the rates of rent,
because the lands and methods in use remain the same, what changes is only the extent of
cultivation of the no-rent land, or the proportions between the two methods adopted on an intensiverent land. And in other cases the changes in no-rent land can be taken to be only minor, only
marginally modifying the no-rent technology. In these cases, the determination of a change in the
profit rate induced e.g. by a change of the real wage can take technology as given in spite of the
indubitable change in the composition, and perhaps even in the general level, of social output.
It might be argued, however, that when real wages change relevantly, the changes in the
quantities produced might be so extensive as to relevantly alter the no-rent land, thus questioning
the right to take technology as given when determining the effect on the rate of profits. But the
method in two stages sketched in §1.4.1 remains applicable and indeed necessary, owing to the
impossibility deductively to ascertain with certainty how the quantities produced will change; it is
best first to establish the effects on profits assuming given quantities produced (and hence given
technical methods), and then in a second stage to try and guess as best one can, on the basis of the
circumstances, the plausible changes in quantities, and their impact on the no-rent land, so as to
arrive at a better approximation of the effect on the rate of profits − a better approximation that one
can reasonably expect to be anyway of minor importance in most situations[29].
1.6. PROFIT AND RELATIVE PRICES
In the corn economy, product and capital are physically homogeneous; the rate of profits is
determined as a ratio between physically homogeneous magnitudes. No theory of relative prices is
required in order to determine the rates of wages, of rents, and of profit.
In real economies, on the contrary, there are many products, and there isn’t homogeneity
between the goods whose sale generates the profits, and the goods constituting the advanced capital.
The rate of profits must be determined as the ratio of the value of profits to the value of advanced
capital. The values of goods must therefore be determined. If for example in the apple industry corn
29
The importance will likely not be of minor importance when one studies the effects of secular
growth, which must take into account ecological and natural resource constraints. However, it is well known
that these attempts must be based on more or less plausible guesses on e.g. the speed of technical progress,
future growth rates, changes in tastes, discoveries of unexploited natural resources, co-operation among
nations, thus they can do no more than depict possible alternative scenarios, and constitute therefore a good
example of the need for a two-stages method where one stage is more inductive and includes broad social
and political considerations.
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is the sole good advanced as capital (inclusive of advanced wages), and there is no rent, the rate of
profits is given by
r=(value of apples produced minus value of corn advanced)/(value of corn advanced)
and its determination requires knowing not only the physical amounts of corn advanced and of
apples produced, but also the relative price of apples in terms of corn. (It is relative price only that
counts, because a proportional variation of the price of apples and of corn leaves the ratio
unchanged. The value of a good is another term to indicate its normal relative price in terms of the
chosen numéraire − see below.) The same problem arises for the entire economy. We have seen
that, when the rate of profits must be determined, classical analysis can take as given the quantities
produced, the production methods on no-rent land, and the rate of wages. These data allow the
determination of the surplus net of rent, and of the capital advances, in physical terms, as vectors of
quantities. But the rate of profits is the ratio
aggregate value of the physical surplus net of rent
[*]
r = ───────────────────────────────
aggregate value of the physical capital advances
and the two physical vectors at the numerator and denominator of this ratio are generally of
different composition, so the ratio of their values will depend on relative prices.
As clarified by Piero Sraffa (1951) and Pierangelo Garegnani (1984, 1987), the
determination of these relative prices constitutes the central analytical problem of the surplus
approach. This problem was left imperfectly solved by the classical authors, and it made it easier to
dismiss the entire approach as flawed when the alternative marginal approach was born. In order to
determine whether the difficulties that the classical authors encountered on this issue undermine the
approach or not, we must now examine the problem in some detail, and in its historical evolution.
The root of the problem is that, as will be shown below, relative prices depend on income
distribution. Then the rate of profits depends on relative prices which in turn depend on the rate of
profits; equation [*] is accordingly unable to determine the rate of profits until a theory of relative
prices is provided, but the latter theory will fall into circular reasoning if it needs an already
determined rate of profits in order to determine relative prices.
This problem centering on the determination of the rate of profits becomes clear with
Ricardo, but we must first understand Ricardo’s starting point on the problem of the determination
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of relative prices, which is Adam Smith’s distinction between market price, and natural price. The
latter is also often referred to as the value of commodities. First we clarify why not all commodities
are relevant for the determination of the rate of profits. Ricardo writes:
There are some commodities, the value of which is determined by their scarcity
alone. No labour can increase the quantity of such goods, and therefore their value cannot
be lowered by an increased supply. Some rare statues and pictures, scarce books and coins,
wines of a peculiar quality, which can be made only from grapes grown on a particular soil,
of which there is a very limited quantity, are all of this description. Their value is wholly
independent of the quantity of labour originally necessary to produce them, and varies with
the varying wealth and inclination of those who are desirous to possess them.
These commodities, however, form a very small part of the mass of commodities
daily exchanged in the market. By far the greatest part of those goods which are the objects
of desire, are procured by labour; and they may be multiplied, not in one country alone, but
in many, almost without any assignable limit, if we are disposed to bestow the labour
necessary to obtain them.
In speaking then of commodities, of their exchangeable value, and of the laws which
regulate their relative prices, we mean always such commodities only as can be increased in
quantity by the exertion of human industry, and on the production of which competition
operates without restraint. (Ricardo, Principles, p. 12)
The commodities relevant for the determination of the rate of profits are those of the second
type, the ones which “can be increased in quantity by the exertion of human industry”, i.e. by
production; their price tends to be regulated by the variation of supply according as their production
is unprofitable, or particularly profitable. It is to these commodities that the distinction between
market price and natural price applies. For the other commodities, whose value “varies with the
varying wealth and inclination of those who are desirous to possess them”, the classical economists
felt that little systematic could be said, but also that this was no great problem because they
constituted a negligible part of economic transactions.
Market prices are the actually observed day-by-day prices, influenced by transitory and
accidental circumstances (and generally not even uniform, at each point in time, for all the units of
the same commodity, so that to speak of ‘the’ market price of a commodity already presupposes
some kind of averaging). Natural prices are the prices around which market prices gravitate,
continually tending to come back to them after every deviation. This gravitation is due to the
working of free competition, that tends to establish the same price for all units of the same
commodity, and for all units of the services of the same type of land, or of the same type of labour,
or of each unit of capital, owing to the free mobility of labour, land and capital among different
industries. This means − Smith argues − that the prices of produced commodities tend toward the
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levels that allow the payment of rent for the land used, the payment of wages to the labour used, and
the earning of profits on the capital advanced, at their natural rates. If the price of a commodity
were above its natural level, then at least one of the three causes of costs (wages, land rents, or
profits) would be above its natural rate, attracting further units of the better-paid input into the
industry, thus causing an increased production and increased competition among suppliers of that
commodity, which would tend to lower its price while at the same time reducing the reward of the
input which has flocked to that industry.
We must now explain what these natural rates are. The natural level of the real wage rate is
the customary level, explained by the considerations illustrated earlier. The natural levels of the
rates of rent are determined by the theory of differential rent in the way explained in §1.5. The
natural level of the rate of profits is the level residually determined on the basis of the given
conditions of production on no-rent land, and of the given real wage rate; the classicals had
problems in arriving at a correct determination of this rate of profits (more on this later), but the
notion was clear. The prices that allow the payment of wages, rents and profits at their natural rates
are the natural prices of commodities, also called by Marx prices of production. Nowadays they are
also referred to as long-period normal prices.
This notion of long-period price is of course what students are introduced to in any
economics textbook, when, in a partial-equilibrium framework, they study the tendency, in
competitive conditions with free entry, of the price of a product toward the long-period price
corresponding to zero 'profits'[30]. In these analyses the long-period price, equal to the minimum
average cost, is determined on the basis of given input “prices” or, as I shall prefer to call them,
input rentals[31]. But the moment capital goods are admitted among the inputs of the good in
30
Zero 'profits', in the marginalist sense of what is left of revenue after paying all costs including
interest (gross of a risk allowance) on the capital employed, interest which is computed also on the part of
advanced capital supplied by the entrepreneur himself, because on that part it is the opportunity cost of
employing that capital in the firm rather than elsewhere. The Classical authors did not include interest among
the costs to be subtracted from revenue in order to obtain profits, so in them the term 'profit' has a different
meaning: ‘profit’ is what is left of revenue after paying all costs except interest. Therefore the classicals’ rate
of profits is what nowadays is called rate of return on the total capital employed. The tendency to zero
'profits' in the marginalist sense is expressed by the Classical authors as the tendency of profits to become the
normal ones i.e. to guarantee the normal 'rate of profits' (the same rate of return on the capital employed as in
other industries - once account is taken of risk). To avoid ambiguities, where necessary the neoclassical
meaning will be conveyed through the term ‘extraprofits’. The fact that in classical terminology costs do not
include interest is what has suggested the need for the expression “costs inclusive of profits” to refer, in fact,
to the marginalist notion of cost, equal to the natural price.
31
The rental of a factor is the price of its services: the rental of land is its rent per acre, the rental of
labour is its wage per labour unit, the rental of a capital good is what each unit of that capital good can fetch
if rented out. The reason for this terminology is that in this way there is no risk of confusing the price to be
paid e.g. for purchasing the property of a piece of land, with the price (the rent) to be paid for the right to use
that land for a specified length of time. It is the latter price, i.e. the price of the services of land, that enters
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question, the same tendency should be admitted to be simultaneously at work, and with a speed of
the same order of magnitude, for the purchase prices of these capital goods, and (by altering their
quantities) to be influencing their rentals and thus the average cost of the good in question; so, a
consistent determination of the long-period price of a product requires the simultaneous
determination of the long-period prices and rentals of all capital goods directly or indirectly entering
its production[32]. This means that the natural prices, or long-period prices, of products must be
associated with a uniform rate of rent (at its natural level) for the same types of land, a uniform rate
of wage (at its natural level) for the same type of work, and a uniform net-of-risk[33] rate of return
(at its natural level) in all industries; if this did not obtain, there would be quick changes in the
composition of production, brought about by the tendency of existing firms to expand production,
or of new firms to be set up, in industries where extra profits can be earned (because the product
price allows paying at least some of the inputs more than their natural prices), and to abandon the
industries where the opposite is the case.
Let us further clarify with reference to how the firm’s cost is usually represented in modern
microeconomics. Total cost is usually defined as:
[1.3] C=w1x1+...+wnxn,
where C is total cost, wi is the rental (the price of the services) of the i-th factor of production, xi is
the quantity employed of (the services of)[34] the i-th factor. Profit is then defined as revenue minus
the costs of production of commodities. An analogous distinction is useful for capital goods; even when
capital goods are bought, one can consider the payment of the purchase price as an act of saving, rewarded
by the subsequent rentals earned by the capital good; the rate of interest, or of return, on capital results from
the relationship of these rentals to the purchase price. Only for labour the distinction is unnecessary (except
in societies where slavery is admitted). The standard theory of the competitive firm shows that a firm will
tend to equalize the rental of each factor with its value marginal product.
32
The time required for setting up new firms can sometimes be a year or even longer; and the entry
process can take longer than that, if firms need time to make sure that demand is persistently greater than
supply. In such a time span the relative amounts in existence of all capital goods can change considerably,
and must therefore be considered endogenous variables of a situation where prices can be taken to have
reasonably approximated their natural or long-period values. Let us also remember that Adam Smith noted
that the determination of the rate of return on investments in agriculture requires the averaging of profits over
several years, owing to the irregularity of crop yields. Such an irregularity can only make it even more
difficult, and therefore slower, the adjustment of the quantities produced capable of ensuring prices of
agricultural products equal on average to costs of production.
33
. The normal risk surcharge on top of the riskless rate of return will differ from industry to industry
depending on the riskiness, unpredictability etc. of entrepreneurship in each industry. The usual assumption
of a uniform rate of return neglects these differences for simplicity’s sake.
34
It is common, although unrigorous, to speak of the quantity employed of a factor, although what is
meant is the quantity of its services, a quantity requiring for its specification also the indication of the time
unit to which the unit of measurement refers. To say that a firm has utilized ten acres of land is insufficient,
unless a time unit is implicit that specifies for how long; e.g. if the time unit is the year, one is actually saying
that the firm has utilized ten year-acres of land. Thus when one says that the amount of labour employed is x,
what one means is that the firm employs x units of labour time per period (how many labourers this means,
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the total cost thus defined. Such a definition of profit implies that factor costs are calculated
assuming that factor payments and revenue refer to the same time moment: either factor payments
are assumed to be made at the time when revenue accrues; or both factor payments and revenue are
discounted to the ‘initial’ moment of the analysis (this is the more common interpretation in
intertemporal analyses). If some factor payments are paid before the moment when revenue accrues,
and if revenue is not discounted to the initial moment, then in the above definition of costs the
factor prices indicate their future value[35] referred to the same moment when revenue accrues;
interest is implicitly added to the costs actually paid, for the interval between payment of costs and
receipt of revenue.
Thus imagine an agricultural firm producing corn with two factors: x1 is 50 units of seed
bought at the beginning of the year at price 2, x 2 is 50 units of labour which receive, let us suppose
at the end of the year, a wage rate of 4; the product at the end of the year yields, let us suppose, a
revenue of 320; the market interest rate is i=10%. In the standard determination of C, the cost of
seed must be referred to the end of the year, therefore one must add the interest rate to what is paid
for them at the beginning of the year, thus w1=2·(1+i), and C=310; the firm’s 'profit' in the
marginalist sense is 10. A classical author on the contrary would measure profit − in the classical
sense − as 320–(200+100)=20 and would conclude that in this firm the rate of return or of profit on
the advanced capital is 20% (the capital advance is 100; for the wages it is unnecessary to advance
capital because we have assumed that they are paid in arrears, when revenue accrues from the sale
of the product).
Thus when the dominant microeconomics teaches that in the long period the price of
produced commodities tends to equal average cost and profit tends to zero, a classical author would
express the same idea by saying that in the long period the rate of profits on the capital advanced
tends to become just equal to the rate of interest[36].
The role of the notion of natural price is therefore essentially the same as the role of the
notion of long-period equilibrium product price of Marshallian microeconomics. The search by
depends on how much labour time each labourer works per period).
35
The future value of a present sum of money is what one obtains by adding to it the (compound)
interests on it, from the present moment to the moment to which the future value refers. Its calculation is
therefore the opposite of discounting.
36
Both classical and marginalist economists admit that the rate of interest that firms include in their
costs is higher than the market rate on safe loans, the difference being necessary in order to cover the “risk
and trouble” − to use Adam Smith’s expression − of entrepreneurial activity. Therefore profit in the
marginalist sense does not actually tend to zero in the long period, but rather to that level that covers risk;
and the classical rate of profits tends to equality not with the rate of interest, but rather with the rate of
interest increased by a percentage that must cover risks and entrepreneural efforts. Here we will neglect this
complication whenever possible.
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workers of the highest wage rate (and by firms of the lowest wage rate) tends to make the wage rate
the same for labour of the same type; an analogous process tends to bring to uniformity the rate of
rent for lands of the same type; and the tendency of capitals to go where the expected rate of return
is higher tends to bring the rate of profits toward the same level everywhere, because, where the rate
of profits is above average, investment increases, new plants are built, production increases, product
prices tend to fall, and the rate of profits tends to decrease; while the opposite is the case where the
rate of profits is below average[37]. These tendencies logically imply the tendency of market prices
toward the respective natural levels. Indeed when the market price of a commodity is below its
natural price, it means that labour and/or land and/or capital receive less than their natural rates in
the production of that commodity, and will therefore tend to leave that industry, causing a decrease
in the production of that commodity, which will sooner or later cause the price of the commodity to
rise; the opposite tendency will be at work when the market price is above the natural price. Thus
the market price tends to return to the natural price whenever for some reason it comes to diverge
from the latter, and therefore the latter can be taken to indicate with sufficient approximation the
average market price over a period of time sufficient for variations in the number, size and
technology of the firms in an industry.
The quantity demanded of a commodity when its price is the natural price is called its
effectual demand. In the classical authors the notion of a demand curve or schedule, that indicates
the precise quantity demanded of a commodity also at prices different from the natural price, is
absent; hence also absent is the notion of a short-period equilibrium price determinable at the
intersection of a demand curve with a short-period supply curve. All that can be said is that when
the quantity brought to market is less than the effectual demand, the price will tend to be above the
natural price, and when the quantity brought to market is greater than the effectual demand, the
price will tend to be below the natural price. The numerous accidental elements that can influence
the market price when the quantity supplied does not coincide with effectual demand do not allow
one to formulate precise predictions on market prices; the theorist can seldom do more than predict
the sign of the divergence of the market price from the natural price. Thus Ricardo writes: “no
general rule can be laid down for the variation of [market] prices in proportion to [the] quantity
[brought to market]” (Ricardo 1822, p. 220). Much, he warns, will depend on a factor so resistant to
general rules as “the opinions formed on the probability of the future supply being adequate or
37
Actually the tendency toward uniformity only applies to the rates of profit net of risk; the riskcovering addition can be considerably different from field to field of investment. But as long as these
differences can be taken as given, to assume a uniform rate of profits will generally not lead to erroneous
conclusions in comparative-statics analyses on the effects on the average rate of profits of changes in its
determinants, e.g. effect of rise of wages.
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otherwise to the future demand” (ibid.)[38][39].
1.7. SMITH ON NATURAL PRICES AND INCOME DISTRIBUTION
1.7.1. The starting point of the classical analysis of natural price is Adam Smith’s
observation that when “the whole produce of labour belongs to the labourer”, i.e. when there are no
rents and no profit, then relative natural prices will equal ratios of labour ‘embodied’: commodities
will tend to exchange in proportion to the labour required to produce them.
In that early and rude state of society which precedes both the accumulation of stock
and the appropriation of land, the proportion between the quantities of labour necessary for
acquiring different objects seems to be the only circumstance which can afford any rule for
exchanging them for one another. If among a nation of hunters, for example, it usually costs
twice the labour to kill a beaver which it does to kill a deer, one beaver should naturally
exchange for or be worth two deer. It is natural that what is usually the produce of two days’
or two hours’ labour, should be worth double of what is usually the produce of one day’s or
one hour’s labour. (Wealth of Nations Bk. I Ch. VI, vol. I p. 41-2)
The reason, clearly, is that if the exchange ratio were different from two deer to one beaver,
it would be convenient for hunters to hunt only one of the two animals and obtain the other by
exchange. For example if the exchange ratio is three deer to one beaver, whoever desires to obtain
deer will find it more convenient to hunt beavers, because with the labour time required to catch
two deer he can obtain three deer if he hunts beavers and then exchanges beavers for deer; but the
resulting increase in the supply of beavers and decrease in the supply of deer will cause an excess
supply of beavers and insufficient supply of deer, which will tend to make deer cheaper relative to
beavers. The process will continue until the exchange ratio becomes the one – two deer for one
beaver – that makes hunters indifferent between hunting beavers or deer.
There are a number of implicit assumptions in this argument, e.g. that there are no obstacles
Mainly, it would seem, because of the seller’s possibility to choose between trying to sell the
entire inventory of a commodity as quickly as possible, or stocking some part of it in order to sell it later, and
because of the analogous buyer’s possibility to choose to postpone or not the purchase.
39
We find here another example of the lesser ambition of classical economic theory compared with
modern habits, as to how far economic analysis can be pushed on a purely deductive basis. Another reason
why one does not find demand and supply functions in classical authors is the absence of the fullemployment assumption, which in the marginal approach (cf. chapter 3) constrains the quantity supplied by
an industry (it must subtract inputs from other industries, via an increase in the relative price of its inputs),
and through its connection with income distribution determines the incomes of consumers which lie behind
demand functions.
38
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(e.g. taxes) to hunting either animal, and that the labour required for killing a beaver or a deer is of
the same type. On this last issue Smith adds immediately:
If the one species of labour should be more severe than the other, some allowance will
naturally be made for this superior hardship; and the produce of one hour’s labour in the
one way may frequently exchange for that of two hours’ labour in the other.
Or if the one species of labour requires an uncommon degree of dexterity and ingenuity,
the esteem which men have for such talents will naturally give a value to their produce,
superior to what would be due to the time employed about it. Such talents can seldom be
acquired but in consequence of long application, and the superior value of their produce
may frequently be no more than a reasonable compensation for the time and labour which
must be spent in acquiring them. In the advanced state of society, allowances of this kind,
for superior hardship and superior skill, are commonly made in the wages of labour
(Wealth of Nations, ibid., p. 42)
Here − as anticipated earlier − Smith, like all classical authors, treats the ‘equivalence ratios’
between different types of labour[40] as given when attempting the determination of natural prices,
and implicitly reduces all labour to homogeneity on the basis of these equivalence ratios, which “in
the advanced state of society” are represented by relative wages: we have briefly discussed earlier
(§1.3.2) why this approach appears reasonable. For the determination of natural prices, then, if type
A labour has a rate of wages double that of type B labour, then one unit of type A labour counts as
two units of type B labour in the computation of the labour and of the costs necessary for the
production of a commodity; for example a commodity, requiring for its production one unit of type
A labour and one unit of type B labour, can be treated, for the determination of its natural price, as
requiring three units of type B labour. For this reason, after these lines on differences between types
of labour, Smith continues as if labour were all of one type.
Notice that Smith does not say that, for commodities to exchange in proportion to labours
embodied, labour must be the sole input; he only says that rents and profits must be absent. We
show what this means through a simple (but generalizable) example.
1.7.2. Suppose an economy where two products, corn and iron, are produced in separate
industries in yearly production cycles with, as inputs, labour (all of one type), corn and iron. Both
the corn and the iron used as inputs are circulating capital i.e. are completely used up in a single
We speak of ‘equivalence ratios’ rather than ‘relative wages’ because here Smith is describing an
imaginary primitive society in which labour is not wage labour, and the relative esteem of different types of
labour is revealed by the exchange ratios between their products (labour being the only cost). Note how
Smith eschews rigid explanations of relative wages, leaving room for complex social influences (notice the
role of “esteem”, and the adjective “frequently”).
40
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production cycle. The methods of production in each industry are given.
Here too, a method of production is defined by its technical coefficients i.e. quantities of the
several inputs per unit of output: here, tons of corn, tons of iron, and labour-years per unit of
output[41]. We assume that 1) all inputs and all products are perfectly divisible[42], 2) if all inputs
are varied in the same proportion then output too varies in the same proportion (constant returns to
scale). Of course technical coefficients indicate the minimum quantities needed per unit of output:
firms, being interested in minimizing production costs, try not to use more inputs than necessary.
Let us indicate with asj the technical coefficient of input s in industry j, where s=1,2,L and
j=1,2: corn is good 1, iron is good 2, labour is indicated with L. With * standing for ‘together with’,
and → standing for ‘produces’, we can represent the production methods of the two industries thus:
a11 * a21 * aL1 → 1 unit of good 1 (corn)
a12 * a22 * aL2 → 1 unit of good 2 (iron).
The labour embodied or contained in a commodity is defined as the ‘live’ labour directly
employed in its production plus the ‘dead’ labour[43] embodied in the non-labour inputs used up in
its production, which is seen as ‘transferred’ to the product. It will be convenient to have a term for
the non-labour inputs: we will call them means of production. In this economy the labours
embodied in a unit of corn and in a unit of iron − let us indicate them as m1 and m2 − are determined
by:
[1.4] m1 = aL1 + a11m1 + a21m2
[1.5] m2 = aL2 + a12m1 + a22m2.
For example the first equation states that the labour embodied in one unit of corn, m1, results
from the sum of the direct labour aL1, and of the labour (also called indirect labour) embodied in the
means of production used up, a11m1+a21m2.
If there are neither land rents nor profits, the natural price must cover only the wage costs
and the cost of the means of production. Let p1 be the price of corn, p2 the price of iron, w the wage
41
Of course the measurement of labour in labour-years assumes a given average number of labour
hours in a year, with a given average intensity and dexterity of labour.
42
This assumption is to be intended as meaning that the smallest unit is sufficiently small as to allow
neglecting indivisibilities. For example, cars are not perfectly divisible, but if a firm produces 10000 cars of
the same type a year, a variation of output by one unit is a variation of output by only one tenth of a
thousandth, such a small fraction of total output that to treat output as a continuous variable in order to study
e.g. how cost varies with output is legitimate.
43
‘Dead’ in the sense of fixed, no longer alterable, while the amount of ‘live’ labour performed by a
labourer can be altered by lengthening the working day or changing the intensity of work. This terminology
was introduced by Karl Marx.
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rate i.e. the value of the physical wage basket (e.g. if the physical wage basket consists of z units of
corn, it is w=p1z). Then natural prices must satisfy:
[1.6] p1 = waL1 +a11p1 + a21p2
[1.7] p2 = waL2 + a12p1 + a22p2.
These equations can only determine the ratios between p1, p2 and w: if satisfied for certain
values of p1, p2 and w, they continue to be satisfied if these variables are multiplied by the same
scalar. If now in both equations we divide both sides by w, we obtain equations identical to
equations [1.5]-[1.6] with the sole difference that in place of m1 there is p1/w, and in place of m2
there is p2/w. It follows that
[1.8] p1/w=m1, p2/w=m2,
and therefore
[1.9] p1/p2=m1/m2,
the ratios between natural prices coincide with the ratios between labours embodied.
The reason can be more fully grasped by noticing the following fact. In equation [1.6] let us
replace p1 and p2 on its right-hand side with the cost-expressions determining them (i.e. the righthand sides of equations [1.6] and [1.7]); we obtain
[1.10]
p1 = waL1 + a11(waL1 + a11p1 + a21p2) + a21(waL2 + a12p1 + a22p2) =
= waL1 + [wa11aL1 + wa21aL2] + [a11(a11p1 + a21p2) + a21(a12p1 + a22p2)].
This can be interpreted as follows: the price of a unit of corn must equal the wages paid to the direct
labour employed in its production, waL1, plus the wages paid to the direct labour employed in the
production of its means of production, wa11aL1 + wa21aL2, plus the cost of the means of production
of those means of production. In this last term, a11(a11p1 + a21p2) + a21(a12p1 + a22p2), we can again
replace the prices with their cost-expressions, and iterating this procedure we can express the price
as an infinite sum entirely of wages: the wages paid to the direct labour, plus the wages paid in the
production of the direct means of production, plus the wages paid in the production of the means of
production of the means of production, and so on. (We will prove in chapter 2 that this sum
converges to a finite limit, which is precisely the price determined by equations [1.6-1.7].) The cost
of production can be reduced in this way to a sum of wages, direct and indirect. Now, the same
iterative procedure can be applied to the labours embodied. Thus the labour embodied in a
commodity is the sum of 1) living labour employed in its production, 2) living labour employed in
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producing its means of production, 3) living labour employed in producing the means of production
of those means of production, 4)... and so on; and in absence of rents and profits the natural price is
the sum of these quantities of labour, each one multiplied by the wage rate, therefore one can say
that it measures the wages embodied in the commodity, proportional to labours embodied. Hence
equation [1.9].
Since here wages are the only direct and indirect cause of costs, the labour theory of value
holds; that is to say, values i.e. natural prices are proportional to wages embodied and hence to
labours embodied[44], and coincide with labour embodied (and are then called labour values) if one
chooses as measure of value (or numéraire: good in terms of which relative prices are expressed) a
commodity embodying one unit of labour.
The labour theory of value has been and still is often seen as the characterizing element of
the classical approach, its central difference from the marginal/neoclassical approach. This is a
mistaken view that prevents a fruitful recuperation of what the classical approach can contribute; to
dispel it, we must dedicate some pages to the role of the labour theory of value in classical authors.
1.7.3. Smith does not hold to a labour theory of value except for the primitive economy
where labour is the only cost[45]. Indeed he continues (in the following citation ‘stock’ means
capital):
As soon as stock has accumulated in the hands of particular persons, some of them will
naturally employ it in setting to work industrious people, whom they will supply with
materials and subsistence, in order to make a profit by the sale of their work, or by what
their labour adds to the value of the materials. In exchanging the complete manufacture
either for money, for labour, or for other goods, over and above what may be sufficient to
pay the price of the materials, and the wages of the workmen, something must be given for
the profits of the undertaker of the work who hazards his stock in this adventure. The value
which the workmen add to the materials, therefore, resolves itself in this case into two
parts, of which the one pays their wages, the other the profits of their employer upon the
whole stock of materials and wages which he advanced. (Wealth of Nations, ibid., p. 42)
Now a price must also cover normal or natural profits in addition to natural wages and to the
normal cost of the ‘materials’ (means of production); here too, the cost (i.e. price) of means of
44
Exercise: show that in this case the exchange value of a commodity equals the labour embodied in
it, divided by the labour embodied in the numéraire commodity.
45
This has contributed to interpretations that consider Adam Smith less ‘classical’ than Ricardo or
Marx, and in fact closer to marginalism that to these authors. The deep mistake in this view will become
clear when the real distinguishing elements of the classical approach vis-à.vis the marginal one will be
pointed out in chapter 3.
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production can be decomposed into what determines it, that now includes profits besides wages and
cost of their means of production; the latter cost of means of production can again be ‘reduced’ to
wages, profits, and cost of means of production and so on, until the price of a commodity is
‘reduced’ to a sum of direct and indirect wages and profits. When rent is introduced, prices must
also cover direct and indirect normal or natural rents. Then, Smith notes, the principle of
proportionality between value and labour embodied no longer holds: value must also include profits
and rents at their natural rates, and it is not generally the case that the portion of value representing
profits and rents is in the same proportion to wage costs for all commodities − a condition which, if
satisfied, would not disturb the proportionality between values and labours embodied. Now natural
prices, or values, result from the sum of natural wages, natural profits and natural rents in different
proportions for different commodities.
Therefore, given the technologies employed to produce the several commodities, in order to
determine natural prices Smith must determine the natural rates of wages, of rents, and of profits.
His approach to wages is the one we have already illustrated, and appears still fruitful. His
determination of the rates of rent, and of the rate of profits, appears on the contrary unsatisfactory
and not easy to make internally consistent, owing to a defective theory of the rate of profit, to the
absence of a fully understood theory of differential rent, and to statements not easy to reconcile with
other ones.
The intepretation of Smith on rent is debated; one can distinguish a traditional view and a
more recent, let us call it ‘modern’, view. The modern view (Dome, Sinha) summarizes his theory
as follows. Smith determines the rent on mines on the basis of differential rent: the least productive
mines that the demand for a certain mineral makes it necessary to operate will allow the owner to
obtain only the normal rate of profit on the advanced capital; more productive mines will generate a
rent. He also describes differential rent due to differences in transport cost. But for food, he says,
the situation is different: in civilized nations, he says, all the land that produces the main staple food
– in Europe, corn – earns rent; rent in the production of corn is determined residually, as what is left
after replacing the advanced capital and obtaining on this capital the normal rate of profit,
determined independently in the way explained below. Advanced capital is treated as if consisting
only of corn, because real wages consist essentially of food and money wages are strictly
proportional to the money price of corn[46], and Smith tends to reduce capital advances to wage
Smith in other parts of his book freely admits that workers’ consumption includes many other
produced commodities besides corn, but when he discusses changes of the money price of corn in the chapter
on bounties he takes them as causing proportional changes of the money wage.
46
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advances[47]. He furthermore treats corn-producing land as all of the same best quality (resulting
from past labours of improvement); then, with the real wage given in corn, and hence capital
advances consisting of corn, he obtains physical homogeneity between output and capital advances;
the given rate of profit determines profits in corn; given the productivity of labour on corn land, rent
is determined residually. Thus suppose that corn and labour are measured in such units that the real
yearly wage rate per unit of labour is 1 unit of corn; suppose that the advance of 1 unit of corncapital (i.e. the employment of one unit of labour) produces 2 units of corn, and requires the
utilization of 2 acres of land; suppose furthermore that the rate of profit is 20%; this means that out
of the 2 units of output per unit of advanced capital 1.2 units remain with the capitalist-farmer, who
will use 1 unit to reconstitute the capital advance and will appropriate 0.2 units as profit; the
remaining 0.8 units go to the landlord as rent, i.e. the rate of rent per acre is 0.4.
Then the prices relative to corn of other goods are also determined. The conception of
capital advances as consisting essentially of advanced wages implies that in all industries capital
advances can be measured in corn; then, once technology is given, the given real wage rate and
given rate of profit determine the price relative to corn of the goods in whose production no rent is
paid; for example, with a corn wage rate equal to 1 and a rate of profit equal to 20% as above, a
good that pays no rent and requires for its production 10 units of labour will have natural price 12
measured in corn. As for the rent on other lands, Smith through an ingenious reasoning concludes
that it is governed by the rent on corn land. The price of a good (other than corn) that requires land
for its production, e.g. wool, and whose supply therefore encounters a limit, has a price that, starting
from the minimum yielding no rent, will rise with the demand for it, and therefore rent on its land –
which is not well adapted to corn production – depends on demand, but finds an upper limit in the
product price (in corn) that makes it just equally convenient to produce corn or this good on corn
land: at that point, an increase in the demand for the good causes some corn land to be used for
producing the good, the rate of rent must be the same in both productions, and the rent rate in corn
production, determined as indicated above, determines the corn price of the good, and hence also
47
Smith tends to reduce capital advances to wage advances, because after noting that the natural
price includes, besides wages profits and rents, also the value of used-up nonwage advances, he adds that this
value can in turn be decomposed into (previously paid) wages profits and rents, so that ultimately, in a finite
number of steps, one can “resolve” all prices into wages profits and rents (an anticipation of the ‘Austrian’
conception of the vertically integrated production of each good as starting with unassisted labour); but he
then does not see that this ‘fourth’ part of the value of the goods produced in a period does not correspond to
incomes distributed in that period, and writes that “the whole annual produce of the labour of every country
... must resolve itself into the same three parts, and be parcelled out among different inhabitants of the
country, either as the wages of their labour, the profits of their stock, or the rent of their land” (WN I, vi,
para. 17), as if the social gross product consisted only of wage goods besides the goods bought by profits and
by rents – in which case capital advances can only consist of wage advances.
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the rent on the other lands utilized for producing this good.
This reconstruction implies that according to Smith a given rate of wages does not suffice to
determine the rate of profit, because (within limits) there is room for increase in one of these two
rates without a need for the other one to decrease, because the third rate, the rate of rent, residually
determined, absorbs the change in the sum of (corn) wages and profits. Thus there is a constraint
binding the three rates, but not the first two. An increase in the rate of profit without change in the
(corn) rate of wages reduces corn rent and raises the prices of manufactures relative to corn (this
does not affect the real wage, fixed in corn).
On the contrary the traditional interpretation[48] views Smith as often losing sight of the
constraint necessarily binding the three rates, and falling into the mistake of an independent
determination of all three rates, of wages, of profits, and of rent, because Smith conceives the
natural price as resulting from the adding-up of these rates, which makes him sometimes reason as
if a rise in one rate could be accommodated by a rise of the natural price without need for at least
one of the other two rates to decrease. (The rates of rent are explained, according to this
interpretation, differently for different cases, generally as determined by the product price[49].) This
Smithian ‘adding-up’ is, according to Marx, the origin of subsequent shallow theories dubbed by
Marx ‘vulgar’, according to which, in Marx’s ironic words, “the outcome of this competition
between land, capital and labour finally shows that, although they quarrel with one another over the
division, their rivalry tends to increase the value of the product to such an extent that each receives
a larger piece, so that their competition, which spurs them on, is merely the expression of their
harmony”[50] (Marx will on the contrary insist on the conflict of interest between the classes,
especially between capital and labour). According to this interpretation, Smith’s slip was made
easier by his measuring prices in labour commanded. This latter notion deserves explanation.
So as to be able to compare 'real' national products of different years, i.e. in order to avoid
changes over time of the value of the national product due only to fluctuations of the value of the
good chosen as ‘standard or measure of value’ (in modern terminology: numéraire), e.g.
fluctuations in the value of silver or gold, Smith decides to determine relative prices adopting as
numéraire the average real wage basket, in his opinion a very stable quantity. The price of labour,
i.e. the wage, has then value 1; the price of a commodity expresses the number of wages to which
the exchange value of that commodity corresponds, and therefore it measures the number of labour
48
That originates in Marx and is apparently accepted by Sraffa (1951).
Thus Sraffa describes Smith as stating that ‘rent enters as an effect, not a cause, of price’ (1951, p.
xxxvi, fn.1).
50
Theories of Surplus Value, Volume III, Lawrence and Wishart, London 1978, p. 503.
49
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units that one can ‘command’ (i.e. purchase, have at one’s orders) with that exchange value[51], and
prices thus measured are accordingly called labour-commanded prices. For example, if the money
price of a unit of corn is 100 and the money wage is 20, then the labour-commanded price of corn is
5. A rise in the purchasing power of the wage translates then into a decrease in the labourcommanded price of commodities. E.g. in the previous numerical example, the labour-commanded
price of corn becomes 4 if, the money price of corn being still 100, the money wage rises to 25. The
real wage and its changes must then be deduced from the labour-commanded prices of
commodities, a rise of the real wage must be deduced from the decrease of the labour-commanded
prices of goods, and in particular of corn. The effect of labour commanded as measure of value is
that in the ‘surplus equation’ the value of capital is given because measured by labour employment
(the wages constituting capital advances command the productive labour that capital employs), but
the value of the social product net of rent (assuming for the sake of argument that rents have been
determined) is not given: it commands more than the labour employment that produced it, because
it also commands the labour commanded by profits, and this second amount of labour commanded
is not known before knowing profits, and it is not immediately evident that there is a constraint
binding its possible size. This may have misled Smith into believing that there isn’t a constraint
such that, supposing rents to have been determined, once the real wage is given the rate of profits is
given too.
The two interpretations agree on the fact that in Smith a given real wage does not suffice to
to determine the rate of profits. Smith determines it through the competition of capitals, as
explained below. But he also admits in several passages an influence of the level of wages, which is
not easily reconciled with either of the two interpretations just summarized. Smith admits that a rise
of wages reduces profits, for example, in this passage:
In a thriving town the people who have great stocks to employ frequently cannot get the
number of workmen they want, and therefore bid against one another in order to get as
many as they can, which raises the wages of labour, and lowers the profits of stock. (WN,
Bk I, Ch IX, 7; p. 80)
51
The expressions that we have met earlier in [1.18], p1/w and p2/w, are precisely the labour
commanded respectively by a unit of corn and by a unit of iron. In those equations labour-commanded prices
coincide with labours embodied because direct and indirect wages make up the whole cost; then a
commodity whose production has required the direct and indirect use of 10 units of labour must have a price
equal to 10 wages and therefore can command (i.e. purchase) 10 units of labour. If direct and indirect wages
are not the only cost and commodities still exchange according to relative labours embodied, then the labourcommanded price of a commodity is higher than its labour-embodied price. We cannot stop here on all the
reasons why Smith preferred to measure prices in labour commanded, but one must at least note that in this
way the value of the capital of a nation came close (because Smith tended to identify capital use with
advances of wages) to measuring the level of employment of (productive) labour.
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This is not easy to reconcile with the modern reconstruction of Smith’s theory of rent, which
implies that, at least as long as rent in corn production remains positive, the rise of wages (measured
in corn) need not affect profits, which can be maintained by a reduction of rent, and by a rise of
prices of other commodities relative to corn (except possibly for those non-corn agricultural
commodities which now pay less rent). But it is also not easy to reconcile with the adding-up
interpretation, since the latter again does not require the rate of profit to decrease when the real
wage rises; and indeed Marx argues that Smith is inconsistent, sometimes grasping the constraint
binding wages and profits, but at other times not seeing it. On the other influence on profits Smith
writes:
When the stocks of many rich merchants are turned into the same trade, their mutual
competition naturally tends to lower its profit; and when there is a like increase of stock in
all the different trades carried on in the same society, the same competition must produce
the same effect in them all. (WN, Bk I, Ch. IX, 2, p. 78).
This thesis illegitimately generalizes to the entire economy what is true for a single industry.
If supply of a single industry increases and oversteps the effectual demand for the commodity
produced by that industry, the result will be a lower product price with unchanged input prices, and
hence a lower average rate of profits in that industry. But if total capital increases and production
with it, this increases aggregate incomes and Smith, who argues that all savings will be invested[52],
should have accepted that aggregate demand increases as much as the value of production, so there
is no reason why prices should decrease relative to costs. Smith on the contrary seems to think that
a limit on the demand side also exists at the aggregate level, as is particularly clear in the following
passage:
The diminution of the capital stock of the society, or of the funds destined for the
Smith accepted that savings always translate into investment: “In all countries where there is
tolerable security, every man of common understanding will endeavour to employ whatever stock he can
command in procuring either present enjoyment or future profit. If it is employed in procuring present
enjoyment, it is a stock reserved for immediate consumption. If it is employed in producing future profit, it
must procure this profit either by staying with him, or by going from him. In the one case it is a fixed, in the
other it is a circulating capital. A man must be perfectly crazy who, where there is tolerable security, does
not employ all the stock which he commands, whether it be his own or borrowed of other people, in some
one or other of those three ways.” (WN, Bk. II, Ch. I, vol. I p. 249) This implies that whatever income is not
spent on consumption is invested, hence all income is spent, so aggregate expenditure equals aggregate
income always; an increase in production and income raises aggregate expenditure by an equal amount. This
thesis is nowadays called ‘Say’s Law’, cf. §1.11.2 below. Smith does not seem to have grasped it.
52
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maintenance of industry, however, as it lowers the wages of labour, so it raises the profits
of stock, and consequently the interest of money. By the wages of labour being lowered,
the owners of what stock remains in the society can bring their goods at less expense to
market than before, and less stock being employed in supplying the market than before,
they can sell them dearer. Their goods cost them less, and they get more for them. Their
profits, therefore, being augmented at both ends, can well afford a large interest. (WN, Bk
I, Ch. IX, 13; p. 84)
Here Smith again admits an influence of wages on profits, but clearly implies that this
influence does not suffice to determine the rate of profits, which requires determining also the
average price level at which commodities can be sold, an average price level viewed as inversely
related to aggregate supply for no more solid reason that an illegitimate analogy with the case of a
single market.
In conclusion, how the surplus gets divided between profits and rents is not satisfactorily
determined by Smith.
1.8. RICARDO
Ricardo, whose writings go from 1810 to 1823, differently from Smith was clear that if
savings always translate into investment then aggregate demand is always equal to aggregate
supply, and therefore aggregate demand cannot influence the rate of profits. Furthermore, the theory
of differential rent allowed him to separate the determination of the rate of profits from the problem
of determining land rents: if, for each commodity using land for its production, one considers its
natural price as determined by the conditions of production on no-rent land, then rent does not enter
the natural price.
Around 1814 (at least according to Sraffa 1951) Ricardo realizes that then he can reach an
easy determination of the rate of profits, avoiding the need to determine relative prices before or
simultaneously with the rate of profits, through an acceptance of Smith’s description of the corn
sector (corn produced by corn) as a sufficient approximation to reality. (Of course, like Smith,
Ricardo knew that capital advances in corn production did not consist only of corn, but he thought
the assumption a legitimate simplification owing to the great predominance of food in real wages.)
In the corn sector the real corn wage rate is given, and the best productive methods on each type of
land can be determined. The capital advance per unit of output consists of corn because it consists
of advances of wages, the latter viewed as consisting essentially of corn[ 53]. The quantity of corn to
53
Ricardo is clearer than Smith on the importance of fixed capital (machines and buildings) in
manufacture, but he does not seem to consider fixed capital very relevant in agriculture, and he neglects that

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be produced is also given by the state reached by economic development, and the theory of
differential rent then determines the no-rent land. On the no-rent land the surplus product goes
entirely to profits, and both the capital advanced and the surplus product consist of corn, and
therefore the rate of profits is a ratio between physical quantities, a ‘material ratio’. The rate of
profits on other lands and in other sectors cannot but adapt to this rate of profits through the
mobility of capitals[54].
Relative prices only come in when one wants to determine the prices of the other
commodities. But now there is no problem, because the rate of profits is already determined: the
prices of the commodities different from corn will simply have to adapt so as to yield that rate of
profits. Thus, let us again consider the economy that produces corn and iron, but let us now make
the following assumptions that cause the production of corn to require only corn: (i) real wages
consist of corn only, and precisely of a subsistence z1 per unit of labour; (ii) the production of corn
does not require the use of iron, i.e. a21=0 (thus we allow for seed-corn in agricultural capital,
something that Ricardo did not explicitly consider). We restrict attention to the sole production
methods on no-rent land; wages are advanced. The rate of profits r is the same in both industries.
The equality between product price, and costs inclusive of the rate of profits r on the capital
advanced (which includes the wages), requires:
[1.11] p1 = (z1aL1p1 +a11p1)(1+r)
[1.12] p2 = (z1aL2p1 + a12p1 + a22p2)(1+r).
As before, these equations can only determine the relative price p2/p1, because if satisfied by
a triplet (p1, p2, r), they continue to be satisfied if p1, p2 are multiplied by the same scalar. The rate
of profits is unambiguously determined by the sole equation [1.11], owing to the fact that all costs
in the production of corn consist of corn:
p1
1
[1.13] r = ──────── − 1 = ────── − 1 .
z1aL1p1+a11p1
z1aL1+a11
circulating capital also includes nonwage advances, e.g. seed.
54
This is the interpretation of Ricardo around the time of the Essay on Corn (1815) that appears most
convincing to the present writer; originally advanced by Sraffa in 1951, it was initially nearly universally
accepted; it was later disputed especially by S. Hollander and T. Peach, but it was defended, in my opinion
convincingly, by P. Garegnani, G. De Vivo, and others. Corn appears to be intended by Ricardo, in the same
way as in William Petty, “to contain all necessaries for life, as in the Lord’s Prayer we suppose the word
Bread doth”, necessaries mostly – at the time – produced by agriculture.
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As long as z1aL1+a11<1, the rate of profits is positive; it decreases if z1aL1+a11 increases, i.e.
if the real wage rate increases or if technology becomes less productive (e.g. because extension of
corn production to less fertile lands decreases the fertility of no-rent land). Note that the rate of
profits is determined independently of equation [1.12], whose role therefore is only that of
determining p2/p1 such as to yield the same rate of profits as in agriculture. Let us choose corn as
numéraire, p1=1. This makes the passive role of p2 clearest. If technical progress were to alter the
sole production method of iron, the rate of profits would not be altered: the only change would
concern p2, which would have to adapt so as to continue to yield the same rate of profits as before.
An analogous change only of p2, without effect on r, would be associated with the imposition of a
tax on iron.
In this way Ricardo was able to determine the rate of profits before relative prices, and to
demonstrate a necessary inverse connection between rate of wage and rate of profits: if one of the
two is given, the other is determined as well; if one of the two rises, the other necessarily decreases;
thus the constraint is already between rate of wages and rate of profits, and Smith was wrong in
believing in the need for an additional force, the competition of capitals, to determine the rate of
profits once the real wage was given. Finally – the conclusion Ricardo was most interested in – if
with a constant real rate of wage the productivity of agricultural labour decreases because corn
production is extended to less fertile lands, r decreases[55].
Thus the theory of differential rent plus clarity on the implications of the assumption that
savings are reinvested allow Ricardo to realize that Adam Smith was mistaken when conceiving the
rate of profits and the wage rate as determined by at least partly distinct forces (respectively, the
55
Ricardo often reasons as if capital advances consisted only of wages, inheriting here a mistake of
Adam Smith to be discussed later; but equation [1.11] shows that, for the validity of his argument, it is not
necessary that capital advances consist only of wages; what is necessary is that in the production of corn the
capital advances consist only of corn. they can include seed.
The ‘corn model’ approach can be extended to more complex cases. Suppose for example that three
goods are produced, corn (good 1), iron (good 2), cloth (good 3); the production of corn also needs advances
of seed; the production of iron and the production of cloth require advances of corn, iron and cloth besides
wages; then the price equations are:
[1.14] p1=1=(1+r)(p1a11+waL1)
[1.15] p2=(1+r)(p1a12+p2a22+p3a32+waL2)
[1.16] p3=(1+r)(p1a13+p2a23+p3a33+waL3).
Having chosen corn as numéraire (p1=1), w is a quantity of corn; once w is fixed the first equation
suffices to determine the rate of profits. The prices of iron and of cloth, determined by the last two equations,
have the sole role of permitting to earn in those two industries the rate of profits determined in agriculture.
Now the prices of iron and of cloth must be determined simultaneously; but with these equations we are
beyond what Ricardo was able to see; he was unable to write equations of such complexity and
disaggregation, he was not even totally clear on the presence in the natural price of a part replacing the usedup capital goods, cf. the next footnote, and the Appendix on machinery.
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competition of capitals, and a historically determined subsistence) and capable, within limits, of
independent variation.
Ricardo was prompted to formulate this analysis by the debates that arose in Great Britain at
the end of the Napoleonic wars (1814-1815), on whether the Corn Laws adopted during those wars,
that had imposed relevant duties on the importation of corn, should be abolished. He concluded that
the abolition of the import duties on corn, by permitting the importation of corn at a lower price
than the price ruling in that period in Great Britain, would reduce the demand for British corn,
inducing a decrease of the production of corn in Great Britain which would entail the abandonment
of the least fertile lands. This would have an effect opposite to that of the extension of cultivation to
inferior lands: a rise in the rate of profits. Now, both Ricardo and the other participants in the debate
agreed that the abolition of the import duties on corn was to be considered positive if it caused an
increase in the rate of profits, and negative in the opposite case, because they all thought that profits
were the main source of capital accumulation, and hence of economic growth, which was to be
favoured. Ricardo concluded for the abolition of the import duties.
But Thomas Malthus, an opponent of Ricardo in this debate, criticized the assumption of
sufficient homogeneity between capital and product in the corn sector, pointing out that the
workers’ given subsistence also included manufactures[56]; therefore the change in the corn-sector
rate of profit, and hence in the general rate of profit, brought about by changes of no-rent land could
not be ascertained without ascertaining the changes in the prices of non-agricultural wage goods
relative to corn. This argument was advanced to weaken Ricardo’s logic, as part of a more general
attempt by Malthus to defend the Corn Laws by arguing that high land rents contributed to a high
rate of profits by keeping aggregate demand high, and hence by keeping product prices high relative
to costs (an application of Smith’s argument on aggregate demand relative to aggregate supply as a
determinant of the rate of profit, but suffering from the same defect); a decrease of rents according
to Malthus would decrease demand, hence prices, and hence profits. Ricardo rejected this more
general argument by Malthus on the basis of the identification (accepted by Malthus too) of savings
and investment, that made deficiencies of aggregate demand impossible; but, being intellectually a
very honest person, he had to admit that his determination of the rate of profits did not extend to the
case of wages relevantly including non-agricultural products; in that case in no industry there was a
homogeneity between product and capital allowing a determination of the rate of profits as a
material ratio; in order to determine the changes in the rate of profits, he admitted, one had to
determine the changes in relative prices too; so he set out to look for a theory of relative prices.
56
Note how Malthus too accepts that capital advances consist essentially of wage advances.
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He was helped in this by his acceptance of Adam Smith’s thesis that the social product (net
of rents) resolves itself entirely into profits and wages[57]; this made him believe that capital could
be treated as reducible entirely to advanced wages. Then, at least when wages were advanced for
the same length of time for all commodities, the strict labour theory of value was valid and then,
since relative prices were independent of the rate of profits, the size of the ‘cake’ (the value of the
net product) to be divided between wages and profit, as well as – once the real wage was given –
the value of capital advances, were given independently of the rate of profits, and the latter could
accordingly be determined by the ‘surplus equation’ without circular reasoning; furthermore it was
clear that an increase of real wages necessarily caused the rate of profits to decrease.
Ricardo knew that, in general, wages were not advanced for the same length of time for
different commodities and therefore natural prices were not independent of r; he did see, for
example, that if the cost of a commodity consisted of wages advanced for a year, and the cost of
another consisted of the same wages but advanced for two years, then if the natural price of the first
commodity was p, the natural price of the second commodity would be (1+r)p and the ratio
between their prices could not be ascertained without knowing the rate of profits.
However he was convinced that this dependence of relative prices on distribution could not
cause great deviations of exchange rates from the labour-value exchange ratios (in one passage he
speaks of deviations not greater than 7%). Furthermore he reasoned that, for the study of the
problem he was centrally interested in − the sign of the effects of changes in the real wage rate or in
technical conditions of production on the rate of profits − these deviations would largely
compensate one another when the big aggregates relevant for the determination of the rate of profits
(i.e. the social surplus net of rents, and aggregate capital) were considered. If he could assume
relative prices to remain unchanged, then he could ascertain without problems the changes in the
quantites at the numerator and/or at the denominator of the ratio surplus/capital determining the rate
of profits. Now, he reasoned, relative prices do not remain unchanged because, as the rate of profits
rises, those commodities in whose price profits are a greater percentage will have to rise in value
57
Ricardo does not greatly advance relative to Smith on what capital is made of; very often he
reasons as if capital advances consisted of wages only, and he inherits from Smith the mistake of conceiving
the natural price as the sum of wages and profits (not rents, because the theory of differential rent allows him
to exclude land rent from the natural price, with intensive differential rent helping to explain why rent may
appear present on all corn-producing land); he too tends to forget about the value of the used-up nonwage
capital, in nearly all the examples in which he discusses machines these are produced by unassisted labour,
are treated as if eternal (no depreciation), and use no nonwage circulating capital, so both their prices and the
prices of their products still consist only of wages and of (direct and indirect) profits. We will see an example
of this when we discuss his numerical example of the effects of the introduction of machinery. For a full
overcoming of this mistake one must wait for Marx, who was able to avoid it owing to his attentive study of
the Physiocrats.
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relative to those commodities in whose price profits are a smaller percentage[ 58]; then, if one
chooses as measure of value (nowadays we would call it numéraire) a commodity where the
fraction of the price made up by profits is much greater than the average, for this sole fact the rise in
the rate of profits will lower the value of whatever aggregate one is considering, because most
commodities will decrease in value relative to that numéraire; while a numéraire in whose price
profits are a very small fraction will result in a rise in the value of any aggregate when the rate of
profits rises, because most commodities will rise in value relative to that numéraire. Choosing a
measure of value with a less extreme proportion of profits to wages, he continued, would mean that
when the rate of profits rose, the value of some commodities would rise relative to the measure of
value, and the value of some others would decrease. These variations, it was natural for him to
conclude, would roughly compensate one another in the aggregate, if one chose as measure of value
a commodity in whose price the relative fraction of wages and profits was, in some sense, average.
The choice of such an ‘average’ measure of value, he concluded, allows treating the values of the
big aggregates determining the rate of profits as fundamentally unaffected by changes in the rate of
profits – and therefore allows treating them as if determined by the labour theory of value, since the
latter determines them correctly when the rate of profits is zero. Gold, he argued, is perhaps close to
being such an ‘average’ commodity, and so he chose gold as measure of value or numéraire.
On the basis of this reasoning, Ricardo felt that to assume prices proportional to labours
embodied was an acceptable approximation for the study of the effects of changes in the real wage
rate, or in the no-rent land, on the rate of profits. Thus he adopted the labour theory of value – the
theory that relative product prices are proportional to labours embodied – not because he thought
that this was the correct theory of normal relative prices, but because he saw it as a sufficient
approximation to the correct theory (which he was unable to formulate), an approximation which he
had reason to believe was conducive to correct conclusions for the determination of changes of the
rate of profits. The labour theory of value was the provisional way out of the risk of circular
reasoning involved in a rate of profits depending on relative prices in turn depending on the rate of
profits: an imperfect way out as Ricardo admitted, but in all likelihood the sole one concretely
58
If capital advances can be reduced to wages, different proportions between wages and profits in
the natural price of different commodities must be due to wages being advanced for different lengths of time.
For example consider two commodities both produced by one unit of labour; the first commodity is sold one
year after the payment of the wage so its price is w(1+r); the second commodity is sold two years after the
payment of the wage so its price is w(1+r)2, the proportion of profits to wages is greater in the second natural
price, and a rise of the rate of profit causes the second commodity to rise in price relative to the first one. A
similar reasoning remains valid if the presence in the price of a part covering the used-up nonwage means of
production is admitted, as we will see à propos Marx.
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possible at the time, given the complexity of the issue[59].
This conclusion of a compensation of deviations so that the aggregates remain unaltered
was, it would seem, the general tendency of thought at the time; it also appears in James Mill,
another economist contemporary of Ricardo and father of John Stuart Mill, and is very explicit in
McCulloch, a follower of Ricardo who in a note to Smith’s Wealth of Nations writes that, although
a variation of the wage rate may cause the value of some commodity to vary from its ‘real value’,
“the exchangeable value of some other commodity must vary to the same extent in a contrary
direction” (quoted in Whitaker, 1904: 69, 70; on James Mill, cf. ibidem: 70, fn 2); improved and
developed, this is also, in essence, the argument one finds in Marx.
Before coming to Marx, let us show how rents appear in Ricardo’s labour-theory-of-value
approach to the determination of the rate of profits.
Let us first note that, in the absence of rents, the labour embodied in the aggregate net
product of a certain time period – say, a year – coincides with the total live labour performed during
that period. This is true not only when capital is conceived to consist only of advanced wages, but
also when it includes means of production, so we show it for this second more general case. Let L
be the total labour performed during the year, and let C be the labour value transferred to the
products by the means of production used up during the year. Then the labour value of the total
production of the year is[60] C+L, but the labour value of the net product is C+L minus the labour
value of the means of production used up, hence it is C+L–C = L. If capital is conceived to consist
only of advanced wages, then C is absent and the net product coincides with the social product[61],
so it is even more immediate that its labour value is L. In either case, L is the labour value that must
59
The complexity of the issue will be better appreciated when we come to chapter 2; we will see
then that the mathematical instruments necessary for a rigorous analysis of the issue even in the simple case
of only circulating capital were lacking in Ricardo's time and were developed only at the beginning of the
20th century; and that more complex cases such as fixed capital had to wait for several additional decades.
60
We are assuming here that commodities are produced according to normal conditions of
production, so that the labour employed to produce them is what Marx would later call the socially necessary
labour, the labour necessary according to the dominant production technique of that period. If part of the
production of a commodity comes from inefficient producers and uses more than the socially necessary
labour, its labour value is nonetheless determined by the socially necessary labour. This is because labour
values – in the conditions in which the labour theory of value would be a correct theory of relative prices –
must determine the normal prices around which market prices gravitate, i.e. the prices that competition will
tend to impose by eliminating inefficient producers. (The socially necessary labour is not necessarily the
labour associated with the most advanced technique: if for a commodity a new more convenient method has
been just discovered and, being only adopted by a few innovators, has not yet influenced the price of the
commodity, then it is not yet part of the production methods that enter the dominant technique and determine
the ruling uniform rate of profits in the period under study; it will become so only in the future.)
61
I am using here the modern definition of net product, that includes wages. Classical authors on the
contrary used ‘net produce’ to mean what is left after replacing all used-up capital, hence wages too; so the
net produce was the sum of profits and rents only – another confirmation of their view of wages as analogous
to fodder for horses, i.e. as necessary inputs to production.
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be divided between wages and profits; but in the second case L is also the value of the social
product.
Now let us see what difference it makes to admit rent. When a commodity is produced on
several lands, its labour value is determined by the production conditions on no-rent land[62]. For
simplicity let us treat, like Smith and Ricardo tend to do, capital as consisting only of wages
advanced for one period; then the labour theory of value holds. To help intuition, fix at 1 the value
of a good embodying one unit of labour. Then the value of the production of a good produced on
several different lands equals the quantity of labour that would have been necessary to produce it if
all of it had been produced with the technology obtaining on no-rent land, therefore it is greater
than the quantity of labour actually employed in its production, and the difference is the value going
to rent. For example if corn is produced on two lands, 100 units of labour producing 100 units of
corn on no-rent land and 100 units of labour producing 120 units of corn on better land, then the
labour embodied in the 220 units of corn is 220, but the labour employed is 200, and the difference
of 20 is precisely the labour value of the 20 units of corn going as differential rent to the owners of
the better land. Aggregating, we see that the total value of the social (and net) product is greater
than labour employment by the amount corresponding to what goes to rent. If then we call L the
labour actually performed, the labour value of the social product net of rents will be equal to L.
Thus, again, the labour value to be divided between wages and profits is measured by the total
labour employment of the year. If we call V the labour value of the wage goods which have gone to
L, then total profits in labour values are L–V, and if with Ricardo we identify V with the capital
advanced, then the rate of profits is given by r=(L–V)/V.
1.9. MARX
1.9.1. Values
Karl Marx (1818-1883) is an extremely important thinker who has influenced the course of
historical events like possibly no one else in modern times. The Bolshevik revolution that gave birth
to Communist governments in the USSR and then in many other nations was inspired by his
writings, although a number of thinkers consider the authoritarian communism of Stalin (and,
This is Ricardo’s definition, necessary to obtain prices proportional to labours embodied when the
rate of profit is zero. Marx does not adopt this definition of labour embodied in the presence of differential
rent, and this is just one of many perplexing aspects of his treatment of land rent; as this part of his work has
not been studied as much as the rest and there is still little clarity on how to interpret it, in this book I abstain
from discussing it.
62
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according to some, of Lenin too) to have little in common with Marx’s essentially libertarian
aspirations. Here we are interested in Marx as an economist; his analyses, I will argue, remain
extremely useful in spite of some limitations and mistakes; but they are often misunderstood. In
particular I will argue that, contrary to an argument frequently put forth by his marginalist critics,
Marx’s general approach to the nature of capitalism and to the basic forces at work in the capitalist
economy does not stand or fall with the labour theory of value. This requires examining Marx’s
approach to value in some detail.
Marx must be located in his times. When around 1845 he starts studying economics, he soon
discovers that the highest point reached by economic theory up to then is Ricardo. He starts
therefore from Ricardo’s labour theory of value and sets out to improve upon it. Many
commentators have been misled by the fact that in volume I of Capital (1867) Marx takes for
granted (except for some cryptic hints in footnotes) the labour theory of value, to the extent,
differently from Ricardo, of defining values as the exchange ratios (in terms of gold) determined by
the labour theory of value; since in volume III of Capital Marx admits that commodities do not
generally exchange at prices proportional to labour values, some critics have argued that Marx
himself admits that his whole analysis of volume I of Capital, which includes Marx’s
characterization of profits as resulting from the exploitation of labour, rests on indefensible
foundations. This is a misunderstanding. When he writes volume I of Capital Marx already knows
very well that natural prices (prices of production, as he prefers to call them) are not proportional to
labour values and, on the basis of results reached by 1858 (in the manuscript known as Grundrisse),
is persuaded that he has understood more clearly than Ricardo the reason for the nonproportionalities, how these are determined, and how in spite of them the rate of profits can be
determined starting from labour values.
He sees that the social product (net of rent) does not resolve itself entirely into profits and
wages: a part − which he calls ‘constant capital’ − goes to replace the used-up means of production.
He is then able to see, in his terminology, that the divergences of prices from labour-values are due
to the different proportion, in the various commodities, between living labour and ‘dead labour’ (the
labour embodied in the constant capital), a proportion he calls the ‘organic composition of capital’.
Let us follow Marx in provisionally assuming that commodities exchange at ratios
determined by the socially necessary labour they embody[ 63] and for the sake of simplicity let us
consider the economy, already studied in order to define labours embodied, that produces corn
(good 1) and iron (good 2) with seed-corn, iron and labour as inputs. This allows us to leave aside
63
Cf. footnote 60??.
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the complications in defining labours embodied that arise in connection with durable capital and
joint production. Let us choose as unit of measure of corn the quantity that embodies one unit of
labour, thus m1=1; let us choose corn as numéraire, p1=1; then since by assumption p1/p2=m1/m2, it
is also p1=m1 and p2=m2, prices coincide with labours embodied. Marx calls ‘values’ these prices
equal to labours embodied; we will call them labour-values, in order to avoid confusion with
Ricardo’s notion of ‘value’, which is synonymous with ‘natural price’ (i.e price that guarantees a
uniform rate of profits) in terms of the chosen numéraire (gold, in Ricardo).
Since seed-corn and iron used as inputs are circulating capital, they transfer into their
product all the labour embodied in them; therefore labour embodied is given by direct labour (living
labour, as Marx calls it) plus the entire labour embodied in the seed-corn and iron used as means of
production (dead labour, as Marx calls it). Therefore:
[1.17]
p1 = m1 = a11m1 + a21m2 + aL1
[1.18]
p2 = m2 = a12m1 + a22m2 + aL2 .
These equations easily generalize to n commodities (as long as all capital is circulating). But
Marx was unable to write down algebraic equations as disaggregated and simple as these; nor is this
surprising, simple examples are achieved only after reaching analytical clarity on the roots of the
problem in the general more complicated case, but a satisfactory analysis of the general case would
have required several more decades and the development of mathematical tools and theorems in
linear algebra and non-negative matrices still missing in Marx's time. So in Marx we find a more
aggregative treatment. He calls constant capital the labour embodied in the means of production
utilized to produce a product; variable capital is the labour embodied in the wage-goods paid to the
living labour employed[64]. We use the symbol c for constant capital, v for variable capital, ℓ for
living labour, and s=ℓ−v for surplus labour, the excess of the living labour performed over the
labour embodied in the wage goods that that living labour receives. For example if average
subsistence per unit of labour includes z1 units of corn and z2 units of iron, then if we consider a
firm producing 1 unit of corn, the labour value of its product is given by c+ℓ=c+v+s where
[1.19] ℓ=aL1,
[1.20] c=a11m1+a21m2,
64
. As the real wage rate varies, v changes but c does not; this is why Marx calls v variable capital,
and c constant capital.
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[1.21] v=(m1z1+m2z2)aL1.
In a firm producing x units of corn, the corresponding magnitudes are multiplied by x:
[1.22]
ℓ=xaL1, c=x(a11m1+a21m2), v=x(m1z1+m2z2)aL1.
(The reader should write down the analogous expressions for a firm that produces iron.)
Marx too, like Ricardo, conceives wages as advanced, and hence part of capital; therefore in
order to produce products of labour-value c+ℓ the labour-value of capital is c+v; if prices equal
labours embodied, then the difference between living labour and labour embodied in the wage
goods going to that living labour, ℓ–v, is also the difference between revenue c+ℓ and costs c+v [65]
and therefore it measures the firm’s profit. We indicate it with s.
Marx calls s surplus labour, or unpaid labour; and he calls v necessary labour. The reason
behind this terminology can be explained as follows. Assume there is no rent. If the socially
necessary living labour performed in the entire economy is L, and if the labour embodied in the
aggregate constant capital (assumed all circulating) is C, then the labour-value of the social product
is C+L, and the labour-value of the aggregate net product is again L, as we know. (This is a general
property of the labour embodied in a commodity or basket of commodities: it always indicates the
total labour employment in an economic system that produces a net product consisting of that
commodity or basket of commodities. We will confirm this fact mathematically in the next chapter.)
If V stands for the labour embodied in the portion of the aggregate net product that goes to labour,
then S≡L−V is the labour embodied in the physical surplus product, that is, it is the labour-value of
profits. With constant returns to scale, in order to produce a net product equal to the sole part going
to labour the several industries would have to shrink in size until labour employment becomes V
rather than L. For example, if the average length of the working day is 8 hours and if L/V=8/5, a
working day of 5 hours would suffice in order to produce (with the same number of workers) the
workers’ physical income as net product. It is the production of profits that makes it necessary to
work 8 rather than 5 hours. A worker can then be seen as working 5 hours for herself/himself, and 3
hours for the capitalist class; those 3 hours are a surplus-labour that produces the portion of the net
product appropriated as profits by the capitalist. It is the existence of this surplus-labour that permits
the existence of profits.
65
The costs coincide with the capital advanced because of our assumption that all capital other than
wage goods, i.e. all constant capital, consists of circulating capital goods. With durable capital goods this
would no longer be the case, but we postpone discussion of durable capital to chapter 2.
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Example: the corn economy; assume 0.2 units of seed-corn plus 1.6 labour hours produce 1
unit of corn, and the hourly real wage rate is 0.25 units of corn. The labour embodied in a unit of
corn, measured in hours, is determined by m = 0.2m+1.6, i.e. m=2. Suppose that this economy
produces every year 5000 units of corn; then L=8000, seed-corn employed every year is 1000 units,
net product is 4000 units of corn (its labour-value is 8000), of which 2000 units go to labour and
2000 are the surplus product. To produce a net product of only 200 units it would suffice to produce
a social product of only 2500 units, with the employment of only 4000 labour hours, therefore each
worker could work only half the time; Marx would say that, of the 8000 hours of labour performed
every year, only 4000 are necessary labour (i.e., necessary to the yearly production of the workers’
real wages), the remaining 4000 hours are surplus-labour that produces the yearly surplus product.
Surplus-labour is also called by Marx unpaid labour, in the sense that the labour embodied
in the wage goods equals only the necessary labour; for the hours of surplus-labour nothing is
received by the labourer in exchange.
Marx calls value of labour-power the labour embodied in the average subsistence goods per
unit of labour that workers get, and argues that this is the “cost of production” of labour-power. We
must spend a few words on this notion. Labour-power is the name Marx gives to the ability of
workers to perform labour services, an ability that can result in different amounts of labour services
(or labour effort), depending on the length of the working day and on work intensity (workpace).
Marx’s characterization of the real wage as the value i.e. “cost of production” of labour-power
allows him to distinguish the value of labour-power from the value created by the use of labourpower, i.e. by labour. Value creation depends on the amount of labour performed, which can vary
without variations in the value of labour-power. This allows Marx clarity on the effect on profits of
variations in the length of the workday or in workpace. In the numerical example just given,
assuming prices equal to labours embodied, suppose that on average a worker works 1000 hours a
year and receives corn of labour-value 500; the value of his labour-power is 500, the value he
creates is 1000. If the average length of the working day or average intensity of work were
increased 10% without changes in the yearly real wage, the value created would become 1100
without any change in the value of labour-power; profits would increase.
But the main reason why Marx insists that the wage is the value of labour-power and not of
labour is in order to avoid the more or less conscious tendency at the time to identify the wage as
value of labour with the value ‘produced’ by labour, and then to conclude that, since the value
‘produced’ by labour corresponds only to wages, land and capital ‘produce’ the remaining parts of
the product’s value, and therefore labour only has a right to commodities equal in value to the value
it produces, the contributions of land and capital having as well a right to receive as much value as
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they produced. This tendency was helped by the ‘vulgar’ interpretation of Adam Smith’s view of
prices as the sum of independently determined rates of wages, rents and profits, an approach that
suggested that (leaving land aside for simplicity) the passage from a situation of zero profits to one
with positive profits increases the value of the product. When as in Adam Smith’s “early and rude
state of society” labour is the sole cost and the labour theory of value holds, the value of a
commodity equals the value of the wages directly and indirectly paid for its production; more
labour produces additional value equal to the extra wages; it is then natural to view the value
produced by labour as equal to the wage. The same view is natural, in more advanced economies,
for the price of the products of independent labourers (for example whitewashers or laundresses)
where the excess of the price over the cost of the materials used up – the value added, in modern
parlance – is entirely labourer’s income, his/her wage (because the materials are advanced for a
very short time); it is then spontaneous to say that the product’s value is greater than the value of
the materials because to the latter value labour has added its own value, a value equal to the wage.
Now, the income of these independent labourers may well be equal to the wage of labour employed
by capitalists, and yet in the commodities produced with capital, since their value includes profits,
the value added v+s is greater than the wages v: room is thereby created for the claim that a
productive contribution of capital produces the remaining portion of the value of the product: this
was in fact the tendential conclusion of the writers that Marx called "vulgar economists" and
harshly criticized. Against this, Marx intended to stress that the reason for the existence of positive
total profits was the real wage lower than the maximum possible one, that is, the existence of
surplus labour, while the difference in the value of products using capital relative to products
produced by labour alone derived from the different organic composition of capital, that obliged the
total profits to distribute themselves among the several productive activities in proportion to the
capital used.
This critical-clarificatory role of the labour vs. labour-power distinction appears strictly
connected with the theoretical confusions of Marx’s time, which are no longer relevant nowadays,
because of the greater clarity achieved on the structure of the classical approach and on how to
surmount the limits of the labour theory of value, and because the forms taken nowadays by the
thesis that profits reflect a productive contribution of capital have abandoned the confusions of the
“vulgar economists”, and rest upon the marginal approach (as we will see in chapter 3). What
remains highly relevant is the difference between potential and actual labour ‘extracted’ from
workers, in other words, the fact that the amount of labour (or effort) performed in a certain time
period, say a year, can vary without variation of the yearly wage owing to changes in the workday
or in workpace caused by changes in labour’s bargaining power.
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Exercise: Assume corn is produced by seed-corn and labour on no-rent land; suppose the
length of the working day increases by 10% with no change in the daily real wage; the quantity of
seed and number of hours of labour per unit of output do not change. Show how this affects
technical coefficients, w, and Marx’s c+v+s. (What is more convenient as a measure of labour,
labour hours or labour days?)
1.9.2. The determination of the rate of profits
Let us now see how Marx uses these notions to determine the rate of profits. If we suppose
that prices and labours embodied coincide, and that all capital goods are circulating capital, then the
price p of a commodity can be represented as
[1.23] p = c+ℓ = c+v+s
where c, v, ℓ, s are the quantities of constant capital, variable capital, living labour and surplus
labour in the production of one unit of that commodity; the profit (revenue minus costs) is s, and the
rate of profits is (with advanced wages)
[1.24] r=s/(c+v).
Marx calls rate of surplus value or rate of exploitation the ratio s/v, which tends to be the
same in all industries because s/v = (ℓ–v)/v = (ℓ/v)–1: therefore s/v is uniform if ℓ/v is the same in
all firms, and this is the case because competition tends to make the hourly real wage rate the same
everywhere[66], therefore everywhere the ratio between living labour and labour embodied in the
wages will be the same[67].
66
Temporary differences among wage rates can be neglected for the determination of the normal
long-period relative prices and rate of profits; persistent differences are treated by Marx, like by Smith and
Ricardo before him, as allowing the ‘reduction’ of heterogeneous labour quantities to quantities of a common
type of labour (‘simple’ or ‘average’ labour) in proportion to relative labour-values of labour-power, which
means relative wages: “More complex labour counts only as intensified, or rather multiplied simple labour,
so that a smaller quantity of complex labour is considered equal to a larger quantity of simple labour”
(Capital I p. 135); “All labour of a higher, or more complicated, character than average labour is expenditure
of labour-power of a more costly kind, labour-power whose production has cost more time and labour than
unskilled or simple labour-power, and which therefore has a higher value. This power being of higher value,
it expresses itself in labour of a higher sort, and therefore becomes objectified, during an equal amount of
time, in proportionally higher values.” (Capital I p. 305).
67
For example, if in a firm, or industry, or economy, ℓ=10, then in that firm or industry or economy

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Marx calls organic composition of capital the ratio c/v between constant and variable
capital. Given the real wage basket, the organic composition depends on technology, and is high in
the industries where living labour is coupled with large fixed plants and machinery, low where
labour is coupled with few and cheap means of production; the organic composition of capital is far
from uniform. At prices proportional to labour-values the rate of profits earned by a firm depends
on the ratios s/v and c/v, i.e. on the rate of surplus value (rate of exploitation) and on the organic
composition, as we can see by dividing by v both numerator and denominator of s/(c+v) in equation
[1.24]:
s/v
[1.25]
r = ——— .
(c/v)+1
Therefore, since the numerator is the same in all industries, if commodities exchange in proportion
to labours embodied the rate of profits is the same in all industries only if one of the following
conditions holds:
1) s=0, in which case r=0;
2) the organic composition is the same in all industries.
Since neither of these conditions is generally satisfied, but the rate of profits is tendentially uniform,
Marx concludes that commodities cannot exchange at prices proportional to labours embodied. The
relative prices associated with a uniform rate of profits, that Marx calls prices of production, differ
from relative labour values.
Marx is thus able to extend to the general case, where advanced capital does not consist only
of wages, an understanding of why the tendency of profit rates towards uniformity causes relative
prices to deviate from relative labour-values. If prices were proportional to labour-values, the rate of
profits would be lower where the organic composition of capital is greater. At this point he too
adopts the idea of a compensation of deviations on average. The function of these deviations is,
according to Marx, to redistribute among the several industries the total social surplus value S, in
such a fashion that the surplus value, created in proportion to the variable capital in each industry,
is appropriated in proportion to the total capital of each industry and thus permits a uniform rate of
profits. Since this redistribution must be brought about by an increase in relative price (from a
starting point with prices proportional to labour-values) of the commmodities produced with a
v is the labour embodied in 10 average wage baskets. The ratio ℓ/v is always equal to the reciprocal of the
labour embodied in the average wage, or subsistence, basket. Formally: ℓ/v= ℓ/[(h1z1+h2z2)ℓ]=1/(h1z1+h2z ).
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higher-than-average organic composition of capital, and a decrease in price of the commodities with
a lower-than-average organic composition of capital, according to Marx these price variations will
compensate one another if one chooses as measure of value a commodity of average organic
composition. The natural measure of value is then the social product, since its organic composition
is by definition the average one. Therefore according to Marx the general rate of profits will be the
average one resulting from conceiving the whole economy as a single industry, that is (if all capital
is circulating):
[1.26]
r = S/(C+V) =[S/V] / [C/V + 1]
where C, V, S are, respectively, the total constant capital, total variable capital, and total surplus
value in the entire economy, as determined by labours embodied; this rate must then be applied to
the advanced capital of each industry to obtain the prices of production, which are the prices
corresponding to a uniform rate of profits and, resulting from a simple redistribution of labour value
across industries, are seen by Marx as ‘transformed’ labour values. (How to determine the prices of
production starting from labour values has accordingly been called in the Marxist literature the
‘transformation problem’.)
If the economy produces two goods, there is no joint production, all constant capital is
circulating capital, there is no rent, and we choose as unit for each good its total production, then
prices equal to labours embodied must obey the following equations:
[1.27] p1 = c1+ℓ1 = c1+v1+s1
[1.28] p2 = c2+ℓ2 = c2+v2+s2
Unless c1/v1=c2/v2, when s>0 relative prices determined in this way yield different rates of
profit in the two industries. Marx’s ‘transformation’ of labour values into prices of production can
be illustrated in terms of this economy as follows. He would determine the rate of profits as:
[1.29] r = S/(C+V) = (s1+s2)/(c1+v1+c2+v2)
and he then would determine the prices of production as
[1.30] p1 = (1+r)(c1+v1)
[1.31] p2 = (1+r)(c2+v2)
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where r has the value determined by equation [1.29].
Thus, in Marx, prices of production are ultimately determined by labour-values and are only
‘transformed’ (redistributed) labours embodied (note that, owing to how the ‘transformation’ is
performed, p1+p2=C+V+S: the exchange value of the social product equals its labour value).
According to Marx, the labour theory of value therefore yields, when applied to the whole
economy, the correct rate of profits and thus, although not correct as a theory of long-period relative
prices, it is the necessary basis for their determination.
In this way Marx is able to determine the rate of profits before relative prices, and thus to
escape the danger of circular reasoning that worried Ricardo, with significant analytical advances.
First, the presence of ‘constant’ capital is fully recognized. Second, a way is indicated to determine
uniform-rate-of-profit relative prices differing from relative labours embodied. Third, the
consideration of constant capital permits a richer understanding of the causes of changes in the rate
of profits. Ricardo saw only two such causes: changes in the real wage rate, and in the productivity
of labour (on no-rent land). Marx recognizes a third influence: the ratio of constant to variable
capital, C/V, or equivalently (given the rate of exploitation), the ratio of ‘dead’ to living labour C/L
= C/(V+S). Thus technical progress can influence the rate of profits also by affecting the
‘mechanization’ of production, the extent to which labour is replaced by machines: a theme that is
very important in Marx’s analysis of the secular tendencies of capitalist accumulation (see below).
The apparently aprioristic exposition of volume I of Capital, where the labour theory of
value is adopted as if indubitable[68], is therefore due to Marx’s earlier conclusion[69] that the
68
Modern readers have often been perplexed by the fact that in that first volume the passages,
interpretable as justifications of the thesis that exchange value is determined by labour embodied, consist
only of statements such as: “Let us now take two commodities, for example corn and iron. Whatever their
exchange relation may be, it can always be represented by an equation in which a given quantity of corn is
equated to some quantity of iron, for instance 1 quarter of corn = x cwt of iron. What does this equation
signify? it signifies that a common element of identical magnitude exists in two different things....This
common element cannot be a geometrical, physical, chemical or other natural property of commodities. Such
properties come into consideration only to the extent that they make the commodities useful, i.e. turn them
into use-values. But clearly, the exchange relation of commodities is characterized precisely by its
abstraction from their use-value... As use-values, commodities differ above all in quality, while as exchangevalues they can only differ in quantity, and therefore do not contain an atom of use-value. If then we
disregard the use-value of commodities, only one property remains, that of being products of labour... the
same kind of labour, human labour in the abstract. ... they are merely congealed quantities of homogeneous
human labour” (Capital, Vol. I, the Pelican Marx Library, Penguin and New Left Books 1976, pp. 127-8).
As a justification of the labour theory of value such a reasoning would be certainly unsatisfactory: other
properties too are shared by commodities, e.g. to have caused costs of production, or to have usefulness; that
a single thing is the cause of exchange value, and that this thing is ‘homogeneous human labour’, required
proof. But one must remember that in the 1860s, when Marx wrote most of Das Kapital, there was no
serious scientifically credible alternative to the labour theory of value (which was for example accepted in
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uniform rate of profits is the same as the average rate of profits obtained in the entire economy if
commodities exchanged at labour values, a conclusion which authorized him initially to assume
exchanges at labour-values − the assumption easiest to follow for his readers, given the general
acceptance of the labour theory of value in one form or another at the time − since it made no
difference for the problems discussed in that first volume: the origin of profit, the forces
determining wages, the importance and nature of technical progress, and the tendencies of capitalist
accumulation, were all issues for which what was important was the general rate of profits and the
forces tending to influence it, not the differences between labour values and prices of production.
1.9.3. A mistake in Marx’s determination of the rate of profits, and the correct equations.
But there is a mistake in Marx’s procedure. Since the rate of profits is a ratio between the
value of the vector of commodities constituting profits (the physical social surplus net of rents), and
the value of the vector of commodities constituting advanced capital, what is necessary in order for
equation [1.26] to determine the correct rate of profits is not that the value of the social product
remains unaltered when one passes from labour values to prices of production[70], but rather, that
the ratio between the value of the composite commodity ‘profits’ and the value of the composite
commodity ‘capital’ remains unaltered. Now, except in very special cases, the physical composition
of those two composite commodities will not be the same, and then their exchange ratio (which is
the rate of profits) will differ from the ratio between their labour values just like it differs for any
other couple of commodities. Equation [1.26] is mistaken, unless either the labour theory of value
John Stuart Mill’s Principles of Political Economy, the standard reference of the period), the tendency to
develop apologetic views of capitalism – against which Marx struggles – was clear but had not reached yet
any robust alternative theory of value. Therefore the most plausible interpretation is that with those
statements Marx was not trying to justify his thesis that “the value of a commodity is determined by the
quantity of labour expended to produce it” (ibid. p. 129) in opposition to different theories of value, he was
taking for granted in his readers an acceptance of that thesis, and was only trying to dispel the confusions of
use-value with exchange-value, and of concrete labour (that produces different use values) with abstract
labour (that produces exchange value), confusions that according to him had made it possible to criticize the
labour theory of value. That he assumed some acceptance of the labour theory of value on the reader’s part is
evident, for example, when he quotes with approval, in footnote 9 of chapter 1 of Capital vol. I, from an
anonymous predecessor of Adam Smith: “The value of them [the necessaries of life] when they are
exchanged the one for another, is regulated by the quantity of labour necessarily required, and commonly
taken in producing them” (Capital vol. I, Penguin, 1976, p. 129). And as remembered in the text, he thought
that the proof that behind exchange value there is embodied labour could be given.
69
The manuscripts from which, after Marx’s death, Engels put together the third volume of Das
Kapital were written around 1864-65, that is before the publication of volume I, and were in their turn based
on earlier manuscripts of the period 1861-63; the first statement of Marx’s ‘solution’ of the ‘transformation
problem’ is even earlier, it appears in the manuscript called Grundrisse (1858). A very recent more complete
edition of Marx’ manuscripts has shown that Marx returned to the issue in the 1870s, evidently conscious of
the incomplete nature of his ‘solution’, but without being able to make progress.
70
This can always be obtained by an opportune choice of units.
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holds, or the physical surplus vector (net of rent goods) and the physical capital vector have exactly
the same composition.
However, contrary to some interpretations, this mistake of Marx was not due to an
aprioristic desire to show that profits are nothing but exploited labour. Marx’s ‘redistribution’ idea
should be considered an inevitable product of the state of analytical development of the times, as
shown not only by its affinity with Ricardo’s, Mill’s and McCulloch’s ‘compensation of deviations’
but also by the fact that when, in 1884, Friedrich Engels, in his Preface to volume II of Capital,
challenged other economists to discover how to ‘transform’ labour-values into prices of production
before the publication of volume III of Capital (which came out in 1894), all those (Lexis, Fireman
and Schmidt) who accepted the challenge developed that same idea (cf. Howard and King, 1989:
ch. 2; Desai, 1991). Still, Marx was one step ahead of the others, and only one step away from the
correct solution, because, when he described his ‘redistribution’ idea in volume III of Capital
through a numerical example, he admitted that his procedure was defective because he was pricing
the goods included in the constant and variable capital at their labour-values (cf. equations 1.30 and
1.31), while in fact they should be priced at their prices of production: a correction which, when
thoroughly performed, brings one to the correct equations, as we will show presently.
What Marx did not notice (nor did anyone else in his own times: the first one to notice it
appears to have been Tugan-Baranovsky in 1905??REF) is that he had then no right to assume that
in the aggregate the ratio between profits and capital would be the same as if commodities
exchanged at labour-values: if in general commodities do not exchange according to labour-values,
there is no reason why that should be true for the two different composite commodities constituting
the total physical profits, and the total physical advanced capital. So Marx’s formula [1.26] is in
general incorrect.
However, the recent advances in the theory of prices of production have shown that Marx
was correct in this sense: the data − technical conditions of production, quantities produced, and
wage basket − from which he (and Ricardo) attempted to determine the rate of profits passing
through the labour theory of value, are in fact sufficient directly to determine the rate of profits.
We can show this by performing the correction that Marx indicated as necessary but did not
implement. Since the different commodities entering costant capital and wages must each be priced
at its price of production, we must now indicate explicitly these commodities. In order to maintain
the analysis simple, let us again assume that the economy produces corn and iron by using corn,
iron and labour, as in equations [1.4-1.7], and let us assume that real wages are advanced and
consist of corn only, and precisely of a subsistence z1 per unit of labour. Now we modify equations
[1.6-1.7] by introducing the rate of profits, and we obtain
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[1.32] p1 = (1+r)[(z1aL1+a11)p1 + a21p2]
[1.33] p2 = (1+r)[(z1aL2+ a12)p1 + a22p2].
These are two equations in three variables; but they can only determine the ratio between
the prices p1 and p2, because if satisfied by a triplet (p1, p2, r), they continue to be satisfied if p1 and
p2 (not r!) are multiplied by the same scalar; so we can arbitrarily choose a numéraire, e.g. p1=1,
and then we have two equations in the two variables r and p2/p1. This equality between number of
equations and of variables is of course not sufficient to ensure that the solution is economically
acceptable, i.e. real and with non-negative prices. But it can be demonstrated (cf. next chapter) that,
as long as the economy is capable of producing a positive surplus, this system of equations has one
and only one economically significant solution, with positive values both for r and for p2/p1. What
is now relevant is that the rate of profits is determined by these two equations; therefore it cannot be
determined by a separate equation such as [1.26].
It is useful to grasp how these equations determine the rate of profits. If we re-write these
equations as follows we realize that if r is treated as a given real scalar, then this is a system of two
equations linear and homogeneous in the two prices:
[1.34]
[1−(1+r)(z1aL1+a11)]·p1
–
[1.35]
−(1+r) (z1aL2+ a12) ·p1
+ [1−(1+r)a22]·p2 = 0.
(1+r) a21
·p2
=0
Now, a homogeneous linear system with as many equations as variables has non-zero
solutions if and only if the determinant of the matrix of coefficients is zero. The rate of profits,
which enters those coefficients, is therefore determined by the condition that it must render zero that
determinant. In the present case this condition yields a second-degree equation[71], which has two
solutions, which might also be complex, but it can be proved (see next chapter) that one and only
one of these solutions (associated with the smallest value of r in module) is real and economically
significant (because associated with positive prices). Thus the mathematics confirms that Ricardo
and Marx were not wrong in sensing that the rate of profits could be determined before relative
prices: the rate of profits is determined by the condition that a certain determinant be zero, a
The equation is [1−(1+r)(z1aL1+a11)]·[1−(1+r)a22] − (1+r) a21·(1+r) (z1aL2+ a12) = 0. With more than
two commodities, the equation quickly becomes enormously cumbersome, and above all the properties of the
solution remain opaque; but luckily matrix algebra allows a much more concise and enlightening analysis, as
we will see in chapter 2.
71
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condition in which prices do not appear. (Another way to determine the rate of profits before
relative prices, based on Sraffa’s notion of standard commodity, will be illustrated later.)
The generalization to more than two industries is immediate. If (still without joint
production and without rent) the economy produces n different commodities, it suffices to know the
technical coefficients aij (where i=1,...,n,L indicates inputs; j=1,...,n indicates the product) and to
know the vector representing the average physical wage basket or anyway the basket in terms of
which the real wage rate is fixed[72], (z1,...,zn), and one can write the following equation for each ith price:
[1.36]
pi = (1+r)[a1ip1+a2ip2+...+anipn+(z1p1+z2p2+...+znpn)aLi], i=1,...,n.
With n commodities one obtains a system of n equations in the n+1 variables p1,...,pn,r, and
the system will determine relative prices and the rate of profits. The danger of circular reasoning
due to a rate of profits depending on relative prices which depend on the rate of profits comes out
not to exist.
1.9.4. Luxury goods and the rate of profits
The correct equations show that Marx’s approach to the determination of the rate of profits,
embodied in equation [1.26], causes him to be mistaken on an issue where, on the contrary, Ricardo
was right. Ricardo, on the basis of the insights reached through the ‘corn model’, argued that, given
the real wage rate, the rate of profits depends only on the conditions of production of the
commodities entering the real wage basket or directly or indirectly required for their production.
The other commodities, Ricardo argued, are in the situation of the non-corn commodities in the
‘corn model’: their prices must passively adapt so as to yield the same rate of profits as the one
determined in the industries directly or indirectly producing the real wage. Marx, on the contrary,
was induced by his approach to argue that the conditions of production of all commodities were
relevant, because all contributed to determine the average organic composition of capital, and all
took part in the redistribution of surplus value that caused labour values to be ‘transformed’ into
prices of production. But Ricardo was right and Marx wrong. Thus suppose that, besides corn and
iron, the economy produces a third commodity, say, diamonds, which enters neither the constant
nor the variable capital of the other two industries. The price p3 of diamonds (we treat diamonds as
commodity 3) is then determined by adding to equations [1.32-1.33] the following equation:
72
Once the real wage rate is fixed in terms of some good or composite basket of goods, then relative
prices and the rate of profits are determined independently of how wages are actually spent.
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[1.37] p3 = (1+r)[(z1aL3+a13)p1 + a23p2].
Since equations [1.32-1.33] have remained unaltered, they suffice to determine the rate of
profits; equation [1.37] has the sole role of determining p3 such as to yield the already determined
rate of profits[73]. (The real wage here consists only of corn, but the conditions of production of iron
are relevant for the determination of the rate of profits because iron enters the production of corn as
a means of production.)
The conclusion can be generalized to the case in which diamonds use for their production
some commodities whose prices do not enter the costs of the industries directly or indirectly
producing the wage goods. The ensemble of the industries whose products neither directly nor
indirectly enter the production of wage goods can be called ‘non-wage industries’, the other ones
can be called ‘wage-industries’. For example, the means of production of diamonds might include
diamonds, and a fourth commodity used only for the production of diamonds and including itself
and diamonds among its means of production. Let this commodity, e.g. a special steel used only for
cutting diamonds, be commodity 4. We must now modify equation [1.37] by assuming that a 33>0
and a43>0 and therefore that p3 and p4 enter the costs of producing diamonds. And obviously we
must add the equation determining p4. The complete system of price equations now includes,
besides equations [1.32-1.33], the following equations:
[1.38] p3 = (1+r)[(z1aL3+a13)p1 + a23p2+a33p3+a43p4]
[1.39] p4 = (1+r)[(z1aL4+a14)p1 + a24p2+a34p3+a44p4].
Equations [1.32-1.33] are still unaltered and suffice therefore to determine the rate of profits;
equations [1.38-1.39] only have the role of determining the prices of diamonds and steel relative to
corn or iron, so as to yield the rate of profits determined by the first two equations. A change in the
technical coefficients of the last two equations, differently from a change in the technical
coefficients of the first two equations, does not change the rate of profits, it only affects the prices
of the products of the non-wage industries[74].
73
If one chooses diamonds as numéraire, i.e. if one puts p3=1, this makes the three equations
interdependent, but only for the determination of the values of p1 and p2 in terms of diamonds; equations
[1.32-1.33] still autonomously determine r, and p2/p1.
74
This result indicates an easy way to prove that Marx’s equation [1.26] cannot be correct. A change
in the technical coefficients of non-wage industries that alters the labours embodied in non-wage
commodities will generally alter the ratio in equation [1.26], altering therefore the rate of profits as
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1.9.5. The inverse relation between real wage rate and rate of profits
We show now that the correct price equations confirm that the real wage rate measured in
terms of any one commodity, and the rate of profits, are tied by a relationship such that if one
increases the other decreases; Marx’s stress on the inevitable clash of interests between wage labour
and capital is confirmed. Let us re-write equations [1.32-1.33] so that on their right-hand side the
wage payments appear separately:
[1.40]
p1 = (1+r)waL1 + (1+r)(p1a11 + p2a21)
[1.41]
p2 = (1+r)waL2 + (1+r)(p1a12 + p2a22)
In order to render these equations determinate we should of course choose a numéraire and
then either take r as given, or fix the real wage rate e.g. by adding, with z 1 and z2 given[75], an
equation such as:
[1.42]
w=p1z1+p2z2.
But now we are interested in the effects of changes of r on the real wage rate or vice-versa,
therefore we do not add equation [1.42]. Let us choose the wage rate as numéraire, i.e. let us divide
both sides of equations [1.40-1.41] by w so that we obtain w=1. Let us indicate as p’1 and p’2 the
prices p1/w and p2/w. The prices p’1 and p’2 thus obtained measure what Adam Smith called the
labour commanded by each commodity, i.e. the amount of labour services that one can purchase
(i.e. command, have at one’s orders) with a unit of the commodity; their reciprocals, 1/p’1 and 1/p’2,
measure the real wage rate, i.e. the purchasing power of the nominal wage rate, respectively in
terms of commodity 1 and of commodity 2. Note that if no other condition (such as, say, p’1 = 10, or
determined by Marx, while in fact the rate of profits does not vary. Since we are at it, we can point out the
mistake of Marx’s procedure in still another way, applicable even when there are no non-wage industries.
The ratio in equation [1.26] depends, among other things, on the relative dimension of industries: if with
unchanged technical coefficients an industry with a higher-than-average organic composition of capital
expands, this raises the average organic composition and Marx’s equation indicates a decrease of the rate of
profits, while in fact the rate of profits does not change because it only depends on the (real-wage-inclusive)
technical coefficients.
75
This may be the place to note that an equation such as [1.42] need not be interpreted as meaning
that workers actually purchase quantities z1 and z2 of the two goods; all that this equation means is that the
purchasing power of the wage must enable the workers to purchase such quantities, they can well decide to
spend their wage differently. Thus, once a numéraire is chosen, w can also be fixed by setting it equal to a
given scalar, e.g. w=100 will mean that the money wage rate must suffice to purchase 100 units of the
numéraire commodity.
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r = 10%, or equation [1.42] now to be written as p’1z1+p’2z2=1) is added, income distribution is not
determined yet by setting w=1. For example in the economy that produces only corn by using seedcorn and labour, the price equation is p1=(1+r)waL1+(1+r)p1a11 and if we simply put w=1 the
equation still has two variables, p’1=(1+r)aL1+(1+r)p’1a11, hence the real wage rate 1/p’1 is not
determined yet, and is a function of r because, as r changes, p’1 and hence 1/p’1 changes too.
Having only set w=1 equations [1.40-1.41] become:
[1.43]
p’1 = (1+r)aL1 + (1+r)(p’1a11 + p’2a21)
[1.44]
p’2 = (1+r)aL2 + (1+r)(p’1a12 + p’2a22).
Now in the right-hand side of equation [1.43] let us replace p’1 and p’2 with the
corresponding right-hand sides of equations [1.43-1.44]. We obtain:
[1.45] p’1 = (1+r)aL1+(1+r){(1+r)(p’1a11+p’2a21+aL1)a11+(1+r)(p’1a12+p’2a22+aL2)a21}=
=[(1+r)aL1+(1+r)2(aL1a11+aL2a21)] + {(1+r)2[p’1(a112+a12a21)+p’2(a11a21+a21a22)]}.
The last expression shows the cost of production of commodity 1 as the sum of two
components: no price appears in the first term in square brackets, the cost of direct labour plus the
cost of the labour employed one period earlier to produce the direct inputs of corn and iron; prices
appear only in the second component, which is the cost of the corn and of the iron that have
produced the direct inputs of corn and iron. Operating the same replacement on the prices that
appear in this second component, and then replicating the operation again and again, we can
decompose the cost-of-production of corn into an infinite series of smaller and smaller quantities of
‘dated’ labour (direct living labour; labour employed to produce the direct means of production;
labour employed to produce the means of production of the direct means of production; and so on),
each one multiplied by (1+r)n where n indicates how many periods earlier that quantity of labour
was paid. If we write L-1, L-2, L-3 etc. for these ‘dated’ quantities of labour (e.g. L-1=aL1, L-2=
aL1a11+aL2a21), we can re-write equation [1.43] as
[1.46] p’1 = (1+r)L-1+(1+r)2L-2+(1+r)3L-3+....+(1+r)nL-n+....
where the sole variable on the right-hand side is the rate of profits[76]. It is now clear that if r
increases, p’1 increases because all terms on the right-hand side increase. But an increase of p’1
means a decrease of 1/p’1 i.e. of w/p1, i.e. a decrease of the purchasing power of the wage rate in
terms of commodity 1. Exactly the same procedure would show that the same is true for p’2. This
shows that when r rises, the purchasing power of w decreases in terms of both commodities
(although generally not in the same percentage, because p2/p1 changes). As will be shown in chapter
2, the proof is generalizable to n>2 commodities. This shows that when r rises, the real wage rate
76
In the next chapter we prove that the series on the right-hand side of equation [1.46] is indeed
convergent.
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decreases in terms of any (simple or composite) commodity.
1.10. THE DETERMINANTS OF THE RATE OF PROFITS, THE STANDARD
COMMODITY, AND THE MARXIST TRADITION.
1.10.1. The rate of profits depends only on physical inputs
The results we have reached show that the data needed for the determination of rate of
profits and relative prices are physical quantities: the technical coefficients of production and the
real (i.e. physically specified) wage vector; there is no need for labours embodied. Furthermore,
Marx’s formula [1.26] is incorrect; his use of the labour theory of value for the determination of rate
of profits and prices of production must therefore be rejected in favour of the approach expressed by
equations [1.32]-[1.33] or [1.36].
What are the consequences for the surplus approach?
The magnitudes appearing in equation [1.26] are derived from the technical conditions of
production and the real wage rate: labour values derive from the technical conditions of production,
and the division of the working day into a paid and an unpaid part derives from the given real
wage[77]. Thus the data, which permit the correct determination of the rate of profits, are precisely
the same data from which Marx and Ricardo implicitly start in order to determine the rate of
profits: it is only the recourse to labour values as an intermediate step in that determination (on the
basis of the idea of a compensation of the deviations in the aggregate), that comes out to be
mistaken. Ricardo’s and Marx’s persuasion, that the rate of profits is determined once the real wage
and the technical conditions of production are given[78], is fully confirmed. The exclusion of a role
of Adam Smith’s competition of capitals in the determination of the rate of profits is confirmed.
The “inverse relation” between rate of profit and real wage is also confirmed, as well as the
negative influence on the rate of profits of extensions of cultivation to inferior land if the real wage
does not decrease. Thus we can view the recourse to labour values as only an imperfect
approximation in Ricardo, an imperfect algorithm in Marx, for reaching conclusions that now we
can confirm with better instruments. Therefore the abandonment, in the sense specified, of the
77
A third group of data of the determination of the rate of profits, the quantities produced, influences
the technical conditions of production, in so far as they determine the no-rent land and therefore the technical
conditions to be considered in determining the rate of profits. Thus if in the data one includes, not the
technical conditions on no-rent land, but all available technical conditions, then the data necessary for the
determination of the rate of profits also include the quantities produced.
78
In fact the relevant technical conditions of production are only those of the wage-goods industries,
so on this Marx was mistaken as shown in §1.9.4, but this mistake does not involve the validity of the entire
approach, and was indeed avoided by Ricardo.
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labour theory of value is no reason for crisis of the surplus approach, which on the contrary is
strengthened by the proof that Ricardo’s and Marx’s basic insights were correct.
An important implication is the following. A number of marginalist authors (Böhm-Bawerk,
Wicksteed, Pareto) argued that Marx’s entire approach (and thus his claim that profits reflect labour
exploitation) was fatally flawed owing to the deficiencies of the labour theory of value as a theory
of relative prices; but they were wrong. The surplus approach does not fall with the deficiencies of
the labour theory of value; it is capable of satisfactorily determining rate of profits and prices.
1.10.2. The roles of the labour theory of value in Marx
The thesis that the labour theory of value can be dropped without consequences for Marx’s
overall approach − a thesis that derives from viewing that theory as only the provisional way out of
an analytical difficulty (the need to overcome the apparent danger of circular reasoning, deriving
from the reciprocal dependence of the rate of profits on relative price and of relative prices on the
rate of profits) that Ricardo and Marx were unable to surmount in other ways because lacking the
analytical instruments − has been disputed by many Marxist economists. According to them,
Marx’s conception of exchange values as ultimately quantities of labour (albeit ‘transformed’) is
essential to Marx’s characterization of capitalism. We must therefore discuss what is lost of Marx’s
analyses if one abandons that conception of exchange values.
The Marxist tradition has tended to attribute two main roles to such a conception of
exchange values. The first one is to unmask the alienated and fetishistic aspect of social relations in
market economies (important names here are Hilferding, Rubin, Sweezy: cf. Howard and King,
1989-92, vol. I, ch. 3 and vol. II, chs 12 and 17; also Vianello, 1987), to show that the worker’s
labour gets alienated from him/her and that commodities acquire fetishistic characteristics: the
worker’s labour is not controlled by the labourer but by the capitalist, so it is no longer an
expression of his personality but rather serves interests external to the worker; its result, the value
created by a certain amount of labour, is nothing but that amount of labour itself, now crystallized
in the commodities it has produced: but it now stands in front of the worker as an alien thing,
outside his control and endowed with a social recognition and power − the power to exchange with
other things, and to command more labour than it was necessary to produce it − whose social origin
becomes almost impossible to grasp, because resulting from nobody’s conscious action, so that
commodities appear to possess as natural qualities what in fact derives from the social structure. In
this role, the labour theory of value is seen as going beyond appearances, bringing out the
subjugated, oppressed, alienated nature of the condition of the true producers under capitalism
while at the same time explaining why it is difficult spontaneously to grasp it.
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The second role is is to prove that labour is exploited, by showing that, since value is
produced by labour alone, capital does not contribute to the production of value, and therefore the
part of value that constitutes profits does not result from a contribution of capital, has been
produced by surplus labour, and is expropriated owing solely to the greater bargaining power of
capitalists.
A number of Marxists have been greatly worried about the deficiencies discovered in
Marx’s determination of values, and have feared that both exploitation and alienation thereby
become doubtful. The better understanding reached in recent decades of the strict analytical
continuity between Ricardo and Marx suggests that these worries have no foundation, and derive
from the mistaken attribution to the labour theory of value of roles that in fact it did not have in
Marx: as we argue below, the possibility to argue that labour is exploited and alienated rests rather
on the correctness of the overall surplus approach.
The analytical continuity between Ricardo and Marx is shown by Marx’s adoption and
development of the idea of a compensation of deviations which, we have seen, is already in
Ricardo. Marx accepts and develops Ricardo’s approach because he thinks it is the correct approach
to a determination of the rate of profits and relative prices, overcoming the apparent circularity of a
rate of profits dependent on relative prices in turn dependent on the rate of profits. Labour values
plus the idea of a compensation of deviations are the way through which Ricardo and Marx reach
the conclusion that the rate of profits is determined once the production conditions and the real
wage rate are given, and that the rate of profits decreases if the real wage increases, highlighting an
inevitable conflict of interests between wage labour and capital.
Further support for this view of the role of labour values derives from the (seldom noticed)
fact that it would be otherwise difficult to understand why labour values are defined by Ricardo and
by Marx as
-
reflecting only the socially necessary labour[79],
-
based on the production conditions on no-rent land, and
-
based on ‘reducing’ heterogeneous labour to ‘simple’ labour in proportion to wages.
These analytical choices are necessary in order to argue that the labour theory of value
would be the correct theory of relative prices if the rate of profits were zero or if the organic
composition of capital were uniform, thus preparing the ground for the ‘compensation of
deviations’ argument; otherwise they are not easily explained, and in fact, without the analytical
79
That is to say, the labour that is necessary assuming that firms produce efficiently and produce the
effectual demands of the several goods, and not the labour actually employed, which may reflect
inefficiencies or outdated technologies, or mistaken quantities produced.
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aim of determining the rate of profits, the notion of labour embodied would lose all definiteness: for
example, why not include in the amount of labour performed the transport time from home to the
workplace?[80]; or, how should one ‘reduce’ heterogeneous labour to homogeneity, for example,
how should one decide when the workpace in two different occupations is to be considered
equivalent?[81]
The labour theory of value appears to have been no more than the admittedly imperfect
analytical tool (but the only one concretely available at the time[82]) through which Ricardo and
Marx could overcome the difficulty, arising within the surplus approach, of an apparently circular
determination of the rate of profits. Now that we have better analytical tools to overcome that
difficulty, labour values are no longer necessary for the study of relative prices and of the
dependence of the rate of profits on technology and on the real wage. But the use of physical
technical coefficients in equations such as [1.32-1.33] or [1.36] means no loss on the issues of
alienation and fetishism, nor on the issue of exploitation, as I now proceed to argue.
80
Note that sometimes this transport cost does enter production costs (e.g. when the firm itself runs
the buses taking the workers to the factory), and at other times it is left for the workers to bear. If the aim of
the analysis is not to explain normal relative prices, when to include the transport costs of workers into
necessary costs will have to be decided anew.
81
Suppose that two commodities A and B are each produced by one unit of labour and no other
input, but by different types of labour, α and β, with different wages. In both industries wages are advanced
for one period, and the rate of profits is the same. If the wage rate of type-α labour is twice the wage rate of
type-β labour, it is pA=2pB, and this can be made to agree with a labour theory of value only if one unit of
type-α labour is assumed to produce twice as much value as one unit of type-β labour. This has the curious
consequence, not often stressed, that labour-values depend on the relative bargaining power of different
types of labour, and change if relative wages change. Thus, suppose two types of labour, ‘simple’ and
‘complex’ labour, and a ‘reduction’ of complex to simple labour; then if the sole real wage of complex
labour rises, with no change in technical coefficients nor in quantities produced, the result is that the labourvalue of the social product rises, rendering the effect on the rate of profits less clear. (An implication of this
‘reduction’ is that for all wage labour, however differently paid, the ‘unpaid’ portion of the working day is
the same, from which it is easy to slide into an argument that all workers are equally exploited, with potential
political overtones of acceptance of wage differences that may be deeply unjust.) Heterogeneous labour also
creates additional complications for the ‘transformation problem’: for given average real wage baskets of
different labour-powers, relative wages will differ depending on whether measured at labour values or at
prices of production (unless the composition of all wage baskets is the same, an implausible assumption): a
correct determination of prices of production requires relative wages calculated at prices of production, but
Marx can only perform the ‘reduction’ on the basis of labours embodied, an additional difficulty for the
‘transformation’ of labour values into prices of production. All these difficulties disappear with Sraffa-type
equations where each type of labour is treated as a different input with its own technical coefficients, and
with either its wage rate in terms of the chosen numéraire, or its physically specified real wage vector. (If it
is the rate of profits that is taken as given, then one must specify relative wages in terms of the numéraire.)
82
It will be necessary to wait until the very last years of the 19th century and the first years of the
20th century to have the first significant advances relative to Marx on the issue of the determination of the
rate of profits within the surplus approach, with the Russian economists Dmitriev and Tugan-Baranowski,
and then the Russian-German economist and statistician von Bortkiewicz. The mathematical tools required
for a rigorous analysis of the problem were discovered by economists only much later, in the 1940s and
1950s (some of these tools, such as the Perron-Frobenius theorems on non-negative matrices, had been
developed by mathematicians much earlier but remained long unnoticed by economists).
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1.10.3. Fetishism and alienation.
The discussion of fetishism in Marx aims at demonstrating that the form of commodity
assumed by use-values in capitalism, and the exchange value of commodities, “is nothing but the
definite social relation between men themselves which assumes here, for them, the fantastic form of
a relation between things” (Capital I p. 165): in other words, men tend to treat the fact that physical
objects have exchange values, and the relative exchange values themselves, as intrinsic, natural
properties of these objects, without realizing the historical specificity of the social structure that
turns use values into commodities, and the complex social processes determining these exchange
values as unintentional results of individual decisions. Gold, for example, has a high exchange
value not because of some intrinsic quality but because of the role society attributes to it. And the
capacity of land to yield a rent, that appeared to the Physiocrats to reflect natural powers of land, is
on the contrary due to the tendency to a uniform profit rate and thus to the historically specific
social structure that causes that tendency to exist.
It is only because Marx sees exchange values as (redistributed) labours embodied, that he
characterizes the social process determining exchange values in these terms: “The equality of the
kinds of human labour takes on a physical form in the equal objectivity of the products of labour as
values; the measure of the expenditure of human labour-power by its duration takes on the form of
the magnitude of the value of the products of labour” (Capital I p. 164). The more fundamental
argument of Marx – the stress on the historical specificity of the commodity form, and on the
anonymous character of the social processes determining exchange values, processes that result
from the decisions of individuals but dominate the individuals and bring to results that no one
consciously wanted, and are therefore opaque – is independent of his view of exchange values as
ultimately labour values. Exchange values as determined by the correct price equations still result
from a historically specific social organization that produces social processes that are felt by
individuals as external forces that completely dominate them.
Nor do the correct price equations deny the condition of subjugation and alienation of
workers, in the concrete labour conditions, in the determination of wages, and more generally in the
running of capitalist society. There is no necessity that exchange value should be ‘congealed’ labour
time in order to state that
the worker always leaves the process in the same state as he entered it – a personal source
of wealth, but deprived of any means of making that wealth a reality for himself. Since,
before he enters the process, his own labour has already been alienated from him,
appropriated by the capitalist, and incorporated with capital, it now, in the course of the
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process, constantly objectifies itself so that it becomes a product alien to him. Since the
process of production is also the process of the consumption of labour-power by the
capitalist, the worker's product is not only constantly converted into commodities, but also
into capital, i.e. into value that sucks up the worker's value-creating power, means of
subsistence that actually purchase humain beings, and means of production that employ the
people who are doing the producing. Therefore the worker himself constantly produces
objective wealth, in the form of capital, an alien power that dominates and exploits him;
and the capitalist just as constantly produces labour-power, in the form of a subjective
source of wealth which is abstract, exists merely in the physical body of the worker, and is
separated from its own means of objectification and realization; in short, the capitalist
produces the worker as a wage-labourer. (Capital I, p. 716)
nor in order to state
that within the capitalist system all methods for raising the social productivity of labour are
put into effect at the cost of the individual worker; that all means for the development of
production undergo a dialectical inversion so that they become means of domination and
exploitation of the producers; they distort the worker into a fragment of a man, they
destroy the actual content of his labour by turning it into a torment; they alienate from him
the intellectual potentialities of the labour process in the same proportion as science is
incorporated in it as an independent power; they deform the conditions under which he
works, subject him during the labour process to a despotism the more hateful for its
meanness; they transform his life-time into working-time, and drag his wife and child
beneath the wheels of the juggernaut of capital. (Capital I, p. 799)
1.10.4. Exploitation, the automated economy, the standard commodity.
Let us come to exploitation. Here the worries of Marxist economists derive from the belief
that if it is not possible to prove that the exchange value appropriated by the capitalists as profits is
created by surplus labour and by it alone, then it is no longer clear that the existence of profits only
reflects the exploitation of labour and not a contribution of capitalists to value. The worries derive
from the discovery that in general Marx’s equation [1.26] does not correctly determine the rate of
profits: this means that, if – on the basis of the thesis that all value is created by labour – through an
opportune choice of units one renders the total exchange value of the social product equal to the
labour embodied in it[83], then the labour embodied in the goods appropriated as profits will not
83
This can always be achieved by an opportune choice of units for exchange value and for labour
embodied. For example if one chooses as numéraire the social product itself, then its exchange value is 1; if
one chooses as labour unit the amount of labour embodied in the social product, then the labour embodied in
the social product is 1, the same as its exchange value. This equality of course has no relevance for the

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generally equal the exchange value of those goods. Hence the thesis that exchange value is
produced by (and hence equal to) labour, and the thesis that the exchange value of profits is
produced by (and hence equal to) surplus labour, cannot be simultaneously held.
But the reasoning, from which such worries arise, confuses ‘contribution to production’, and
‘cause of relative exchange values’ – a confusion largely due to the influence of the marginal
approach, where the two are intimately linked. As we will see in chapter 3, in the marginal approach
the relative value of goods reflects their cost of production, which derives from the quantities of the
several factors required for their production, and from the prices of these factors, prices that – being
equal to the marginal value products of the factors – reflect the contributions of the factors to the
production of social utility, and therefore reflect what these factors deserve to be paid. In such a
perspective, if value derives solely from labour it must mean that the other factors give no
contribution to social utility (their marginal product is zero) and therefore deserve nothing, labour
deserves to receive all the value of the products, and if it does not receive it, then part of the value
of the products is being undeservedly appropriated by others and labour can be described as
exploited. But such a perspective is strictly connected with the marginal approach, and stands or
falls with it. (This is why we will have to discuss whether the marginal approach is or not
scientifically more convincing than the surplus approach.) Since the surplus approach is different,
and its theory of income distribution is different, the question we must discuss now is not, whether
labour is exploited if the marginal theory of income distribution is correct, but rather: does the
deficiency of Marx’s equation [1.26] undermine the view of the origin of profits derivable from the
overall surplus approach and in particular from its theory of wages? The answer is a clear no, as
shown by the following considerations.
Why do we speak of exploitation of slaves, or of feudal serfs? Because another class takes
away part of their product owing solely to its superior force. But then tracing the origin of profits to
the exploitation of labour does not need the labour theory of value to be confirmed: what it needs is
the correctness of the classical approach to wages, which sees the positivity of profits as due simply
to the power, given to the owners of the means of production by the institutional structure of
capitalism, to appropriate part of labour’s product, by virtue of their collective monopoly of the prerequisites for production (capital goods): a view that makes it possible to retort against the
bourgeoisie itself the accusation, moved by the bourgeoisie against feudal lords, that the latters’
theory of what determines exchange value, relative prices, or the rate of profits, because it can be obtained
whatever the explanation of those variables. Otherwise, since one could, by an opportune choice of the unit
for measuring distances, make the distance from the Earth to the Moon coincide with the population of New
York City, one would be authorized to conclude that the population of New York City is the cause of the
distance of the Moon from the Earth - or the opposite.
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revenue was the fruit of exploitation, being due to their monopoly of land which obliged the serfs to
accept performing corvées in order to be granted the possibility to produce for themselves and thus
to survive.
Obviously, in order to be acceptable, such a view of income distribution must be shown to
be consistent with a satisfactory determination of relative prices and of the rate of profits; and
precisely the deficiencies of Ricardo’s and Marx’s solution of this problem made it possible for
subsequent economists to criticize the entire surplus approach and thus that view of distribution too,
and to argue for the superiority of their different explanation of value and of income distribution,
the marginal one. But since those deficiencies can be overcome, the surplus approach’s view of the
origin of profits does not depend on the labour theory of value, it only depends on the explanation
of the existence of a surplus appropriated as profits.
The thing can be made clearer with the help of the following hypothetical example. Let us
imagine a small nation, a Proudhonian competitive market economy where all firms are cooperatives, and there is no rate of profits nor rate of interest. Prices are proportional to labours
embodied, ‘reduced’ to simple labour on the basis of given relative wages (determined by social
conventions). Then this nation is conquered by an invader people, who imposes on the basis of its
military domination that each firm must pay each year to the invaders’ army a tax proportional to
the value of its capital advances, at a real rate r. This tax is a pure tribute, but it functions like a rate
of profits, prices must cover it besides the other costs, and prices then gravitate toward the same
relative prices of production as if there were a rate of profits equal to r. Clearly the changes in
relative prices due to the appearance of the (1+r) term in the costs cannot be viewed as proof of a
contribution of the invaders to production. The positivity of r is due solely to the capacity of the
invaders to compress the real incomes of producers, i.e. the real wages, below the previous levels,
and the changes in relative prices are only due to the need to pay a tax proportional to capital
advances. Now, according to the surplus approach, as evidenced already by Smith much before
Marx, the positivity of the rate of profits in capitalist economies has the same basic cause as the
positivity of the tax in our hypothetical example: it reflects the capacity of the social group that
appropriates the profits to compress real wages below their potential maximum[84]. If one finds it
reasonable to describe the income of the invaders in this example as the fruit of the exploitation of
the labour of the local inhabitants, and if one finds the classical theory of wages convincing, then
one must also describe profits in capitalist society as the fruit of the exploitation of wage labour.
On this basis, the question whether it is useful, or possible, to conceive exchange value not
84
Or to oblige workers to work more hours (or more intensely) for the same real daily wage, thus
again reducing the real wage per unit of effective amount of labour performed.
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as a ratio (the ratio at which two commodities exchange) but rather as a substance, a quantity,
produced by labour, can now be discussed without the tensions connected with fears for the
tenability of the view of labour as exploited[85]. Certainly this conception of exchange value as a
quantity of labour encounters a serious difficulty: the direct determinants of normal prices and of
the rate of profits are only physical quantities of commodities, and prices and the rate of profits
would remain determinable even if there were no labour behind these quantities of commodities, as
in a hypothetical completely automated economy. To see this point with the utmost clarity, assume
advanced wages and define subsistence-inclusive technical coefficients cij (i input, j output) as
follows: in an economy where there are n commodities, if the average real wage rate physically
specified consists of the vector (z1, z2, ..., zn), then
cij ≡ aij+ziaLj.
Then the price equations can be written without any explicit appearance of labour quantities,
by using the coefficients cij. For example, in the corn economy c11 is the total corn advance (seedcorn plus corn advance as wages) per unit of corn produced; the rate of profits, putting the price of
corn as equal to 1, is determined by 1=(1+r)c11; labour enters the determination of r only through
the physical costs it causes. How much of c11 is wages and how much is seed-corn is irrelevant. The
same holds true in more complex economies. E.g. in the case of the two-goods economy the price
equations can be written as follows:
[1.47] p1 = (1+r)(c11p1 + c21p2)
[1.48] p2 = (1+r)(c12p1 + c22p2).
Again, here labour does not appear at all, only the physical inputs per unit of product are relevant. It
is physical inputs, not labour per se, that determine the rate of profits and prices of production.
This was clear to the best classical economists. Perhaps the clearest expression is found in
James Mill’s Elements of Political Economy, first published in 1821. Mill insisted that, in the last
instance,
The agents of production are the commodities themselves ... . They are the food of the
labourer, the tools and the machinery with which he works, and the raw materials which he
works upon. (Mill, [1821] 1826, p. 165)
This means that the rate of profits and relative prices would remain determinable even in a
science-fiction completely automated economy which used no labour at all, only robots; in such an
economy it would be clear that prices of production cannot be seen as ‘transformed’ quantities of
85
Some recent approaches to the labour theory of value, that attempt to salvage the thesis that profits
are redistributed surplus labour by redefining labours embodied, appear motivated precisely by such a fear.
These approaches are presented in an Appendix to chapter 2.
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labour.
The exclusive role of physical quantities of commodities in the direct determination of the
rate of profits is confirmed by the notion of standard commodity, due to Sraffa (1960).
In the corn economy it is clear that it is the existence of a physical surplus over the
necessities of reproduction that causes the existence of profits; and the rate of profits depends on a
physical ratio, the fraction of the product that must be advanced as capital in order to produce that
product. The same insight can be obtained also for more complex economies via an auxiliary
construction. Here we illustrate it for the two-goods economy.
The solution of the price equations is not altered by changes in the dimensions of industries
as long as these leave technical coefficients unaltered. Let us then imagine to alter the relative
dimensions of the two industries of the two-goods economy in such a way as to reach the
proportions necessary for maximum potential growth of both industries at a common rate. To such
an end, call x1 the quantity produced of corn and x2 the quantity produced of iron, and define the
rate of physical surplus of commodity i=1,2 as
σi ≡ (xi−ci1x1−ci2x2)/(ci1x1+ci2x2),
that is, the ratio of the physical surplus of that commodity to the quantity of it employed in the
entire economy as capital (i.e. both as means of production and as part of wage advances). This
ratio indicates the maximum percentage by which the employment of that commodity for
productive advances can be increased: e.g. σ1=20% means that in the next production cycle the
amount of commodity 1 available as means of production and subsistence can be at most 20% more
than in the current production cycle. It suffices to divide both numerator and denominator by x2 to
see that the rates of physical surplus depend on the composition of production x1/x2, and that if x1/x2
increases, then σ1 increases and σ2 decreases. If the composition of production is given, and if both
industries are to grow at the same rate, then the lower one of the two rates of physical surplus is the
highest common rate of growth achievable with that composition of production. The maximum
potential rate of growth g* is therefore achieved when x1/x2 renders σ1=σ2=g*. For both industries
to be able to grow at rate g*, the quantity produced of each product must be (1+g*) times the
quantity of it advanced as capital (both as means of production and as wages) in the entire
economy:
[1.49]
x1=(1+g*)(c11x1+c12x2)
[1.50]
x2=(1+g*)(c21x1+c22x2)
(Note carefully the difference from equations [1.47-1.48] in the sequence of indices: note,
for example, that c11x1+c12x2 is a quantity of good 1.) In an economy satisfying these equations, the
composite commodity “social product”, consisting of x1 and x2, and the composite commodity
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“aggregate capital”, are two different quantities of the same composite commodity. Then the
surplus product (i.e. social product minus aggregate wages-inclusive capital) is again a quantity of
the same composite commodity: Sraffa calls it standard commodity; the proportion x1/x2 associated
with it is called the standard proportion. This standard proportion is unique, because any deviation
from it would reduce the rate of physical surplus for one of the two commodities, and would
therefore reduce the highest common rate of growth.
The rate of profits in such an economy is simply the common rate of physical surplus, or of
potential growth, r=g*, a physical ratio. The economy has become formally equivalent to the corn
economy, because the standard commodity uses only itself for its production. The ratio between
value of surplus product and value of aggregate capital, which is the actual rate of profits, cannot
but be equal to that physical ratio, whatever the relative prices, because any price change would
alter the two values by the same percentage.
In this way the rate of profits is determined before relative prices (in this sense, it answers
Ricardo’s quest for a way to determine the rate of profits without having simultaneously to consider
the influence of the rate of profits on relative prices); but what interests us now is that the rate of
profits can be seen as reflecting a ratio between quantities of physical commodities, analogous to
the ratio between surplus and corn-capital (inclusive of wages) in the corn economy. This confirms
that it is physical inputs per unit of output, not labour per se, that determine the rate of profits.
Having thus understood what directly determines the overall rate of profits, relative prices of
production have the sole function of allowing this rate of profits to be the same in all industries −
Marx would have said: of allowing all units of capital equally to share in the plunder.
Of course the fact that work is produced by human beings and not by robots does have a
crucial role in that the bargaining strength and attitude of labour influences wages, the length of the
working day, workpace, the efficiency with which production is carried out (e.g. the percentage of
defective products); the choice of production methods too (e.g. amount of supervision) is influenced
by the need to control workers, to prevent shirking or sabotage, to divide the workforce by
introducing specializations and differentiations. But it is not easy to see how the study of the
indirect influence of all these factors upon the rate of profit through their influence on the elements
directly determining it would be improved by conceiving exchange values as representing
crystallized quantities of labour.
1.11. MORE ON MARX
1.11.1. Wages
A full reappropriation of the rich analyses of wages, competition, technical progress, crises,
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growth, etc. contained in the writings of classical economists is still largely to be carried out by the
economic profession. It is therefore opportune to say something more at least on the analyses of the
author, Karl Marx, with whom on many issues the surplus approach reached its most advanced
stage of development before being ‘submerged and forgotten’ (to use Sraffa’s terms) owing to the
rise of the marginal approach.
We start with Marx’s views on the determinants of wages. Marx agrees with Smith and
Ricardo on the importance of customary, social elements in the determination of normal wages or
‘subsistence’. He is Smithian (or, one might say, Smith was Marxist before Marx) in his stress on
class conflict as a key element of capitalist society. Das Kapital is full of ferocious sarcasm against
the representations of capitalism as a harmonious society, or as a natural society instead of a
historically contingent form of social organization destined – according to Marx −, precisely
because of the dynamics of class conflict, to be supplanted by other and more civilized forms of
social organization. Indeed the main purpose of Capital would appear to have been, to refute the
apologetic picture of capitalist society which was becoming dominant at the time[86], and to reestablish with theoretical argument and factual evidence the Smithian-Ricardian view of capitalism
as a class society dominated by conflict, with the addition of 1) a harsh denunciation of the
conditions of the working class; 2) a greater stress than in earlier classical authors on the importance
of the length of the working day and of the struggles determining it as an influence on the rate of
profits[87]; 3) the prediction that the immanent laws of development of capitalism would pave the
way for a proletarian revolution which would abolish the private property of means of production;
and 4) a scathing indictment of the tendency of intellectuals to be apologists of the status quo[88].
In Marx’s time Nassau Senior’s thesis that profit was the necessary recompense for the capitalists’
“abstinence” (from consuming their entire gross income), abstinence that permitted the existence of capital,
was more and more generally accepted among renowned economists. John Stuart Mill (whose 1848
Principles of Political Economy supplanted Smith’s and Ricardo’s books as the basic reference treatise on
economics), although declaring himself a Ricardian, accepted this very non-Ricardian
explanation/justification of profit, whose logic becomes clearer if one applies it to the income of slave
owners: a slave-owner too might argue that his income is justified by the fact that his abstinence (from
consuming himself the slaves’ subsistence, as well as from consuming the resources that keep whip and
chains in good order) is what allows the slaves not to die of hunger.
87
Marx considers the normal daily wage to be largely independent of the length of the working day
(except for the need for more nourishment in particularly heavy work); thus a lengthening of the working day
decreases the wage per hour, i.e. the wage per amount of labour performed, and thus causes a rise of the rate
of profits. He views the legal limitations to the length of the working day as important results of labour
struggles.
88
This is how Marx explains the tendency to abandon Ricardian theory:
“In so far as political economy is bourgeois, i.e. in so far as it views the capitalist order as the
absolute and ultimate form of social production, instead of as a historically transient stage of development, it
can only remain a science while the class struggle remains latent or manifests itself only in isolated and
sporadic phenomena.
86
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On this last issue, here is how Marx cites a writer of the end of the 18th century, Joseph Townsend:
About ten years after Ortes, the High Church Protestant parson, Townsend, glorified
misery as a necessary condition of wealth in a thoroughly brutal way. ‘Legal constraint’ (to
labour) ‘is attended with too much trouble, violence, and noise, ... whereas hunger is not
only a peaceable, silent, unremitted pressure, but as the most natural motive to industry and
labour, it calls forth the most powerful exertions.’ Everything therefore depends on making
hunger permanent among the working class, and this is provided for, according to
Townsed, by the principle of population, which is especially applicable to the poor. ‘It
seems to be a law of Nature that the poor should be to a certain degree improvident’ (i.e. so
improvident as to be born without silver spoons in their mouths) ‘that there may always be
some to fulfil the most servile, the most sordid, and the most ignoble offices in the
community. The stock of human happiness is thereby much increased, whilst the most
delicate are not only relieved from drudgery ... but are left at liberty without interruption to
pursue those callings which are suited to their various dispositions ... it [the Poor Law]
tends to destroy the harmony and beauty, the symmetry and order of that system which
God and Nature have established in the world’. (Capital I, p. 800)[89]
Also, many pages of Capital describe the role of violence and oppression in establishing and
maintaining capitalism. Marx has greatly stimulated historical research on the origins of capitalism
by arguing that at these origins there is a ‘primitive accumulation’ characterized by violence and
forcible expropriation of the lower classes, not unlike the behaviour of conquerors toward natives in
colonies.
Let us take England. Its classical political economy belongs to a period in which the class struggle
was as yet underdeveloped. Its last great representative, Ricardo, ultimately (and consciously) made the
antagonism of class interests, of wages and profits, of profits and rent, the starting-point of his investigations,
naïvely taking this antagonism for a social law of nature. But with this contribution the bourgeois science of
economics had reached the limits beyond which it could not pass.....
The succeeding period, from 1820 to 1830, was notable in England for the lively scientific activity
which took place in the field of political economy ... Splendid tournaments were held ... Ricardo’s theory
already serves, in exceptional cases, as a weapon with which to attack the bourgeois economic system ...
With the year 1830 there came the crisis which was to be decisive, once and for all.
In France and England the bourgeoisie had conquered political power. From that time on, the class
struggle took on more and more explicit and threatening forms, both in practice and in theory. It sounded the
knell of scientific bourgeois economics. It was thenceforth no longer a question whether this or that theorem
was true, but whether it was useful to capital or harmful, expedient or inexpedient, in accordance with police
regulations or contrary to them. In place of disinterested inquirers there stepped hired prize-fighters; in place
of genuine scientific research, the bad conscience and evil intent of apologetics.” (K. Marx, Postface to the
Second Edition of Capital, in Capital I, p. 96-7)
89
The ‘Old Poor Law’, which is the one Townsend is referring to, is the name given to the ensemble
of British laws (prior to the Poor Law Amendment of 1834) which since the 17th century had established the
institution of poor relief paid for by taxation. Townsed condemns this primitive unemployment subsidy
because it makes the poor less ready “to fulfil the most servile, the most sordid, and the most ignoble offices
in the community”.
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However, once capitalism has established itself − Marx continues −, open violence against
the working classes, although always present in the background as a potential last resort, is not often
used. As long as private property is respected, the spontaneous working of the laws of the capitalist
economy suffices to maintain the capitalist domination over workers. In describing how these laws
establish a tendency of wages to gravitate around a subsistence level, Marx is a harsh critic of
Malthus and of the generality of thinkers at the time, who relied on the effect of variations in real
wages on population to explain why a rise in wages would tend to increase unemployment and thus
weaken the bargaining position of workers. Marx accepts the influence of unemployment on the
bargaining power of workers, although he qualifies that influence by giving great importance to
ideological and organizational elements (precisely for this reason, he dedicates great energies to the
refutation of ‘harmonicist’ theories denying the existence of a fundamental conflict between capital
and labour and justifying profits as the recompense for a contribution of capitalists to production;
and he gives great importance to the birth of trade unions and of workers’ parties). But he rejects
the Malthusian population mechanism as the explanation of the tendency of real wages to remain
low, for two reasons.
The first argument against Malthus is that (as noticed already by Adam Smith) it is by no
means guaranteed that wage rises will induce the workers to have more children: indeed, Marx
thinks that more probably the opposite is the case: “not only the number of births and deaths, but
the absolute size of families, stands in inverse proportion to the level of wages, and therefore to the
amount of the means of subsistence at the disposal of different categories of worker” (Capital I, p.
796-97). One cause of the tendency of the poor to have many children is the firms’ demand for
child labour: this labour, although underpaid, helps poor families to survive, at horrible costs that
Marx denounces in many angry pages of volume I of Capital.
The second and decisive argument against Malthus is that the latter’s theory is unable to
explain the length of the cyclical fluctuations in wages and profits, fluctuations which last much less
(the average length of economic cycles in the first half of the 19th century had been, according to
Marx, around 10-11 years) than required by the Malthusian population mechanism, which requires
two or more generations to produce a complete cycle.
Marx explains the tendency of wages to decrease back toward subsistence through the effect
of changes in real wages on capital accumulation and technical progress, rather than on population.
For Marx, the normal situation of capitalism is the existence of a vast reserve army of unemployed
labour, that includes not only the openly unemployed people but also vast amounts of disguised
unemployment and potential labour supply (in agriculture, in petty commerce, among women and
children). If rapid economic growth sufficiently reduces the size of this reserve army, the bargaining
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power of workers increases and real wages rise. But when wages rise, profits decrease, and with
them the rate of profits. The capitalists then have both less profits to reinvest, and a lesser incentive
to invest them, since the rate of profits that one can expect to obtain is lower. On the other hand, the
purchasing power of workers has increased, consumption increases, and this is an incentive to
invest; therefore it is by no means certain that wage increases always cause an economic crisis,
sometimes they can be a stimulus to growth. But if the wage increase is strong, most probably the
discouragement effect on investment is stronger than the incentive to invest deriving from the
increase in consumption expenditures; the capitalists feel that their class domination is endangered;
they stop investing. The money profits they obtain are left idle, waiting for better times. The crisis
of investment is reinforced by the difficulties many firms encounter in repaying their debts, because
the lower rate of profits makes it difficult to repay the rates of interest accepted when the rate of
profits was higher[90]; in the meanwhile technical progress continues and even accelerates, because
in order to avoid bankruptcies the capitalists become more than normally active in looking for and
introducing cost-reducing innovations[91], and especially labour-reducing innovations, since it is the
rise of wages that is causing their difficulties. This causes further firings of labourers, besides the
ones already due to the decreases in quantities produced. The reserve army of labour swells again,
and this sooner or later reduces real wages enough, and for a long enough time, to restore the profits
and the self-confidence of capitalists; then accumulation starts again, and a new economic cycle
begins[92].
The tendency of wages to decrease back toward subsistence is explained, in conclusion,
through the influence of wage increases on the demand for labour rather than, as in Malthus, on the
90
Thus for Marx the downturn in the cycle exhibits a sharp increase in bankruptcies. A first wave of
bankruptcies is caused by the impossibility to repay a rate of interest now higher than the rate of profits; but
the closed-down firms stop purchasing inputs from other firms, and this causes further bankruptcies. Thus,
while in Ricardo an increase in wages simply slows down accumulation, in Marx it can cause a very sudden
and violent crisis entailing a sharp drop in output.
91
There is here an implicit suggestion, only recently taken up by modern economic theory, that
technical progress depends to a great extent on the amount of efforts and resources dedicated to producing it.
In modern times the thesis of Marx, that labour-saving innovations increase in periods of crisis, has been
questioned by some authors; but even if he came out to have been wrong on this issue, Marx would have
contributed to the progress of economics by raising the issue, and stimulating research on it.
92
“The rise of wages is therefore confined within limits that not only leave intact the foundations of
the capitalist system, but also secure its reproduction on an increasing scale. The law of capitalist
accumulation, mystified by the economists into a supposed law of nature, in fact expresses the situation that
the very nature of accumulation excludes every diminution in the degree of exploitation of labour, and every
rise in the price of labour, which could seriously imperil the continual reproduction, on an ever larger scale,
of the capital-relation. It cannot be otherwise in a mode of production in which the worker exists to satisfy
the need of the existing values for valorization, as opposed to the inverse situation, in which objective wealth
is there to satisfy the worker’s own need for development. Just as man is governed, in religion, by the
products of his own brain, so, in capitalist production, he is governed by the products of his own hand.”
(Capital I, pp. 771-2).
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supply of labour. In a long-run perspective, the stimulus of economic crises to labour-saving
innovations guarantees that capitalism always re-creates the excess population, the reserve army of
labour, that it needs for its functioning.
1.11.2. Quantities.
We have seen that Marx did not accept Say’s Law, i.e. the thesis that all savings are always
invested and that therefore aggregate demand is never inferior to aggregate supply. Indeed among
the classical economists there are deep differences on the issue of what determines aggregate
output, and therefore also labour employment, as well as on the evolution over time of these
variables.
One group accepted the impossibility of ‘general gluts’, i.e. of generalized overproduction of
commodities relative to demand. In the XX century this thesis was named ‘Say’s Law’ because
attributed to Jean-Baptiste Say, a French economist contemporary of Ricardo, who argued that,
whatever the overall production level of an economy, in the aggregate (i.e. apart from sectoral
mistakes of adaptation of the composition of production to the composition of demand) there would
not be problems in selling the entire product at cost-covering prices, because the overall value of
aggregate demand is always equal to the overall value of production owing to the fact that goods
purchase one another; behind the ‘veil’ of monetary exchange, commodities exchange against
commodities, and − Say writes − one half of the commodities produced necessarily buys the other
half. Ricardo accepted Say’s argument but reformulated it in a clearer way: on the basis of Adam
Smith’s argument that nobody will be so fool as to leave some of his income idle when he can
employ it for a positive return, he stated that the value of production is distributed as gross income,
and what of this income is not spent on consumption is, directly or indirectly (by lending it to
others), invested in production; thus saving is investment, and aggregate expenditure is necessarily
equal to the aggregate value of production. Thus except in cases of extreme perturbation of
economic activity (such as the sudden cessation of a big war, which requires an enormous reorientation of economic activity; or a crazy decree suddenly suspending all banking operations),
according to Ricardo general overproduction is impossible: there can only be overproduction in
some industries, to which there will correspond underproduction in other industries; that is, there
can only be errors of adaptation of the composition of production to the composition of demand
which, unless of enormous entity, will not significantly influence the pace of accumulation.
The theory of growth deriving from Say’s Law is simple: capital is fully employed, and
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what is not consumed is invested[93]. As said earlier, savings originate nearly exclusively from
profits, because the workers are too poor to save, and the landlords are usually spendthrifts. Thus
the share of savings in aggregate income depends on income distribution. Ricardo, who under the
influence of Malthus’s theory of population tends to take the average level of real wages as given
(although remaining open to the possibility that a rise in real wages above subsistence, if it persists
for some time, may end up by raising the social-conventional component of subsistence), stresses as
the main influence of capital accumulation on the rate of profits the extension of cultivation to less
and less fertile lands, which causes the rate of profits to decline. His conclusion is that the rate of
profits will tend to rise, remain constant, or decline secularly, depending on whether its tendential
decrease will be more than compensated, just compensated, or less than compensated, by the
increase in the productivity of labour in agriculture due to technical progress.
Other authors of the period, for example Malthus and Sismondi, rejected “Say’s Law” and
admitted the possibility of generalized overproduction, on the basis first of all of observation, which
suggested that generalized selling difficulties could indeed be observed in certain periods. But they
were unable to formulate convincing theoretical refutations of Say’s Law. Malthus, for example,
was a tenacious opponent of Ricardo but accepted as much as Ricardo that savings was
synonymous with investment, and, because of this, Ricardo’s logic came out as ultimately
victorious in their debate.
Marx too rejects Say’s Law, first of all on the basis of the historical evidence, which showed
to him a tendency of capitalism to undergo periodic general crises; on the theoretical causes,
although without arriving at the modern distinction between ex-ante (or programmed) and ex-post
(or realized) investment, Marx at least notices that, since exchanges are against money, it is not
93
This is connected with a topic on which for space reasons we cannot spend more than a footnote,
the classical distinction between productive and unproductive labour. Fundamentally, and leaving aside
important differences among classical economists on this issue, productive labour is labour employed by
capital, that contributes to the production of profits and therefore contributes (or is potentially capable of
contributing) to capital accumulation, while unproductive labour is employed by revenue and does not
produce a profit. The extent and speed of capital accumulation, i.e. of the growth of the wealth of the nation,
depends on how much of the social surplus is devoted to maintaining productive rather than unproductive
labour. The basic intuition motivating the distinction is made clear by Smith’s sentence “A man grows rich
by employing a multitude of manufacturers; he grows poor by maintaining a multitude of menial servants”
(Smith, WN, Bk. II, Ch. 3, p. 295). Thus according to Smith one can distinguish workers who produce a
surplus from workers who live off the surplus and reduce the amount of it that is reinvestible; the former,
according to Smith, must produce some material good utilizable for further production, hence he tends to
identify unproductive labour with labour that produces no material product and is therefore unable to
increase the stock of capital goods: Smith cites soldiers, musicians, artists, servants, lawyers, priests,
politicians. Marx, on the contrary, calls productive all labour that produces a profit; hence musicians whose
exhibitions produce profit for the concert organizers are productive workers for Marx (Smith considered
musicians unproductive, but in Smith’s times musicians were generally not working for capitalists). The
precise definition and usefulness of the notion are still an open issue.
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guaranteed that whoever has sold will immediately use again the money thus obtained: he can
choose to hold in monetary form the purchasing power thus obtained, if for some reason he does not
expect to obtain from its immediate re-employment a higher profit than by waiting. Then savings do
not translate into investment. According to Marx this breakup of the monetary circulation will
happen for example when significant wage increases or social turmoils discourage capitalists from
investing; an analogous breakup can happen when significant mistakes in the adaptation of the
composition of production to the composition of demand cause crises simultaneously in a number
of important sectors: the resulting difficulties of selling at cost-covering prices can extend to the
firms and sectors selling inputs to the sectors in crisis, so the crisis can become general (some
interpreters have found here an anticipation of Keynesian insights).
In conclusion, the classical or surplus approach to distribution and prices is open on the
issue of the determinants of the aggregate level of production, being compatible both with the
acceptance, and with the rejection, of Say’s Law, and does not supply strong reasons to accept it, so
that several thinkers of the classical period found it not difficult to reject it. The rejection of Say’s
Law implies of course the need for an alternative theory of what determines the aggregate level of
production, and one does not find in the classical authors, not even in Marx, a very satisfactory
theory; but it will be argued later in this book that the Keynesian-Kaleckian principle of effective
demand (that states that aggregate supply tends to adapt to an autonomously determined level of
aggregate demand) can be such a theory. But this is for later. Now what may be useful to stress, in
view of the comparison to be effected in ch. 3 of the classical approach with the marginal approach,
is that in the classical approach the acceptance of ‘Say’s Law’ only implies that, apart from sectoral
errors, demand is always adequate to absorb the entire production, but it does not imply that
aggregate production will be at the level ensuring the full employment of labour; in each period
labour employment depends on the level reached by capital accumulation and on the prevalent
methods of production (which are treated as essentially given and only gradually modified by
technical progress), and can only be increased by further capital accumulation. In the classical
authors one does not find the notion of capital-labour substitution that, in the marginalist authors,
will be the basis of the thesis that labour employment can be increased without a need for further
capital accumulation because the average capital-labour ratio can be varied. In the classical authors
who accept Say’s Law, employment will increase from a period to the next only if the increase in
the scale of production, due to capital accumulation, will more than compensate the tendency of
labour-saving innovations to cause a decrease of the demand for labour. The Appendix to this
chapter, on Ricardo on machinery, illustrates these statements.
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1.11.3. Growth, technical change, the ‘law’ of the tendency of the rate of profits to fall, and
the future of capitalism.
Marx’s writings on crises do not amount to a full and coherent theory, and they are mostly
found in the manuscripts he left unfinished; anyway from his writings a clear prediction emerges of
a tendency of capitalism to encounter greater and greater functioning difficulties, in particular to
incur in crises of increasing gravity, owing to three main reasons:
1) increasing difficulties of co-ordination of a more and more complex economy;
2) the tendency of capitalism, owing above all to labour-saving technical progress, to
increase the reserve army of the unemployed and to worsen the condition (at least the relative
condition) of the working class, with a resulting tendential decrease of the share of workers’
consumption in aggregate income which makes it more and more difficult to avoid insufficiencies
of aggregate demand;
3) the tendency, again due to labour-saving technical progress, of the rate of profits to fall.
Let us expand a bit on these three central elements of Marx’s views on the very-long-run
tendencies of capitalist accumulation.
The first element is the increasing difficulty of co-ordinating the composition of production
with the composition of demand. Marx produces attempts at a disaggregate treatment of the
economy (his ‘schemes of reproduction’, on which we do not stop, but which have been very
important in the history of economics, being the basis both of Soviet planning and of Leontief’s
input-output analysis), and concludes from them that it is very unlikely that ‘disproportions’ will be
avoided. Production decisions and investment decisions must be taken before demand becomes
manifest. Changes in the composition of demand cannot generally be predicted. For Marx this is
one main cause of crises, owing to the tendency of sales difficulties and of bankruptcies to extend to
the suppliers of the sectors undergoing a crisis. The growing complexity of the economy, due to the
increasing division of labour and thus to the increasing number of sectors to be co-ordinated, is a
first reason for the prediction of crises of increasing gravity.
The second element is the tendency of technical progress to cause a worsening of the
conditions of the proletariat. This worsening has two causes, both based on developments of
Smith’s observations on the importance of the division of labour.
One cause is the tendency of the increasing division of labour to cause a deskilling of labour.
Here Marx utilizes observations of other writers, in particular Ure and Babbage, who had observed
that, when the progress of the division of labour entails that the complex activities of an artisan are
subdivided into different tasks assigned to different labourers, only a small part of these tasks will
require advanced skills, while most of them will be fairly simple and repetitive operations which
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can be entrusted to unskilled workers. Thus the extension of the division of labour increases the
proportion of unskilled workers, and entails therefore a decrease of the average wage rate.
The other cause is mechanization. The increasing division of labour makes the single,
repetitive operations of unskilled workers more easily replaced by machinery. The result is a
tendency of machines to replace workers; this causes an expulsion of workers from the productive
process, hence unemployment. Marx argues that, because of increasing mechanization, capitalism
has a tendency to increase over time the rate of unemployment (its average over the cycle), i.e. the
unemployment situation tends to become worse at each successive economic cycle. The increased
unemployment aggravates the tendency – already created by the tendential deskilling of labour – of
average wages to decrease. Thus it is not surprising that Marx predicts a growing immiseration of
workers. In his early writings Marx seems to have envisaged a tendency to absolute immiseration
(decrease of the average real wage rate), in later writings he admits the possibility that immiseration
be only relative (increase of the real wage rate inferior to the growth of labour productivity,
implying a worsening of the living conditions of the proletariat relative to the standard of living of
the dominant classes), but even if only relative, immiseration still has two very important
consequences in his view. It still means a worsening of the perceived living conditions of the
proletariat (this is important for the thesis of Marx that the proletariat will grow increasingly restless
and dissatisfied with capitalism):
A notable advance in the amount paid as wages presupposes a rapid increase of productive
capital. The rapid increase of productive capital calls forth just as rapid an increase in
wealth, luxury, social wants, and social comforts. Therefore, although the comforts of the
labourer have risen, the social satisfaction which they give has fallen in comparison with
these augmented comforts of the capitalist, which are unattainable for the labourer, and in
comparison with the scale of general development society has reached. Our wants and their
satisfaction have their origin in society, we therefore measure them in their relation to
society, and not in relation to the objects which satisfy them. Since their nature is social, it
is therefore relative. (Marx, Wage Labour and Capital, 1849, as repr. in Freedman, Marx
on Economics, p. 63)
The other consequence is that immiseration even if only relative still means a tendential decrease in
workers’ consumption as a share of the social product. Although without reaching Keynes’s model,
Marx does argue that decreases of consumption’s share in total demand can create problems of
overproduction, i.e. (in more modern terminology) of insufficient aggregate demand. This is,
according to him, a difficulty of increasing relevance in the course of capitalist accumulation, that
tends to make the overcoming of crises more and more difficult. This contributes to the thesis that
capitalism will undergo periodic crises of increasing gravity.
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The third element is the ‘law of the tendency of the rate of profits to fall’. There isn’t
complete agreement among interpreters as to what Marx meant by this ‘law’[94], but the following
seems to be the core of it. We have seen above that according to Marx technical innovation takes
the prevalent form of replacing labour with machines, i.e., in Marx’s terminology, of replacing
living labour with dead labour, i.e. with machines. Another reason for this predominant character of
technical progress according to Marx is, that autonomous labour is more difficult to control than
labour constrained by machines, and furthermore, labour struggles are an incentive to replace labour
with machines. According to Marx this character of technical change means a tendency to an
increase in the proportion C/L of constant capital to living labour, which, even if the rate of
exploitation is constant, results in an increase in the average composition of capital C/V. Owing to
his approach to the determination of the rate of profits, Marx concludes that technical progress
tends to cause a decrease of the rate of profits. The basic idea was, it seems, the following. When
an innovation that replaces labour with machinery is discovered that is capable of reducing costs at
the current prices[95], it will be introduced because it allows higher profits for the capitalists who
first introduce it; but when this innovation becomes generally adopted, by causing a rise in the
average organic composition of capital it causes − behind the back of capitalists, so to speak − a
decrease of the rate of profits. True, this decrease might be contrasted for a time by a rise in the rate
of exploitation S/V (a rise that will in fact generally occur if the real wage rate remains constant,
owing to the decrease in the labour embodied in the wage basket generally caused by innovations),
but such neutralization cannot go on indefinitely, because S/(C+V) can be re-written as:
S/L
[1.32] r = ————— .
C/L + V/L
Remembering that S=L-V, we see that even with a wage (and V) tending to zero, and the
numerator tending therefore to 1 and the denominator to C/L, an increase in C/L will sooner or later
cause a decrease of the rate of profits.
This ‘law’ (like the ‘transformation of values into prices of production’) is discussed in volume 3
of Capital, assembled by Engels from provisional manuscripts; so ambiguities and contradictions are not
surprising, and it remains unclear how much of the analyses in these manuscripts the later Marx would have
endorsed. After all, if Marx did not finish and publish himself those manuscripts, he must have been
dissatisfied with at least some of the analyses in them.
95
Here Marx reasons in terms of labour values, so a cost reduction means a reduction of the total
labour embodied in the product. But the reduction of c+v+s in the industry where machines replace labour
goes together, according to Marx, with a rise in c/(v+s), and this affects in the same direction the economywide organic composition of capital.
94
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This conclusion explains at least part of Marx’s pessimism on the future of capitalist
accumulation and on the possibility of increases of real wages: the tendency of the rate of profits to
fall would eventually compel wages to fall and would eventually slow down capitalist
accumulation, both through the effect on wages and thus on aggregate demand, and through the
effect on the rate of profits, helping to cause crises of increasing length and gravity.
Given its importance in Marx’s predictions on the evolution of capitalist growth, this ‘law’
has been intensely debated. After Marx’s death many Marxists advanced doubts on its validity,
observing that technical progress would generally decrease the labour embodied in commodities,
and could therefore result in a decrease in the labour embodied in the commodities composing the
constant capital; therefore the adoption of more mechanized methods using less labour per unit of
output and more powerful machines did not necessarily imply an increase in C/L because the new
ensemble of machines might embody less labour than the previous one. The conclusion drawn from
this observation was that the tendency of the rate of profits to fall was a possibility, not a certainty.
Modern analysis has added a stronger criticism in the shape of the following result, often called
‘Okishio’s theorem’[96], that will be proved in chapter 2:
Suppose that in a certain economy, at the going real wage rate and associated rate of profits
and relative prices, a new method of production is discovered (of a commodity directly or indirectly
entering the real wage) which allows production of its product at a lower unit cost than with the
ruling method. Then, if this new method thoroughly replaces the old ruling method and prices tend
to the new prices of production, the new uniform rate of profits is necessarily higher than the old
rate of profits if the real wage rate has remained the same; if the rate of profits remains the same,
then it is the real wage rate that becomes higher.
The implication of Okishio’s theorem is that a new method that, at the old prices, results in a
reduction of the cost of production of a product cannot, when its adoption becomes generalized,
cause a reduction of the rate of profits (if the real wage rate has remained the same): if it concerns a
'wage industry', then the rate of profits rises (this may go together with a rise in the average organic
composition of capital, but the latter will never be able to prevent the rate of profits from rising).
Thus, except when it concerns luxury goods[97], the introduction of cost-reducing new methods
opens up spaces for increases either of the rate of profits, or of the real wage rate, or of both.
Technical progress always opens up new margins for increases in real wages, whose utilization in
96
The Japanese economist Nobuo Okishio was among the first ones to prove this result, in 1961. In
fact it was implicit in Sraffa’s results in his 1960 book; and some verbal statements by Samuelson in 1958
also allude to it.
97
In this case the rate of profits is unaffected, as noted earlier.
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favour of wages rather than in favour of profits depends on the relative barganing power of classes.
w
wI(r)
wII(r)
w”
w’
O
r’ r”
r
Fig. 1.2. Example of effect of technical progress. The straight line is the old w(r) curve; initially
r=r’ and w=w’; if a new method is more convenient at the associated prices, then its
introduction shifts the w(r) curve outwards at least in a neighbourhood of the point (r’,w’),
hence if the real wage rate remains unchanged the rate of profits rises, to r” in the diagram; if r
remains unchanged then w rises to w”; or both r and w can rise.
This result can be illustrated graphically. Given the methods of production adopted in each
industry, we have seen (cf. §1.9.5, and ch. 2 for a more general demonstration) that, if one treats the
real wage rate as variable, then, whatever the good or basket of goods chosen as numéraire, the real
wage rate varies in a direction opposite to the rate of profits. Once a numéraire is chosen, the
function w(r) is a decreasing continuous and differentiable curve that intersects both axes. If a
method is changed in any one of the wage-industries, the w(r) curve changes. Okishio’s theorem
implies the following: suppose the w(r) curve is given, and r (and hence w) is given. A new method
is discovered which, at the ruling prices, permits to reduce the cost of production of a product in the
wage-industries. If this method replaces the old method and one calculates the new w(r) curve (in
terms of the same numéraire) and draws it in the same diagram as the old w(r) curve, then at the old
level of r the new w(r) curve is above the old curve (it need not be above the old curve at other
levels of r). As Fig. 1.2 shows, this means that there is room for a rise of w, or of r, or of both.
Marx’s analysis of the tendency of wages to decrease again when they increase, owing to a
crisis due to the wage rise, must then be modified: the technical progress which goes on during the
crisis means that when the increase of the reserve army of labour causes the real wage to fall and
the rate of profits to rise, if the level of the rate of profits necessary for accumulation to start again
has not changed this level is reached for a level of real wages higher than previously; each upturn
starts with a higher initial real wage than in the previous cycle; the average real wage over the cycle
tends secularly to grow.
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Thus if for example the rate of profits necessary for the upturn is r’ in Fig. 1.2, and the
upturn that starts one cycle happens when the real wage decreases to w’ because the w(r) curve is
wI(r), if technical progress during that cycle causes the w(r) curve to shift from w I(r) to wII(r) then
the next upturn happens when the real wage decreases to w”.
This result permits an explanation of the indubitable secular increase in the standard of
living of the working classes in the main capitalist countries; and no doubt it weakens Marx’s
reasons for pessimism on the future of capitalism. On the tendency of capitalism to crises of
increasing gravity, however, Marx’s intuition appears not to have been off the mark, at least up to
the Great Crisis of the 1930s: afterwards, the discovery of Keynesian demand management
techniques has changed the picture, but crises still happen.
Two more elements of Marx’s predictions deserve mention.
One is the tendency toward an increasing concentration of capitals: bigger capitalists –
Marx argues – tend to win in the competition against smaller capitalists because favoured by scale
economies, so the smaller producers are pushed out of business or absorbed; the winners in the
competitive struggle become ever bigger. The development of the credit system significantly helps
in this process of concentration of capitals, by making it easier to buy out other firms[ 98]. (This
prediction has been largely confirmed by historical experience. Indeed a modern problem is how to
prevent the people who control giant corporations from having too much political influence. The
time might not be far in which a single person will decide the economic fate of millions of people
because he owns or controls the firms that employ them.) An important aspect of this tendency,
according to Marx, is that the increasing role of planning in ever more gigantic firms teaches the
proletariat the possibility and the advantages of centralized, ex ante planning.
The other prediction, very important for Marx’s political views, is the tendency toward an
increasing social polarization: according to Marx, the advantage of big capital in the competitive
struggle tends to destroy the independent middle class, by destroying petty commerce and small
manufacture; thus a growing majority of population ends up having to sell their labour as wage
labour, while the concentration of capitals decreases the number of capitalists. Wealth becomes
more and more concentrated, while an increasing majority of the population falls into the
proletariat. Marx includes in the working class all dependent, salaried workers, therefore well-paid
technicians and managers too (the so-called “workers’ aristocracy”), but owing to the process of
Thus Marx’s conception of competition is very different from the perfect competition of modern
neoclassical economics: it is a continuous, ruthless struggle that operates mainly through incessant
innovations of products and of methods of production, and therefore continually revolutionizes markets and,
also through its influence on the character and composition of the working class, the whole society.
98
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deskilling he views this privileged portion of the working class as becoming less and less numerous;
the tendency of capitalism according to him is toward an increasing homogeneity of the working
class.
On these foundations, Marx views the class struggle as turning sooner or later decidedly in
favour of the working class. A smaller and smaller minority of capitalists, weakened by a capitalist
economy that encounters greater and greater difficulties of functioning, is confronted by a working
class that is more and more a majority of society, is more and more exasperated by its (at least
relative) immiseration and by the worsening crises, is more and more homogeneous, and is more
and more prepared by its work experience (the realization of the advantages of ex-ante coordination, made evident by the organization of giant firms) to appreciate the potential
improvements in the running of the economy made possible by replacing the ex-post co-ordination
via markets with the ex-ante conscious co-ordination achievable via planning. The smaller and
smaller minority of ruling class members will become sooner or later incapable of resisting the
increasing rage, and the increasing clarity on an alternative project of social organization, of the
vast majority of society[99]. In a justly famous passage in the penultimate chapter of Capital vol. I,
Marx summarizes his predictions as follows:
The expropriation of the direct producers was accomplished [in the process of primitive
accumulation at the origins of capitalism] by means of the most merciless barbarism, and
under the stimulus of the most infamous, the most sordid, the most petty and the most
odious of passions. Private property which is personally earned, i.e. which is based, as it
were, on the fusing together of the isolated, independent working individual with the
conditions of his labour, is supplanted by capitalist private property, which rests on the
exploitation of alien, but formally free labour.
As soon as this metamorphosis has sufficiently decomposed the old society throughout its
depth and breadth, as soon as the workers have been turned into proletarians, and their
means of labour into capital, as soon as the capitalist mode of production stands on its own
feet, the further socialization of labour and the further transformation of the soil and other
means of production into socially exploited and therefore communal means of production
takes on a new form. What is now to be expropriated is not the self-employed worker, but
the capitalist who exploits a large number of workers.
This expropriation is accomplished through the action of the immanent laws of capitalist
production itself, through the centralization of capitals. One capitalist always strikes down
many others. Hand in hand with this centralization, or this expropriation of many
capitalists by a few, other developments take place on an ever-increasing scale, such as the
99
Owing to the increasing difference in numerosity of the two opposing groups, according to the
mature Marx the revolution would not be necessarily violent. One of the tasks of trade unions was to
contribute to the politicization of the working class in view of this final aim.
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growth of the co-operative form of the labour process, the conscious technical application
of science, the planned exploitation of the soil, the transformation of the means of labour
into forms in which they can only be used in common, the economizing of all means of
production by their use as the means of production of combined, socialized labour, the
entanglement of all peoples in the net of world market, and, with this, the growth of the
international character of the capitalist regime. Along with the constant decrease in the
number of capitalist magnates, who usurp and monopolize all the advantages of this
process of transformation, the mass of misery, oppression, slavery, degradation and
exploitation grows; but with this there also grows the revolt of the working class, a class
constantly increasing in numbers, and trained, united and organized by the very mechanism
of the capitalist process of production. The monopoly of capital becomes a fetter upon the
mode of production which has flourished alongside and under it. The centralization of the
means of production and the socialization of labour reach a point at which they become
incompatible with their capitalist integument. This integument is burst asunder. The knell
of capitalist private property sounds. The expropriators are expropriated. (Capital I, pp.
928-29)
I have quoted these predictions above all in order to show that in the classical approach there
is no clear line of demarcation between economics, sociology, and politics. A classical economist is
inevitably also a sociologist and a political scientist, because of the inevitable role that the approach
attributes to social and political elements in the explanation of central economic phenomena.
1.11.4. The ‘core’ of the surplus approach.
On the basis of what we have learned on the determinants of the real wage rate, of the
quantities produced, and of the methods of production according to classical authors, it is possible
to point out an aspect of the classical method of analysis that sharply distinguishes the classical
approach from the marginal/neoclassical approach. As probably the reader already knows from her
previous contacts with economic science (but anyway will be stressed in subsequent chapters), the
marginal or neoclassical or supply-and-demand approach argues that prices, income distribution,
quantities produced, resources utilized are determined simultaneously and interdependently by the
forces of supply and demand; deductive reasoning based on this interdependence allows univocal
conclusions e.g. on the effects of a change in real wages on the demand for labour and on the
general level of production. The scope of strictly deductive reasoning is less wide in the classical
than in the marginal approach. Deductive reasoning holds full sway only in that part of the
classical general analysis that has been called its analytical ‘core’ by P. Garegnani (1984): the
determination of the rate of profits on the basis of given real wage rate(s), given quantities
produced, and given methods of production, and the comparative-statics study of the effects of
changes in these data on the rate of profits. In the study of the determinants of these magnitudes
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taken as given in the ‘core’, and of the reciprocal influences among them, the classical approach
admits such an importance of historical, social and political influences that the analysis must be
much more inductive, attentive to historical specificities, and generally incapable of arriving on a
simply deductive basis at univocal predictions analogous to those reachable in the marginal
approach.
One can accordingly distinguish two different types of analysis in classical explanations and
predictions. The analyses of the causes of changes in one or more of the data of the ‘core’ (real
wages, quantities produced, technical conditions of production) are ‘out of the core’ analyses, rich
in historically specific details and open to a variety of influences; the analysis of the effects of such
changes on the rate of profits and relative prices are ‘core’ analyses, strictly deductive, and
provisionally treating the other data in the ‘core’ as given and unaffected by the initial change; the
analyses of the influences of these changes (both the direct influences, and the indirect ones
operating through the change in profit rate and relative prices) on the other data of the ‘core’ are
again ‘out of the core’ analyses, and may also include an ‘out of the core’ analysis of repercussions
on the magnitude(s) that changed first, or a second round of ‘core’ analysis if the other data of the
‘core’ are significantly affected to the point of requiring a new examination of the effects on the rate
of profits.
Thus for example Ricardo’s study of the effects of the abolition of the duty on corn imports
started by considering the probable effects on the quantity of corn produced in England, an ‘out of
the core’ analysis; the implication of the conclusion that British corn production would certainly
decrease (because some of the demand for corn would be satisfied by cheaper corn imports) was,
that less fertile lands would be abandoned (the inverse process of the one due to extension of
cultivation) and the new no-rent land would be more productive, a change in one of the data of the
‘core’; the ‘core’ then allowed the conclusion that the rate of profits would rise (the real wage was
taken as given). Ricardo stopped at this, but he might have gone on to ask about the effects on
accumulation and then on real wages and population: in this ‘out of the core’ analysis he would
have been compelled to take into consideration the variety of different influences already
considered by Adam Smith, and to admit for example that a more intense accumulation might be
discouraged by new wars or by a tendency of capitalists to become aristocratic spendthrifts, or that
a rise in wages might or might not stimulate an increase in population. Another example: in Marx’s
analysis of cyclical wage fluctuations the “core” is used to demonstrate that, when the real wage
rate rises, the rate of profits decreases; this is a purely deductive, univocal result; in the ‘out of the
core’ analysis of the causes of rises of real wages, Marx admits the importance of social,
organizational, ideological elements; on the ‘out of the core’ effects of the variation of the real wage
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rate on accumulation, again Marx is open to the possibility of different outcomes: a rise in real
wages can discourage accumulation, but, if not excessive, in certain cases − depending also on
political circumstances − it can on the contrary stimulate accumulation by raising the demand for
consumption goods.
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APPENDIX 1 TO CHAPTER 1
RICARDO AND THE MACHINERY PROBLEM: OR, TECHNICAL PROGRESS CAN
INCREASE UNEMPLOYMENT
1A1.1. Let us now study an important argument by Ricardo, which highlights his intellectual
honesty, evidences the difference between classical and marginalist ways of conceiving the effects
of technical progress on unemployment, and also supplies one example of Ricardo’s mistaken
conception of the natural price as including only wages and profits. Some of the notions that will
appear here (durable capital as one instance of joint production; choice of technique) will be treated
in greater detail in the next chapter.
In Chapter 31 of the 3rd edition (1821) of his Principles of Political Economy and Taxation
Ricardo writes that he must correct a mistaken opinion he had entertained: contrary to what he had
previously thought, the introduction of machines can cause unemployment, because part of the
capital destined to advance subsistence to workers can be absorbed by machines, and therefore “the
substitution of machinery for human labour, is often very injurious to the interests of the class of
labourers” (p. 388 of the Sraffa edition).
Ricardo’s argument rests on a numerical example in terms of money values. He considers a
capitalist who produces both “food and necessaries” on no-rent land. The capitalist is assumed to
produce himself the food and necessaries needed by the labourers he employs. The example is
compatible with assuming that the workers’ subsistence consists of corn only, and that the capitalist
produces corn only, so in order to help intuition this is what I will assume.
Ricardo assumes that at the beginning of the yearly production cycle the capital of this
capitalist, worth 20000 livre sterlings (pounds), consists partly of “fixed capital” (buildings etc.)
worth 7000 pounds, and for the remaining 13000 pounds is “circulating capital in the support of
labour”, i.e. food and necessaries “all of which he sells in the course of the year to his own
workmen” for the same value as the money wages he is paying them (p. 388)[100]. The rate of
profits is assumed to be 10%, which means − Ricardo argues − that at the end of the year the labour,
of the workers set to work by the 13000l. pounds of circulating capital, must produce a product
100
Ricardo evidently assumes that the capitalist need not borrow money in order to pay the wages in
money, or rather, that when he pays the money wages the money comes back to him immediately as payment
for food, so he has no need to advance money capital for the payment of wages for any significant length of
time and hence he need not pay any interest for this reason. The sole advance for wage payment that he
needs is the food and necessaries for a value of 13000 pounds at the beginning of the year. It is as if the
wages were all paid in kind at the beginning of the year (alternatively, we can imagine that the capitalist
advances the wages in money at the beginning of the year, having obtained the money from the sale of corn
produced in the preceding year for a value of 13000l.).
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worth 15000l., of which 13000 replace the circulating capital used up (the wages), and 2000 are a
10% profit on the total capital of 20000l..
Note how Ricardo neglects the need for seed-corn or for any other intermediate (circulating)
capital different from wage goods: the circulating capital consists entirely of wage goods.
Furthermore, he does not see that, even conceding this, the value of the product, in order to yield a
rate of profits of 10%, must be greater than 15000 because it must also cover the depreciation of the
fixed capital. This shows the limits of the conception of natural price that Ricardo inherits from
Adam Smith: in spite of considering a capital not consisting only of advances of wages, the natural
value of the produce is described as consisting only of wages and profits; there is no recognition of
the need for the natural value to cover also the costs connected with the part, of the capital
advanced, that Marx would later call ‘constant capital’[101].
To give logical consistency to Ricardo’s numerical example, we must suppose: a) that the
durable capital goods (fixed capital) do not depreciate, i.e. are eternal (the same must be assumed
for the machine that will appear below); b) that the circulating capital different from advanced
wages, e.g. seed, is so small as to be negligible.
Ricardo’s example continues as follows. At first the capitalist consumes all and only his
profits, maintaining his capital intact at a value of 20000, and produces 15000 pounds worth of corn
year after year. At a certain point, a machine is invented, which can aid agricultural production, and
can be produced by employing agricultural labour for a year, and such that it requires the advance
of 6500 pounds in wages for its production. The capitalist decides to utilize it, and one year he
employs half of his workers to build the machine, and only the other half to produce corn; the
production of corn is therefore one half that of the previous year[102]. Ricardo assumes that also in
that year the capitalist earns a profit rate of 10%, therefore, since the value of the produce
(corn+machine) must be again 15000 in order to replace the circulating capital advanced (13000)
Let us remember that Marx’s constant capital includes not only fixed capital but also non-wage
circulating capital. Two observations are apposite here. First, Ricardo’s lack of clarity about non-wage
circulating capital has persisted for a long time in the history of economic theory: fifty years later, when
wages were no longer considered advanced and therefore wage advances were no longer part of capital,
Walras conceived the capital needed to start a production cycle as consisting only of durable capital goods,
forgetting about the need for seed-corn, or iron, etc. Second, although the example we are discussing shows
that when considering concrete examples of individual firms Ricardo recognizes the presence of fixed
capital, still when he discusses the determinants of the rate of profits at the level of the entire economy,
Ricardo tends to consider changes in the rate of profits as depending solely on two circumstances, changes in
the level of real wages, and changes in the productivity of labour in the direct and indirect production of the
real wage basket; only with Marx it is recognized that changes in the ‘organic composition of capital’ are a
further determinant of changes in the rate of profits.
102
Since the capitalist is assumed to utilize no-rent land, and to be only one of many producers of
corn, his decision to reduce production can be assumed not to change the no-rent land, thus one can assume
production to be proportional to the labour employed by the capitalist.
101
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and to yield a profit of 2000 on the total capital of 20000, evidently the value of the machine is
7500. The capitalist is assumed again to consume his profits, thus after consuming 2000 pounds he
finds himself with 13000 pounds worth of produce, now consisting of the machine (worth 7500
pounds) and of 5500 pounds worth of corn. Thus at the beginning of the next production cycle his
capital is again worth 20000: the previous fixed capital is worth 7000, the machine is worth 7500,
and the corn stored for wage advances is worth 5500. Now the fixed capital is 14500 and the
circulating capital (wage advances) is 5500.
The decision to dedicate, that year, half the labour employed to build the machine rather
than to produce corn would not be taken by the capitalist if he thinks it would entail a diminution of
profits; therefore the next year the corn produced by the workers employed by the 5500 pounds of
circulating capital must be worth at least 7500 pounds (which is what Ricardo initially assumes): in
this way the replacement of the circulating capital leaves a profit (Ricardo calls it ‘net income’) of
2000, which yields again a rate of profits of 10% on the total capital. The value of the gross
produce, or gross income, of the capitalist, has decreased from 15000 to 7500, and labour
employment has decreased with it[103]; “but if this be done, − writes Ricardo − if the net income be
not diminished, of what importance is it to the capitalist, whether the gross income be of the value
of 3000l., of 10,000l., or of 15,000l.?” (p. 389). Technical progress has decreased the demand for
labour.
Ricardo concludes that in cases of this type the effect of the introduction of machinery is
that “as the power of supporting a population, and of employing labour, depends always on the
gross produce of a nation, and not on its net produce, there will necessarily be a diminution in the
demand for labour, population will become redundant, and the situation of the labouring classes will
be that of distress and poverty” (p. 390).
In the numerical example Ricardo assumes that profits (or net produce, as he calls it) do not
increase, but only as a simplifying device (he writes “The case which I have supposed, is the most
simple that I could select”, ibid.); of course he is aware that the conversion of circulating into fixed
capital, i.e. the introduction of machines, is effected in order to increase profits by reducing costs,
and that the result of their generalized adoption in an industry is indeed to increase profits.
(Although Ricardo does not do it explicitly, the example can be modified without difficulty to
become a case in which the capitalist is not indifferent − as here − between passing or not to
production with the aid of machines, but finds it to be a positive improvement: for example after the
introduction of the machine the corn production might be 8500 instead of 7500, yielding a rate of
103
Labour employment becomes 55/130 of what it was previously, i.e. less than half.
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profits of 15%; the decrease in labour employment would still be there.) Then, he notes, one
probable consequence of the greater amount of profits is an increase of investment; the rise in the
rate of growth can then re-absorb every year “a portion of the people thrown out of work in the first
instance” (ibid.). But the disappearance of the unemployment created by the introduction of
machinery is due to the growth of capital, not to changes in the capital/labour ratio as in the
marginal approach[104], and therefore it is a slow process requiring years, and possibly continuously
postponed by further introduction of machinery; also, we may add, it depends on the re-investment
of at least part of the increased profits, something which is not guaranteed to happen (especially
because, as we will see later in this book, Ricardo’s acceptance of Say’s Law cannot be
convincingly defended).
Ricardo concludes:
"That the opinion entertained by the labouring class, that the employment of machinery is frequently
detrimental to their interests, is not founded on prejudice and error, but is conformable to the correct
principles of political economy." (p. 392)
1A1.2. Ricardo was intellectually very honest; but this support for the arguments of the
Luddites was not liked by the British ruling classes. After his death even Ricardo’s closest
followers, like McCulloch, tried to argue that he was not correct. But the possibility pointed out by
Ricardo can be confirmed with other examples. We will now show with an example that Ricardo’s
argument does not depend on having considered a single producer, nor on having assumed that
circulating capital only consists of advanced wages, nor on having implicitly assumed that durable
capital is eternal; with another extremely simple example we will also show that Ricardo’s point
can be extended beyond the case of introduction of machinery, to the case where all capital is
circulating capital (but includes seed besides wages).
Our first example assumes that the production of corn also requires seed-corn, and that the
machine (tractors) lasts two years. Land is free. Initially corn is produced by labour and seed-corn
without tractors; the method of production is:
104
In the marginal approach, as we will see in chapter 3, the full employment of labour can be
reached without the need for a growth of the capital stock, because the average proportion in which labour is
combined with capital is argued to be a decreasing function of the real wage rate, and therefore a decrease in
the real wage rate will increase the demand for labour corresponding to a given total capital endowment of
the economy. This conception is clearly absent in Ricardo, who accordingly can only hope in the
accumulation of capital in order to increase the demand for labour. As to his belief that this accumulation
will be accelerated by the increase in profits, it derives from his belief that savings increase if profits
increase, coupled with his acceptance of Say’s Law, an acceptance which must be questioned after Keynes
and the subsequent theoretical developments that will be discussed later in this book.
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1 unit of seed-corn * 1 unit of labour → 3 units of corn,
or, more briefly, with C standing for ‘corn’ and L for ‘labour’:
1 C * 1 L → 3 C.
The real wage rate is 1 unit of corn and is advanced. In terms of capital advances, the
method of production can be represented, with CK standing for ‘corn-capital (inclusive of advanced
wages)’, as:
2 units of corn-capital → 3 units of corn, or, more briefly, 2 CK → 3 C.
The rate of profits is therefore r = 50% .
The economy is initially stationary, it produces 300 units of corn per period. Thus we can
write
200 CK → 300 C.
Labour employment is 100 L. Capitalist consumption is 100 C.
Then tractors are invented. We assume that the method of production of a new tractor is,
with T0 standing for ‘new tractor’:
1 C * 1 L → 1 T0 or 2 CK → 1 T0
Thus in order to produce tractors one only needs corn and labour. Tractors last two years,
with constant efficiency. With the use of tractors the method of production of corn is
1 C * 1 T * 1 L → 28/3 C.
But if one uses new tractors, the production of corn also produces, at the end of the year, a
one-year-old tractor as a joint product. If one uses one-year-old tractors, we assume that at the end
of the year the two-year-old tractors are useless and can be disposed of without any cost. Then we
must distinguish the process that produces corn using new tractors T0 from the process that uses
one-year-old tractors T1:
1 C * 1 T0 * 1 L → 28/3 C * 1 T1.
1 C * 1 T1 * 1 L → 28/3 C.
We choose corn as the numéraire, and indicate the price of new tractors as p, and the price
of old tractors as p1. The production of corn with the use of a new tractor also ‘produces’ a oneyear-old tractor, the value of the product therefore includes, besides the value of the corn produced,
also the value of the one-year-old tractor. The uniformity of the rate of profits therefore requires, if
production of corn is with tractors:
2(1+r) = p
in the tractor industry
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(2+p)(1+r) = 28/3 + p1 in corn production with new tractors
(2+p1)(1+r) = 28/3
in corn production with one-year-old tractors.
This is a system of three equations in three variables, r, p, p1, and the solution, which is
easily reached by substitution, yields r=100%, p=4, p1=8/3. At the old rate of profits it is convenient
to introduce tractors: if the rate of profits is r=50%, a new tractor costs 3, and the cost of producing
28/3 units of corn with a new tractor is (inclusive of the rate of profits) only 7.5, which is less than
28/3, and would guarantee extra-profits even if tractors only lasted one year instead of two[105].
Thus tractors are introduced.
The replacement of the old corn production method with the new one can happen in many
different ways. Let us assume that it happens as follows (we accept Say’s Law in order to remain
close to Ricardo):
1st year: at the beginning of the year the capitalists have the 300 C produced in the previous
year; they consume 100 C as before; the remaining 200 C are subdivided between 60 C producing
new tractors and 140 C producing corn with the old method. Labour employment is 100 L as
before. The production processes are:
60 CK  30 T0 
 Employment : 100 L .
140 CK  210 C 
2nd year: the capitalists start with 210 C and 30 new tractors; they consume 90 C and
employ the remaining 120 C and 30 T0 as follows:
30T0  60 CK  280 C  30T1 
 Employment: 60 L .
60 CK
 30T0

3rd year: the capitalists start with 30 T0, 30 T1, 280 C; they consume 100 C and produce as
follows:
30 T0  60 CK  280 C  30 T1 

30 T1  60 CK  280 C
 Employment : 90 L .

60 CK  30 T0

Fourth year and following years: the economy is stationary at the production levels of the
third year; the production of 30 new tractors every year replaces the 30 old tractors that are thrown
away, the production of corn is 560 C, employment is 90 L, and capitalist consumption is 380 C.
105
Cf. chapter 2 for a more general analysis of when it is convenient to introduce a new method of
production.
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The capitalists have considerably improved their lot, but the workers are worse off, because
the introduction of tractors caused a decrease of employment, very considerable for a year (from
100 to 60), and only partially compensated subsequently: employment in the new stationary state
has decreased to 90. The Luddites’ fears are confirmed.
1A1.3. The simpler example is the following. Let us assume the same economy as in the
previous example before the invention of tractors. But now we assume that, instead of inventing the
tractor, a new more efficient tilling method is discovered, that allows the production of corn again
with only seed-corn and labour, as follows:
3 C * 1 L → 8 C or (still assuming w=1)
4 CK → 8 C .
This means a rate of profits r = 100% .
If the capitalists allocate to production with the new method the same corn-capital as before,
production rises to 400 C but employment falls to 50 L, one half of what it was.
Subsequent labour employment depends on capitalists’ decisions as to investment. If for
example there is growth at the high rate of 10% per year and there is no further labour-saving
innovation, it still takes 7 years for employment to go back to its previous level.
As we will see in chapter 3, in the marginal approach the possibility is admitted of
unemployment created by the discovery of technologies that, at the given real wage rate, use less
labour per unit of capital than the old technologies, but the resulting unemployment is only
frictional as long as wages are flexible, because the assumption of a decreasing and sufficiently
elastic demand curve for labour means that, were such technological unemployment to arise, a
sufficient decrease of the real wage rate would induce a change in production methods causing an
increase in the demand for labour, until full employment were reached again[106]; unemployment
would only arise during the transition period required for the decrease of wages and for the
adaptation of the ‘form’ of the given stock of capital to the new lower real wage; capital
accumulation is not necessary for the disappearance of technological unemployment, all that is
needed is a change in the average capital-labour ratio adopted by the economic system. In Ricardo,
on the contrary, where there is no notion of a decreasing demand curve for labour nor of a variable
capital-labour ratio, technological unemployment is not frictional, it can only be eliminated by
economic growth (capital accumulation), a process that is not guaranteed and that in any case
106
Depending on how the form of the demand curve for labour, and in particular the fullemployment marginal product of labour, is shifted by innovations, it is not excluded that it might happen that
the new full-employment real wage rate is lower than before; cf. chapter 3.
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requires years and can be countered in the meanwhile by new labour-saving innovations.
The question that obviously arises is whether we, after almost two centuries of further
reflection, should side with Ricardo or with the marginal/neoclassical approach. This question will
be an important thread in subsequent chapters.
Anyway innovations do not necessarily create technological unemployment. If, in the last
example, the new production method had resulted, for example, from the discovery of a way to
reduce the fraction of seed eaten by birds, bringing to:
0.5 C * 1 L → 3 C
then no technological unemployment would have arisen with its introduction. Furthermore, in these
examples we have assumed Say’s Law; the amount of corn-capital destined to production is
determined by the capitalists’ saving decisions, capital is fully utilized, aggregate demand has no
role. If aggregate demand is admitted to be an important influence on decisions to produce and
hence on labour employment, then even labour-saving innovations need not create unemployment if
at the same time aggregate demand increases and stimulates sufficient increases in production. On
the other hand if a decrease of employment is forecasted to be a result of technical progress, the
expectation of a reduction of demand coming from wages may discourage investment and hence
aggregate demand, and the reduction of employment can then be greater than under Say’s Law.
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APPENDIX 2 OF CHAPTER 1 - Some recent reformulations of the labour theory of value.
1A2.1. The considerations advanced in the main text of Ch. 1 and in particular in §1.10
allow an evaluation of recent proposals – that have gained some consensus among Marxist
economists – to redefine the labour theory of value. These proposals attempt to defend the thesis,
that exchange value is produced by labour alone and represents labour time, through a
reinterpretation of prices as forms of labour value, and through a different determination of labour
values themselves. A synthetic mathematical description of the three approaches to be discussed
here will be provided at the end of ch. 2.
The first and most influential new proposal has been put forth by Gérard Duménil (1980,
1983-4) and Duncan Foley (1982, 2000) and is usually referred to as the “New Interpretation”.
Starting from a decision “to hold to the idea that labor produces value, and that money is a form of
value” (Foley 1982 p. 41), it is claimed that “The basic insight of the labor theory of value is its
claim that value forms, money, commodities, and so on, are expressions of abstract social labor.
Thus in any transaction involving value, what is changing hands is control over some part of total
abstract social labor time” (ibid. p. 42); the proposal then is to view “the labor theory of value as the
claim that the money value of the whole mass of net production of commodities expresses the
expenditure of the total social labor in a commodity-producing economy” (ibid. p. 37). Foley insists
that “the important issue for Marx was the idea that money represents social labor time, and that one
can therefore use a measure of the monetary expression of labor appropriately defined at the level of
the aggregate system of commodity production to translate flows of money in real-world capitalist
accounts into flows of labor-time and vice versa” (Foley 2000, pp. 20-21). In order to effect this
‘translation’ of flows of money into flows of labour-time it is postulated that the period’s total
monetary value added “expresses” the living labour performed in that period (the labour embodied
in the period’s net product). For each commodity one can define its labour embodied in the
traditional way, but when the commodity is exchanged against money its seller obtains “control
over” the same percentage, of the “total abstract social labour time” embodied in the net product, as
its monetary value is a percentage of the total monetary value of the net product
107
. Thus the
traditionally defined labour value of a commodity (equal to the labour embodied in it) differs from
107
However, the social product includes other commodities besides those entering the physical net
product, but the approach does not explain over whose labour the sellers of these commodities obtain
‘control’. It is also perplexing that living labour (i.e. employment) may be ‘expressed’ by the prices of a
vector of quantities of commodities, some of which may be negative. These aspects will not be further
discussed, but they confirm the lack of concreteness of the approach that will be evidenced in the text.
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the labour value the commodity’s price represents because the latter corresponds to the amount of
labor ‘expressed’ or ‘represented’ by the money the commodity’s owner obtains (or might obtain)
by selling it. Quantitatively what is done is to choose such a money unit that, given the money
prices of commodities, the exchange value (in terms of money) of the net product becomes
numerically equal to the labour embodied in it as traditionally determined, i.e. equal to total labour
employment: this amounts to choosing as numéraire for relative money prices the physical net
product vector per unit of labour employment; then it is postulated that money magnitudes thus
normalized "express" quantities of abstract labour time, so when one gets money from the sale of a
commodity one in fact obtains labour time. To determine how much labour time one gets control
over, the approach defines the “monetary expression of labour time” (MELT), i.e. the the money
value considered to “express” one unit of labour time, as the money value of the net product per
unit of employment, or 1/m where m is the labour value ‘expressed’ or represented by one unit of
money:
m=
employment
1
=
.
MELT
money value of net product
Multiplying m by the money price of a commodity (or dividing the price by the MELT) one
obtains the labour time over which one gains “control” by selling the commodity. If for example
labour employment in a period is 200,000 labour hours and the money value of the net product is 1
million dollars, then m=0.2, MELT=5, and a commodity worth 100 dollars yields its seller “control”
over 20 hours of labour. In this way the prices of commodities are seen as representing or
“expressing” quantities of abstract labour and can therefore be seen as redistributed labour values.
The approach goes on to view the price of labour-power, i.e. its monetary wage, as
representing an amount of labour value as well, the amount of labour value the worker gets by
selling his labour power against money; this amount of labour value, it is argued, and not the labour
embodied in the average physical wage basket, is the “value of labour-power”, which is accordingly
defined as “the ratio of the money wage to the monetary expression of labour” (Foley 2000 p. 22),
that is, mw if w is the money wage; .
This definition of the value of labor-power identifies it numerically with the share of wages
in the money value of the net product: mw has the total money wage bill at the numerator and the
money value of the net product at the denominator. If there are no land rents (as this literature
generally assumes), the share of profits is the complement to 1 of the share of wages; the rate of
exploitation is defined as the ratio between share of profits and share of wages, on the basis of the
argument that if the money price of the net product is the form taken by the live labour performed in
the period, then its part going to wages represents paid labour while the part going to profits
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represents unpaid wages: thus if workers produce a net product of aggregate money price 10 and
they receive an aggregate money wage bill of 6, it means that 40% of their working day is unpaid
labour
108
; and profits too are 40% of the net product (which coincides with total labour
performed), hence “the paid and unpaid portions of the total expended labor are definitionally equal
to the wage and gross profit share in the net domestic product” (2000 p. 22). Also, since prices
represent or express labour values, one can see the monetary price of any aggregate as representing
an amount of labour value; then when prices are prices of production, the rate of profit can be seen
as a ratio between two amounts of labour value, the labour value expressed by the monetary price of
profits, and the labour value expressed by the monetary price of advanced capital. It is admitted that
Marx’s formula r=S/(C+V) is generally false if calculated on the basis of labours embodied, but it is
argued that the formula becomes correct if one reinterprets the magnitudes appearing in it as the
labour values expressed by prices on the basis of the MELT: “The rate of surplus value is
interpreted in terms of prices of production; the ‘sum of profit = sum of surplus value’ condition
thus becomes a tautology” (Duménil 1983-84 p. 445-46).
1A2.2. It should be clear, on the basis of what has been argued in the main text of ch. 1, that
the New Interpretation totally misses the role of the labour theory of value in Marx, and reduces the
labour theory of value to a choice of coloured glasses, through which to look at prices that remain
unexplained, or independently determined. That the labour theory of value had in Marx an
indispensable role for the determination of normal prices and profits is totally lost sight of. The
really “important issue for Marx” was to prove that once the real wage is determined, the rate of
profit is determined as well. To prove the surplus approach correct on this issue – against the
tendency, in Marx’s time, increasingly to distance economic analysis from the surplus approach and
to find an independent cause for the magnitude of profits – was fundamental for the argument that
Smith’s class-struggle explanation of wage determination (of course enriched by Marx but still
basically the same) was a sufficient foundation for an explanation of all incomes, and thus – leaving
108
Since relative prices differ from relative labours embodied as traditionally defined, if out of 8
hours of daily labour only 4 are paid labour as defined by the New Interpretation because the share of wages
in the value of the net product is 1/2, this does not mean that if with the same technical coefficients the net
product were reduced to include only the workers’ consumption the length of the working day would be
reduced to 4 hours. For example, assume an economy where a gross product consisting of 1 unit of corn
(good 1) and 1 unit of diamonds (good 2) is produced in a certain period by corn-capital and labour
according to: a11⊕aL1→1 unit of corn, a12⊕aL2→1 unit of diamonds, with the following technical
coefficients: a11=0.2, aL1=3, a12=0.8, aL2=2; the wage rate allows the purchase of a subsistence z per unit of
labour, consisting of 0.1 units of corn; wages are advanced; the rate of profit is uniform. Then the paid share
of the working day is 37.5% according to traditional labours embodied; it is 25% according to Duménil and
Foley’s definitions (and it changes with changes in the composition of production).
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no room for abstinence or the other vulgar-economy mystifications – for the conclusion that profits
have an origin analogous to that of the revenue of feudal lords, or of slave owners. Marx’s
enormous labours to understand and surmount the limits of Ricardo’s attempt to reach the same
proof, and his sense of triumph for having achieved what he thought was the solution of the
problem, totally disappear from sight with the New Interpretation. And yet Marx thought he had a
solid theory of the functioning of capitalism, he was persuaded he knew how the rate of profit is
determined; how could he reach that persuasion, if not through the determination, made possible by
the labour theory of value plus the idea of a compensation of deviations, of the aggregates S, and
C+V, whose ratio he thought yielded the rate of profit? That the rate of profit could be determined
starting from the given real wage was the real “basic insight of the labour theory of value”.
Nothing of this survives in Foley’s characterization of “the basic insight of the labour theory
of value” or of “the important issue for Marx”. His approach needs independently determined
relative prices of commodities, which means that it does not tell us anything on how prices or
profits are determined. Surprisingly, Foley presents the thing as an advantage: “The New
Interpretation ... is completely general, in that it is consistent with any theory of price formation”
(2000, p. 23). In this way he admits that the New Interpretation is a quasi-religious statement with
no practical content, irrefutable, a choice of coloured spectacles.[109]
109
An imperfect understanding of the surplus approach, and hence of the role of the labour theory of
value in it, would also seem to emerge from Foley’s 1986 book Understanding Capital: Marx's Economic
Theory, where when contrasting the neoclassical and the Marxian approach to the explanation of the rate of
interest he writes that "It is not clear that these two analyses are contradictory" (p. 48) and gives no analytical
reason why one approach chooses to adopt “the subjective point of view of the consumer”, while the other
one chooses the “objective” point of view of “seeing” commodities as “carrying a certain part of the social
labor time of the society”: both choices are apparently defensible, a matter of “point of view” (ibid.). The
radical difference in the explanation of wages is not stressed; it is nowhere noted that if the marginalist factor
substitution mechanisms existed and determined the working of the economy in the way argued by
neoclassical theory, then the view of profits as originating in the exploitation of labour would be disputable,
because the sacrifice consisting of abstinence from present consumption could be plausibly argued to
contribute to social production in a way strictly analogous to the contribution of the sacrifice consisting of
labour, and therefore to be analogously deserving of a reward (as will be made clear in ch. 3). It is the view
that no such role can be attributed to abstinence because the marginalist substitution mechanisms do not
exist, and that wages are kept below their potential maximum simply by the greater bargaining power of the
capitalist class, that allows one to speak of exploitation of labour. Foley on the contrary writes: “If you do
not accept the postulate that labor produces the whole value added, you will not see much basis for the claim
that wage-labor is exploitative” (1986 p. 39). This expresses the view criticized in §1.10.4 that the validity of
the labour theory of value is indispensable to exclude a reward-deserving contribution of the capitalist to
production; but note that the thesis that “labor produces the whole value added” is presented as a postulate
that one may accept or not, not as a hypothesis susceptible of confirmation, in accord with the New
Interpretation where the claim that “labor produces the whole value added” is precisely a postulate not
susceptible of confirmation or disproof because it has no practical implication – with the consequence that
the existence of exploitation too becomes a postulate, a matter of point of view.
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1A2.3. Foley has subsequently tried to defend the usefulness of the approach as follows: “It
opens the way to an interpretation of the substantive parts of Marx’s theory (his discussion of
relative surplus value, induced technical change in capitalism, and the long-term tendencies of
capital accumulation, or his theory of the circuit of capital, for example) as testable empirical
hypotheses that can be confronted with widely available statistical data” (2000 p. 23); “while the
New Interpretation does not itself propose any operational hypotheses about the evolution of the
monetary expression of labor time or the rate of exploitation, its definitional framework allows us to
measure the evolution of the monetary expression of labor time or the rate of exploitation in real
capitalist economies, and to link these magnitudes to other aspects of capital accumulation, such as
the bias of technical change, or the class relations of particular societies.” (2000 p. 28). But, given
the redefinitions, what one would be examining is hypotheses, not about the labour embodied
magnitudes Marx talked about, but rather about the wage share and other well-known monetary
magnitudes, and to call them with the different terminology proposed by the New Interpretation
would only obscure the issues
110
. And even if the choice of the net product per unit of labour as
numéraire for monetary magnitudes were to allow the reaching of new insights, still it would remain
mysterious how calling its monetary value "monetary expression of labour" could add to our
understanding of the forces at work.
Duménil's (1980, 1983-84) defence of the usefulness of the New Interpretation is no better.
He defines the labour theory of value as identical with the law of value, by which he intends the
claim that value is produced by labour (and prices only redistribute it). To support this claim
Duménil argues that there is a substance which does not change when the product vector is given
and prices change, a substance which must exist because (with Q the vector of quantities produced
and P1, P2, ... different price vectors):
On the basis of the same quantities, any variation in the price system settles a question
of distribution. If prices change, the wealth of society is distributed in a different pattern, but
the aggregate quantity expresses a type of invariance ... If the system of prices is allowed to
vary, bearing in mind that only the distribution of the product is being modified:
P1Q = P2Q = ... = PmQ.
To proceed in this manner is to implicitly refer to a social substance that is conserved
through variations of prices. (Duménil 1983-84 p. 430)
After thus taking for granted what should be proved (those equalities only indicate the
choice of the social product vector as numéraire, with no implication of existence of an unvarying
110
An example of such a risk of confusion was given in the preceding footnote.
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‘substance’), Duménil argues that since this substance is increased by production, it must consist of
labour, because “only human labour is productive ... a machine does not produce ... Land does not
produce by itself either ... To maintain that land itself is productive is to reject the labor theory of
value” (1983-84 p. 432-33), again taking for granted what should be proved, and in addition
confusing production of use value and production of exchange value, a mistake that Marx
vigorously condemned. Then Duménil presents essentially the same reinterpretation of prices as
redistributed amounts of labour as Foley, and he finds “the explanatory power of the labor theory of
value” thus redefined to lie in the fact that “It allows us to interpret the price system as a
reallocation of social labor according to strictly defined rules consistent with the capitalist character
of society. The act of pricing does not create the social substance, but merely distributes it.” (p.
436). In other words, the redefined labour theory of value does not explain anything, its
"explanatory power" consists of ... repeating its claims 111.
Why such a dogmatic attachment to the labour theory of value, capable of rendering
Duménil blind to the circularity of his arguments? Most probably, the reason is the identification of
the validity of the labour theory of value in some form with the possibility to argue that labour is
exploited, as revealed by statements such as that Sraffa's analysis “achieves the exploit of being at
the same time a critique of Marxist analysis and of neoclassical analysis. It believes it refutes the
first because it formalizes the prices of production while discarding the theory of value (and with
the same act exploitation too)” 112 (1980 p. 9).
In conclusion, behind the proposal of the New Interpretation there appears to be a lack of
understanding of the role of the labour theory of value in Marx
113
, that entails the belief that the
111
Duménil explicitly denies that the labour theory of value had the role in Marx of allowing the
determination of exchange values and of the rate of profit: “The explanatory power of the law of value does
not lie in the mathematical derivation of this or that quantitative tendency” (1983-84 p. 435). It is not noticed
that this view leaves in the dark how Marx thought that the rate of profit is determined; anyway how to
determine the rate of profit is not considered an important problem by Duménil, who writes “to calculate
prices of production on the basis of a mathematical description of a technique without ever mentioning value
... is certainly no great discovery” (ibid. p. 434). Seldom one meets such an enormous misapprehension of
the relevance of scientific advances.
“Sraffa a ... construit une Économie politique ...[qui] réussit le tour de force d’être à la fois la
critique de l’analyse marxiste et de l’analyse néoclassique. Elle croit réfuter la première parce qu’elle
formalise les prix the production en écartant la théorie de la valeur (du même coup de l’exploitation).” The
view of Sraffa’s analysis as a refutation of Marx’s analysis has been aided by the unhappy choice of
Steedman (1977) to concentrate on the aspects of Marx’s analyses in need of correction, omitting to stress
that Sraffa, by showing that the rate of profit and prices of production can be determined on the basis of the
same data Marx starts from, confirms the consistency of Marx’s surplus approach and therefore strengthens
it.
112
113
This is also shown by how labour heterogeneity is treated by them in a recent joint article. Labour
heterogeneity did not prevent Ricardo or Marx from talking of labour embodied as a homogeneous
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possibility to argue that labour is exploited depends on viewing exchange value as an amount of
labour and profits as an amount of surplus labour, rather than on the overall validity of the surplus
approach. The argument of Section 1.10 aimed precisely at surmounting these misunderstandings.
Of course profits would not exist if there were no surplus labour, but this tells us nothing on why
surplus labour exists; it's the answer to this ‘why’ – the theory of wages – that determines whether
one can speak of labour exploitation. So a resumption and development of Marx's approach requires
proving that his approach to wages allows a satisfactory explanation of price formation, rate of
profit, and the other aspects of the capitalist economy within a theoretical structure free of logical
inconsistencies and yielding predictions confirmed by the historical record. To this task the New
Interpretation risks causing only damage, by obscuring the specificity of the surplus approach and
its differences from the marginal one.
1A2.4. From a partly different starting point very much the same redefinition of the labour
theory of value is reached by Wolff, Roberts and Callari (1982; WRC below) (also Wolff, Callari
and Roberts (1984)) owing to the same idea of money as a form of (labour) value and hence of
monetary prices as representing quantities of (redistributed) labour. WRC accept that prices of
production are fundamental to the explanation of price formation and of the rate of profit, and that
Sraffa-type equations show how to determine them on the basis of a given real wage. But they argue
that prices of production can all the same be seen as quantities of labour, as redistributed labour
values, and the rate of profit can be seen as the ratio between surplus labour value and the labour
value of advanced capital. The gist of their reasoning can be re-expressed in rather simple terms.
Marx, WRC contend, argues that the labour value of a commodity is the living labour directly
magnitude because they ‘reduced’ labour to homogeneity in proportion to relative wages, i.e. stipulated that
a type A labour paid twice as much as a type B labour produces twice as much value in the same time (and
the rate of exploitation is therefore the same): which is what their analytics required them to do, because
labours embodied had to be proportional to wages embodied in order to be proportional to relative prices
when the rate of profit was zero or the organic composition of capital was uniform. On the contrary Duménil,
Foley and Lévy (2009 p. 560) state that “Wages are not necessarily proportional to the value productivity of
workers” (the opposite of what Marx assumed) and then limit themselves to proposing how in the New
Interpretation one should derive the rates of exploitation of different workers from given relative value
productivities of heterogeneous labour. On what determines these different value productivities they remain
silent, saying only that in order to determine them “some additional assumption about relative rates of
exploitation (which Marx often explicitly assumes to be equal) is required”: where the lack of understanding
again emerges in that ‘often’, and no reason is indicated why Marx assumed equal rates of exploitation, as if
he might as well have made a different assumption. But such a view is in accord with the New Interpretation,
where prices are determined independently of labour values and can ‘express’ a redistribution of labour
values whatever the way the latter are determined (as will be shown in ch. 2), so one loses the classical
analytically necessary criterion for determining the relative value-creating capacities of different labours, and
no other necessary criterion replaces it; thus relative value-creating capacites of different types of labour
remain undetermined and need some additional criterion in order to be determined.
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performed in its production, plus the labour value transferred to the commodity by the nonwage
capital inputs used up in its production; but he argues in Volume 3 of Capital that prices of
production represent amounts of labour value, but of redistributed labour value; shouldn’t then we
see the nonwage capital inputs as bringing to the production process and transferring to the labour
value of the product these redistributed labour values? Since labour values have already been
redistributed when capital goods are bought at prices of production, WRC argue that the labour
value a capital good can transfer to its product is only the labour value that remains ‘attached to’ the
capital good after that redistribution. Let us accept this as a postulate and in order to understand its
implications let us ask where it takes us (in the simple case of single production, only circulating
capital). We must distinguish the labour value transferred to a commodity by its inputs, to be called
pre-redistribution labour value, from the post-redistribution labour value that remains attached to
the commodity after the redistribution of labour values that determines prices of production; if the
commodity is used as means of production, since it is bought at its price of production it is its postredistribution labour value that is then tranferred forward to form, together with the labour value
added by live labour l, the pre-redistribution labour value of the product; then aggregate preredistribution labour value is redistributed and becomes prices of production, that are therefore
quantities of (post-redistribution) labour value. The (post-redistribution) labour value of the
constant capital c of an industry coincides with the price of production of those nonwage capital
inputs. The price of production of wage goods too is a quantity of (redistributed) labour value;
hence the post-redistribution labour value of labour-power is the price of production of the wage
basket. Thus, according to WRC, Marx’s determination of the pre-redistribution labour value of a
commodity in Vol. III of Capital can still be written as λ=c+v+s=c+l , except that c and v are now
the price of production respectively of the nonwage capital inputs and of the wages, seen as
quantities of redistributed labour value; surplus labour is l minus the price of production of the
wage basket. In the entire economy the labour value of the social product is then C+L, where C is
the aggregate value in prices of production of the nonwage capital inputs but is seen as a quantity of
labour value, and L is total employment. (However, the numerical value of C depends on the
numéraire chosen; I will come back on this shortly.) Now let us apply Marx’s idea that this labour
value redistributes itself across products so as to generate the prices associated with a uniform rate
of profit over the capital advanced C+V (evaluted, remember, in post-redistribution labour values
i.e. at prices of production). The total price of production of the social product is again C+L
because it comes out of a redistribution of labour value that does not alter its amount, hence
aggregate profit is C+L–(C+V). The rate of profit is determined by
[C+L–(C+V)]/(C+V)=(L–V)/(C+V)=r.
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But, supposing relative prices of production to be known (the legitimacy of this assumption
will be soon discussed), these are relative prices; the numerical values of C and V depend on the
standard of value, or numéraire, that one chooses. However, if the total price of production of the
social product is C+L while the price of production of constant capital is C, then L must be the price
of production of the net product. Thus WRC set the aggregate price of production of the net product
equal to labour employment L (cf. equation (6), p. 579), the same choice of the net product vector
per unit of labour as numéraire as in the New Interpretation (but applied now to prices of production
while in the New Interpretation prices are unexplained). They claim that this respects Marx’s
statement, at the beginning of chapter 51 of Vol. III of Capital, that the (labour) value added
annually by live labour divides itself among wages and profits (land rents are neglected by our
authors). And this gives a nice result: when will the ratio (L–V)/(C+V) correctly determine r? at the
denominator there is the aggregate price of production of capital advances; hence the rate of profit r
will be correctly determined if at the numerator there is the aggregate price of production of profits;
this will be the case if L, employment, coincides with the aggregate price of production of the net
product, because then L minus V (total wages at prices of production) is profits.
With their reinterpretation of prices of production as redistributed labour values our authors
obtain that the social product is the same, C+L, in labour values and in prices of production; that the
same equality holds for profits and surplus labour; and that the rate of profit is a ratio between
unpaid labour and the sum of ‘dead’ labour and paid labour – a recuperation of the equalities
claimed by Marx, that cannot all simultaneously hold if labour values are defined as traditionally.
A basic difficulty of this approach as an interpretation of what Marx really meant is that it
requires that the correct relative production prices (but then also the rate of profit!) be already
determined when one writes down (L–V)/(C+V), otherwise knowledge of quantities produced,
production methods and wage basket plus the choice of a numéraire do not suffice to determine V
and C: for this purpose the authors have recourse to Sraffian price equations (cf. equation (2), p.
578), but these were not available to Marx: Marx could believe he had found how the rate of profit
was determined only because he thought he had found a way to determine the numerator and
denominator of the ratio yielding the rate of profit before the rate of profit itself. Therefore the
traditional interpretation of S and C+V in Marx’s equation r=S/(C+V) remains clearly more
convincing
114
. Indeed WRC argue at one point that “Nowhere in his works did Marx carry this
Then Marx’s identification of the aggregate price of production of the net product with labour
employment is only a consequence of his ‘compensation of deviations’ thesis that made him believe that the
equality between sum of labour values and sum of prices held for the social product and also separately for C
and for V, the thesis (clearly argued in Vol. III of Capital) that allowed him to conclude that the same
114
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project, like some of his others, through to completion” (p. 568), thus suggesting that their proposal
is not exegetically faithful but rather reconstructs from some hints what Marx would have arrived at
if (with the help of Sraffa?) he had been able to “carry his project through to completion”. Well,
perhaps had he had Sraffa's equations at his disposal, Marx would have abandoned the labour
theory of value! Indeed one may ask, since in this approach the prices of production are determined
by Sraffian equations, what is gained by viewing these prices as redistributed amounts of labour
time, a redistribution visualized (like in the New Interpretation) through an arbitrary choice of
numéraire? Aren't the authors again putting on coloured spectacles that do not add anything to our
understanding of the economic process? Can one find in these authors more convincing arguments
than in Foley or Duménil in support of a usefulness of viewing prices as redistributed amounts of
labour? The only argument to such an effect supplied by the authors is that “the basic thrust of the
transformation discussions in Capital III is to show that the particular form taken by that income
(average profit) can be conceived as a specific relation between paid and unpaid labor time” (1982
p. 568), a sentence reworded later in the article as: “A Sraffian approach uses the concept of
‘surplus’ only in the restricted sense of a physical surplus product ... In contrast, Marx’s focus on
class relations as his object of discourse requires him constantly to link the existence within
capitalism of a physical surplus to the parallel necessity for there to be surplus labor which creates
surplus value.” (ibid. p. 580) But if employment, production techniques and composition of the
average wage basket
115
are given, the Sraffian equations coupled with the usual definition of
labours embodied suffice to highlight a univocal connection between the rate of profit and surplus
or unpaid labour, while WRC’s thesis that the exchange value of profits coincides with surplus
labour value results simply from an opportune choice of units and adds nothing to the
independently determined relative prices and profit rate. Given the weakness of the argument, one is
given to suspect that here too the real motivation of the authors is a desire to view prices as in fact
quantities of labour, explained again by the mistaken belief that unless exchange value is nothing
but labour, the characterization of profits as originating in the exploitation of labour is endangered.
1A2.5. The third redefinition we consider has been proposed by the Temporal Single System
(TSS) approach, cf. Freeman and Carchedi (1996a). This approach has produced a considerable and
partly diverse literature which cannot be analyzed in any detail here. We concentrate on its central
idea. The approach argues that market prices too should be seen as redistributed labour values, and
equality also held for S and therefore r=S/(C+V).
115
This composition might also be taken as not given but a function of the rate of profit.
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that labour values reflect the historically performed labour. Prices are always, by definition, forms
of value, redistributed labours embodied; it is as if commodities were containers of amounts of a
fluid produced by living labour; through valuation of the commodities against money (again viewed
as representing labour time) this fluid gets somewhat magically redistributed among commodities
so as to render the value (amount of labour) attached to each commodity proportional to its market
price; if the commodity is used as a means of production, the fluid ‘human labour’ thus attached to
it is then transferred to the product: “the value transferred by constant capital is equal to the value as
measured by the money advanced to purchase the elements of this capital” (Freeman and Carchedi
1996b p. xi). Hence, supposing production to happen in separate one-period cycles, it suffices that
for period t–1 relative market prices be given and the price level be fixed so as to render the total
price of the social product equal to the total labour embodied in it, and then the labour embodied
(before the redistribution operated by market prices) in a commodity produced in period t can be
determined as the sum of the living labour expended in its direct production, plus the historical
normalized market price of the nonwage capital inputs, which represents the fraction of the total
labour embodied in the social product of period t-1 that has gone into those means of production so
as to make their labour content proportional to their market price. The sum of these preredistribution labour values of the commodities produced in period t is then redistributed among
these commodities in proportion to their market prices, which come again to represent quantities of
labour once they are normalized so that the total market price of the social product equals the total
labour embodied in it.116 Given this reintepretation of prices as in fact quantities of labour, Marx’s
several equalities between sums of labour values and sums of prices are all recuperated here too, by
definition 117.
116
As pointed out by Veneziani (2004) the reference to actual historical past prices in this procedure
creates a problem of infinite regress. The hypothesized redistribution of labours embodied due to the
exchange process renders relative post-redistribution labour values equal by assumption to relative market
prices, but the approach is unable to determine the magnitudes of the labours embodied to be redistributed,
unless one assumes the magnitudes of the labour values of the constant and variable capital goods utilized to
produce the several goods to be known; but this requires in turn the knowledge of the magnitudes of the
labour values of the capital goods used by those capital goods, ad infinitum. In conclusion, labour values are
indeterminable in their amounts; only relative post-redistribution labour values are determinable (if market
prices are known), and this is trivial but also useless, because they coincide with relative market prices by
assumption.
117
Cf. Appendix 1 to ch. 2 below. Prices of production are redefined (Kliman and McGlone 1999 p.
50) as those prices at time t that, on the basis of given input prices (prices of time t-1) and of an assumption
of sum of values equal to sum of prices, would determine a uniform rate of profit on the capital advanced.
The relevance of such a notion of prices of production is unclear, because it lacks persistence and therefore
cannot be an indicator of the average around which market prices gravitate. But as will be explained shortly
the TSS authors are against the gravitation idea.
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This redefinition of labour values again adds nothing to our understanding of the forces at
work in the economy: it too amounts to a decision to view given, unexplained prices as amounts of
labour, with no concrete consequence for the explanation of economic phenomena
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, and again it
creates the problem that how Marx thought the rate of profit is determined becomes mysterious.
Also, the same question arises as with the two other approaches, what is the advantage of viewing
independently determined prices as amounts of labour. The answer lies, according to the TSS
advocates, in the more correct interpretation thus reached of Marx on value and price, with the
implications (i) that the criticisms advanced by Bortkiewicz against Marx’s ‘solution’ of the
transformation problem are misplaced, and (ii) that one can at last abandon the dominant but false
interpretation of Marx that reduces him to a general equilibrium theorist, and in this way hopefully
the road is opened up toward more fruitful economic analyses.
This is because the advocates of the TSS approach argue that their approach to value is in
fact Marx’s own, and that the traditional interpretation of how Marx defines labour values is
mistaken: the TSS authors contend that Marx defines labour values according to the traditional
interpretation only in Volume I of Capital, where for pedagogical purposes Marx assumes prices
equal to values; in Volume III, they argue, Marx defines labour values in the way they indicate.
Since the TSS labour values depend on past prices and have no role in determining relative prices,
an implication of this thesis is that Marx did not try to use independently determined labour values
in order to determine prices of production and the rate of profit; it is even denied that Marx was
interested in determining prices assumed to be the same for a good as input and as output (an
approach that TSS authors call 'simultaneist'), because Marx knew that prices are incessantly
changing.
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The irrelevance of the TSS redefinition of labour values is shown by the attempt by Kliman
(1996) to criticize Okishio’s theorem, an important motivation behind the birth of the TSS approach. The
formal analysis concentrates on the behaviour of the ex-post, or realized, monetary rate of profit on historical
monetary capital advances when a continuous flow of innovations causes a continuous decrease of labour per
unit of output; as one might have expected from the TSS identification of price and value, given the
assumptions on technology the analysis is only dependent on the assumptions on the behaviour of money
prices, assumptions unaffected by whether one views these prices as ‘expressing’ labour or not. With the
occasion a comment may be advanced, not on the model, whose assumptions are debatable and anyway do
not refute Okishio’s theorem, but rather on Kliman’s general assessment of Okishio’s theorem. Interestingly
he concedes that, if sufficient time is allowed, “capital does eventually become revalued in practice at its
new, lower reproduction cost ... Here Marx and Sraffians agree ... It is not an exaggeration, then, to
understand the comparative static equilibria of Okishio’s model as a comparison of slumps.” (p. 212-13) It
seems to escape him that in this way he admits that if one looks at the average effect of innovations over a
succession of time periods long enough so that the transitional disruptive effects of innovations can be
presumed to be equally present on average in all periods, then it will be the tendency of the normal or
‘Sraffian’ rate of profit that will give us indications on the tendency of the average over booms and slumps of
the realized (and perhaps constantly lower than the normal) ex-post rate of profit; now, Marx was interested
precisely in the very long run effects of technical progress.
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This interpretation of Marx, unique to the TSS approach, flies in the face of the textual
evidence, but we refer for this to Mongiovi (2002) and the literature critical of the TSS approach
there cited
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. A double misunderstanding appears to lie behind the obstinacy with which the TSS
adherents defend their interpretation of Marx: first, the belief that the writing down of ‘Sraffian’
price equations means to accept general equilibrium theory: “the formalization of Marx’s theory of
value which descends from Bortkiewicz is a dead end which has served primarily to assimilate
Marx to General Competitive Equilibrium” (Freeman and Carchedi 1996b p. xiii); second, the belief
that admitting a mistake in Marx’s solution of the ‘transformation problem’ means “the failure of
his project” (ibid. p. ix). Dispelling the first misunderstanding will also dispel the second one, which
we have already discussed but while assuming some familiarity of the reader with the difference
between the surplus approach and the marginal/neoclassical approach, a familiarity that on the
contrary appears to be lacking at least in some of the TSS economists.
Thus Freeman interprets the ‘Sraffian’ equations as reflecting an assumption that “All prices
are constant” and comments: “Swallow this and it transports you to a different place from the planet
earth: a timeless wonderland in which life repeats endlessly and unchangingly; the world of the
dormhouse and the white rabbit: the world of General Equilibrium.” (Freeman 1996b p. 19). In fact
in modern general equilibriun theory prices are not constant (cf. ch. 8), but apart from this mistake
what seems to emerge in this sentence is an inability to distinguish market prices from normal
prices: Freeman seems to think that what economic theory determines must be what one can
119
We add one passage by Marx not mentioned by Mongiovi, a footnote in vol. I of Capital (Bk. I,
Pt. 2, Ch. 5, last page, fn. 24; p. 269 of the 1970 paperback Penguin edition):
....The continual oscillations in prices, their rise and fall, compensate each other, cancel each other
out, and carry out their own reduction to an average price which is their internal regulator. This average price
is the guiding light of the merchant or the manufacturer in every undertaking of a lengthy nature. The
manufacturer knows that if a long period of time is considered, commodities are sold at neither over or
under, but at, their average price. If, therefore, he were at all interested in disinterested thinking, he would
formulate the problem of the formation of capital as follows: how can we account for the origin of capital on
the assumption that prices are regulated by the average price, i.e. ultimately by the value of commodities? I
say ‘ultimately’ because average prices do not directly coincide with the values of commodities, as Adam
Smith, Ricardo, and others believe.
In these lines Marx accepts the idea of a gravitation of market prices around long-period ‘average
prices’ whose description identifies them as the prices of production of Ricardo and of Volume III of Capital
(the term 'prices of production' is not introduced in this quote because requiring further theoretical
developments postponed by Marx to volume III of Capital, but it is announced that average prices “do not
directly coincide with the [labour] values of commodities”). The explicit characterization in terms of long
periods also confirms that Marx thought of the ‘average price’ of a good as being the same as an input and as
an output. The absence of textual basis for the TSS interpretation is also evident in the fact that, from an
author as critical of others as Marx was, one would expect very explicit and repeated statements stressing his
rejection of the indispensable role assigned by Smith and Ricardo to normal or natural or production prices
for an understanding of market phenomena – if he really had differed from them in these respects. But there
are no such statements.
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immediately observe, so if the equations treat the price of a good at the beginning and at the end of
a period as coinciding it means that those equations cannot apply to an economy where this is
generally not rigorously true. On the contrary, from Smith onwards the traditional argument – only
abandoned by the modern versions of general equilibrium theory – has been that little can be said
about the market price of a commodity at each instant because of the indefinite multitude of
possible accidental and transitory influences affecting it, but that the behaviour over sufficiently
long periods of its average can be approximated by looking at the corresponding normal price,
because the search for maximum profits causes investment to go in greater proportion toward the
sectors where the rate of profit is higher, and the resulting changes in supply tend to push the rates
of profit toward uniformity; Marx agrees, and at least sometimes some of the TSS adherents too:
“As Carchedi and de Haan argue, prices of production are a tendency produced by the actual
movement of market prices” (Freeeman and Carchedi 1996b p. xvii). Now, it is true that much the
same distinction market price/normal price can be found in traditional marginalist authors from
Jevons to Wicksell and Knight, but this does not at all mean a fundamental similarity between the
theory of capitalism of these authors and the one of Smith or Ricardo or Marx, as shown for
example by the absence in the latter authors of any notion of a decreasing demand curve for labour.
Freeman also argues that “the simultaneous equation formalism introduced by Bortkiewicz ...
enshrines in mathematically pure form the dogmatic and false proposition of Jean-Baptiste Say that
supply creates its own demand” (Freeman 1996b p. 3), but this is another misunderstanding. The
tendency toward a uniform rate of profit does not imply Say’s Law, it is compatible with any theory
of the level of aggregate demand; as explained in Garegnani (1978), Say’s Law was accepted by
Ricardo but only because of an insufficient analysis of whether savings will translate into
investment; the surplus approach does not provide analytical elements proving the validity of Say’s
Law. It is only in the marginal approach, with its factor substitution mechanisms which are argued
to ensure the tendency toward equilibrium on all factor markets, that Say’s Law acquires analytical
support. But the Sraffian critique of neoclassical capital theory has undermined those factor
substitution mechanisms and therefore the neoclassical justification of Say’s Law. The
reconstruction of the theory of aggregate investment (cf. here ch. 13) no doubt must deny Say’s
Law and make room for an influence of accelerator-multiplier interactions, credit crunches, debt
deflations, and so on, thus admitting the possibility and probably likelihood of instabilities and
crises in accord with Marx; but there is no contradiction between admitting on the one hand
instabilities of the aggregate level of investment, and admitting on the other hand that the, perhaps
wildly fluctuating, amount of total investment will have a composition which will tend to change in
favour of the sectors offering the better prospects of profit, and that this will tend to equalize the
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rates of profit. Attributing a central explanatory role to normal prices in no way denies instability
and crises.
The contrary view may derive from an inability to get rid of the marginalist belief,
inculcated by standard economic education, that the existence of technical and consumer choices, if
allowed fully to bring out its effects, generates decreasing demand curves for labour and for capital
(cf. here chapter 3). In the Cambridge controversies in capital theory it has been proved that this is
not the case (cf. here chapter 7), thereby showing that the absence of those decreasing factor
demand curves in Smith, Ricardo or Marx, far from being a deficiency of their analyses, prevented
them from ‘shunting the car of economic science on to a wrong line’, a reversal of Jevons’s
evaluation of Ricardo: his evaluation appears to apply to the marginal approach instead. There is
therefore no contradiction between Marx’s adherence to the method of normal positions, and his
rejection of any spontaneous tendency of the capitalist economy toward full employment or smooth
growth.
1A2.6. To sum up the argument of this Appendix: the birth in recent decades of attempts to
redefine or reinterpret the labour theory of value appears motivated by a fear that being content with
‘Sraffian’ price equations for the purpose of determining normal prices and the rate of profit would
amount to losing essential insights of Marx on the nature and ‘the laws of motion' of capitalism. In
fact no such essential insight is lost, and the ‘Sraffian’ equations strengthen Marx by showing that
on the basis of the data he started from (real wage and conditions of production) it is indeed
possible to determine the rate of profit and prices of production, and to study how they are affected
by changes in those data. The fear motivating these attempts appears due to a survival of wrong
interpretations of the connection between labour theory of value and possibility to interpret profits
as due to exploitation, plus an unclear grasp of the difference between surplus approach and
marginal approach. That these attempts cannot be seen as more correct interpretations of Marx is
evident, if for no other reason, because they cannot explain how Marx could think he knew how the
rate of profit is determined; that they are sterile is confirmed by their inability to produce
convincing arguments for their usefulness – they amount to a decision to view independently
determined prices as representing amounts of labour, a view that adds nothing to our understanding
of ‘the laws of motion of modern society’.
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