MARSHALL AND KEYNES ON SUPPLY BEHAVIOUR
Gerson LIMA1
1. INTRODUCTION
In the British Palgrave Dictionary (1987) Prof. Harcourt states that post Keynesian
economics has no universal interpretation and analyses three of its strands. One of these,
associated with the works by DAVIDSON & SMOLENSKY (1964) and WEINTRAUB
(1958), leads to Marshall and to supply and demand analysis. As Davidson quoted in his
Preface, for Keynes "the true law relating the aggregate demand and supply functions ... is
a vitally important chapter of economic theory". This work is intended to be a contribution
in this field: based upon Marshallian principles on producer's behaviour it proposes a
notion of supply which is connected with Keynesian features. The proposition is that the
notion of supply behaviour and supply curve developed here is the one Keynes searched for
on the work of Marshall.
Neoclassical theory, following its process of "marginalization" of economic notions
pointed out by PASINETTI (1961, page 20), has tried to "appropriate" the notion of supply
and demand. However, considering that there is no neoclassical theory of supply outside
the world of perfect competition, this appropriation cannot be said to be a success.
Accordingly, the broad purpose of this study is to suggest a possible way for emancipating
supply and demand analysis, in such a way that it would no longer necessarily be seen as
stemming exclusively from a procedure of optimization through differential calculus. This
process of marginalization tries to involve Marshall himself, by absorbing his principles on
supply into the neoclassical foundations, but this involvement is not stressed here; instead,
it is suggested that there are at least two Marshallian approaches to supply behaviour.
The first Marshallian approach to supply is well known: it is basically connected with his
peculiar definition of short run/long run and with his supply curve, which is constructed on
the assumption that price is equal to marginal cost, or more specifically, to his definition of
marginal cost. These notions have traditionally been associated with marginalist principles,
thus giving Marshall the role of pioneer of neoclassical theory. This approach and the lack
of compatibility between different Marshallian approaches are outside the scope of this
work.
The second Marshallian approach stems from his analysis of classical notions prevailing at
his time. This approach, to which economic litterature has deserved less attention than the
first one, is concentrated on the description of price formation in the very short run, or daily
market period, when real transactions take place and real prices are observed, but there is
no clearing: production never matches consumption, which means that in the daily market
there is no supply curve and no equilibrium. The specific purpose of this paper is to
demonstrate that Marshall's description of the daily market may be developed into a
producers' decision-making process which in turn may define a dynamic market model for
price and production setting. This model may bring about a long run theoretical status in
1
The Federal University of Paraná, Brazil. An earlier version of this paper was presented at the 1993 Meeting
of the National Association of Post-Graduation Courses in Economics, Belo Horizonte, Brazil.
which the notion of supply curve emerges, providing thus a general model for supply and
demand analysis. A comprehensive empirical example is presented.
This paper is organized as follows: section 2 presents Marshallian principles on the very
short run, and proposes a simple mathematical formalization of the decision-making
process described by Marshall; section 3 develops the decision-making process into a
dynamic analytical model for price formation and production setting, from which the
supply curve may be brought about, and section 4 develops an empirical example. These
sections condense the theoretical discussion and empirical work at the microeconomic
level developed in LIMA (1992a) and, finally, section 5 outlines the link between
Marshallian microeconomics and Keynesian macroeconomics. Unless specified, page
numbers in brackets refer to the Marshall's "Principles".
2. MARSHALLIAN PRINCIPLES ON SUPPLY BEHAVIOUR
The Marshallian method of economic analysis may be described by a simple proposition:
"the general theory of the equilibrium of demand and supply is a Fundamental Idea"
(Preface to the first edition). His model has thus two groups of agents, consumers and
producers, who interact with each other in such a way that, under certain conditions, a level
of price will be expected to allow the consumption amount to match the production
amount. Accordingly, the system must have three basic endogenous variables:
consumption, price and production. The final objective is thus to build a market model,
based upon the relations between supply and demand, to explain how the levels of those
endogenous variables are determined.
This is Marshall's subject in Book V of his "Principles of Economics", from which two
particularly important assumptions must be stressed. Firstly, competition between agents is
said to be "free"; and this proposition has been interpreted by specialists such as SHOVE
(1942), HAGUE (1958), and NEWMAN (1960) as meaning that Marshall assumes that
imperfect competition prevails; more specifically, GILLEBAUD (1952), MAXWELL
(1958), and SHACKLE (1967) propose that Marshall rejects the notion of perfect
competition. The intensity of competition is a crucial feature only for neoclassical theory
and its discussion is outside the scope of this paper; it is here sufficient to admit, without
any pretension to precision, that "free" competition is an indefinite blend of some rivalry
and some cooperation.
Secondly, although Marshall supposes buyers and sellers to be optimizing agents, he
carefully avoids the neoclassical procedure of profit maximization through differential
calculus. His unity of analysis on the producer side is, instead of the single producer, the
industry of a homogeneous product; when it is necessary to explain the behaviour of the
industry, he uses the notion of a "representative firm". Comprehensive analysis of the
representative firm may be found in FRISCH (1950), HAGUE (1958), and MAXWELL
(1958), with divergent conclusions.
Most of this paper is dedicated to the analysis of one principle which seems to be especially
important for Marshall: the time component, or the dynamic movement of the endogenous
variables towards their equilibrium levels. The purpose here is to stress that there is a
Marshallian decision-making model which contains in a latent form a natural dynamic
component which can be isolated and formalized mathematically in an explicit form. This
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analysis is intrinsically associated with the Marshallian notions of gravitation and
equilibrium.
In its simplest form, the Marshallian model, or more generically the supply-and-demand
model, is composed of at least three simultaneous equations, because the endogenous
variables are at least three: consumption, price, and production. In Marshall terms (Preface
to the first edition), one must be "sure that he has enough, and only enough, premisses for
his conclusions (i. e. that his equations are neither more nor less in number than his
unknowns)". One of the equations is the demand curve, which provides a relation between
price and consumption. The second relation could be the equilibrium condition: the
equality between the amount demanded and the amount produced.
Considering that equilibrium is unfeasible in the real world, Marshall proposes that the
market clears for any commodity only under "normal" conditions, defining as normal a
theoretical supply curve in which "the supply price of any amount of that commodity may
be taken to be its normal expenses of production" (page 285). The normal supply curve is
thus the third relation searched for. Marshall breakes normal conditions into two
categories: the short and the long run. In the short run the industrial production capacity is
given, and in the long run all factors are variable and may be adapted to the level of
demand. However, there is no clear line between long and short run: "Nature knows no
absolute partitions of time into long periods and short" (Preface to the first edition); in any
period of time "price is governed by the relations between demand and supply" (page 314).
Beyond the short and the long run there is also the "very short run", or the "daily market"
period, in which the Marshallian normal conditions cannot be observed. In the daily market
period production only ever matches consumption incidentally: market does not necessarily
clear in actual day-to-day transactions. There is no supply curve in the daily market;
production is given and hence "Market values are governed by the relation of demand to
stocks actually in the market" (page 309), with less influence from cost. This is the subject
of this section: the Marshallian principles on producer behaviour in the daily market
period.
2.1. The Marshallian Decision-Making Model
It is in the daily market that actual trading takes place, including the purchase of those
production factors which will be used in the next period. It is during the daily market that
decisions made on price and production are transformed into real transactions: observable
values, those collected for statistical purposes, are those realized in this period.
Considering that in the daily market period price may be adapted to existing conditions, but
production cannot because it always takes time, each of these variables may follow
different decision patterns, which would be partially independent of each other.
Accordingly, Marshall proposes a model of daily market supply behaviour in which
producers follow a decision-making process divided into two components, the supply price
and the production decision: "Production and marketing are parts of the single process of
adjustment of supply to demand" (Industry and Trade, page 181).
2.1.1. Decision-Making on Supply Price
Marshall states that each firm interacts with its customers proposing daily market prices
which are not equilibrium values; the market would only be in equilibrium when and if the
exogenous variables stopped varying. Prices are never determined by cost or demand alone:
3
particularly in the daily market prices are mainly governed by the available stock in relation
to the demand (page 290), in such a way that "As a general rule, the shorter the period
which we are considering, the greater must be the share of our attention which is given to
the influence of demand on value" (page 291). Despite playing a less important role, cost of
production is also considered in the producers' decision-making process on price,
associated with the principle that "The amount which each farmer or other seller offers for
sale at any price is governed by his own need for money in hand" (page 277), money which
is necessary to finance at least part of the next production cycle.
Given that the market is a permanent entity, a daily market never occurs only once, and the
explanation for the sellers' behaviour in the daily market period must be searched for in the
long run: "a controlling influence over the relatively quick movement of supply price
during short periods is exercised by causes in the background which range over a long
period; and the fear of spoiling the market often makes those causes act more promptly"
(page 313). For example, after a fall in demand the seller will not necessarily cut prices to
the point at which all stock could be sold, either because "Each man fears to spoil his
chance of getting a better price later on from his own customers" (page 311), or because
"he is more or less in fear of incurring the resentment of other producers, should he sell
needlessly at a price that spoils the common market for all" (page 311).
Marshall describes the relationship between buyers and sellers in daily transactions as a
"higgling (sic) and bargaining" process in which both parties try to show some degree of
indifference so as to induce a reduction in the rival's targets. Sellers "will not show at once
that they are ready to accept that price" (page 277) which will eventually be accepted;
buyers insinuate that they are not interested in the purchase, they "pretend to be less eager
than they really are" (page 277). On the other hand, the statement about the relationship
between many competitors is that "though everyone acts for himself, his knowledge of
what others are doing is supposed to be generally sufficient to prevent him from taking a
lower or paying a higher price than others are doing" (page 284).
This approach to price formation stems from the classical side of Marshall; it may also be
found in SMITH (1776) who had already remarked that in the daily market selling prices
depend upon the need of the seller "to get immediately rid of the commodity" (page 57).
This means that if the seller is not in immediate need of cash he does not sell, or he would
sell at whatever price only an amount sufficient to solve his immediate cash problems. If
the seller does not sell all the quantity available, then there will be a rise in stock, in such a
way that in the next decision it will probably be more important to "get rid" of the
commodity, but again without excessively cutting prices in order not to "spoil the market".
Therefore, "not spoiling the market" is associated with inventories, and the stock imposes a
downward pressure on prices: to greater inventory, smaller price.
These notions have probably been developed by classical authors for the general purpose of
explaining why the daily market price is not determined exclusively by demand, why there
is no daily market supply curve which would simply be given by the existing stock, and
why there is no vertical daily market supply curve. The same purpose may be identified in
some other post-Marshallian propositions; for example the "user cost" by KEYNES (1936),
the "convenience yield" by KALDOR (1939), the "normal stock" by SAMUELSON (1948,
page 268), and the "shadow inventory" by BLINDER (1982). All these approaches seem to
be intended to explain the reason why the supply curve cannot be a vertical line, why
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producers do not offer all available stock, accepting the price imposed by consumers,
clearing thus the market in such a way that the inventory level would always be null.
Alternatively, given the fact that some inventory almost always exists, some authors have
proposed that it results from a decision to retain stocks, and not necessarily from a decision
not to sell all that has been produced. The purpose of stockpiling in this case would be
twofold: to keep the price to a certain level for a certain period of time, and to "smooth" the
production changes, preventing excessively large variations. More precisely, in the
neoclassical approach some stock necessarily results from the hypothesis of the
maximization of the present value of future profits, apparently first suggested by
SMITHIES (1939): if demand is expected to grow, then it is more profitable to build up
stock for selling in the future, and vice versa. One competing idea, perhaps introduced by
KIRMAN & SOBEL (1974), is to propose inventory as a strategic variable in game
models.
These neoclassical propositions lead to the notion that stock exists because there is a policy
for it, or a demand for it, and the demand for stock, or the investment in stock, has
generally been associated with a target or a planned inventory level. In the neoclassical
tradition two approaches have more frequently been proposed to deal with inventories: the
"buffer stock/production smoothing" and the (S,s) models; WILKINSON (1989) and
BLINDER & MACCINI (1991) present comprehensive surveys on this subject. However,
it is not difficult to realize that if producers can make decisions on price and production,
then the market model has as many equations as variables and the neoclassical equation of
the demand for inventory would therefore be redundant or, worse, inconsistent.
At the macroeconomic level the existence of two particular inventories may be noticed.
Firstly, a reserve fund may be seen as a stock of money which would be a corollary for the
Keynes' speculative reason for holding money, as noted by ARROW, KARLIN & SCARF
(1958). It is worthwhile to observe the inverse relation: the greater the reserve of money,
the lower the interest rate. Secondly, the Phillips curve is a relation between wage and
another macroeconomic inventory: unemployment. PHILLIPS' (1958) proposition is that
"the rate of rise (of prices) being greater the greater the excess demand” (page 283). When
demand is growing small inventory levels allow for larger price variations. A corollary is
that, as a general rule, large stocks are associated with low price levels. Therefore, also at
the macroeconomic level there is an inverse relation between price and inventory which
has been the subject of much empirical analysis, such as that presented by WILKINSON
(1989).
To sum up, the supply price is actually observed only in the daily market, and it is a
function of the cost of production and the stock then available; at the beginning of each
daily market period the stock is given, and if cost were not considered then the price would
be determined exclusively by demand. Nonetheless, whoever says "that the price is
governed by demand (...) does not claim strict accuracy" (page 290). In Marshall's approach
neither the cost nor the demand which is embodied in the inventory are alone sufficient to
explain the price: they are both necessary. The supply price may thus be expressed as a
function of the cost W and the inventory E which comes from the previous period:
supply price: Pt = f (Wt , Et-1)
(1)
where the derivative in relation to costs (dP/dW) is positive and (dP/dE) is negative.
5
2.1.2. Decision-Making on Production
In Marshall's approach the producer's decision-making on production is the complementary
component of supply behaviour. It is important to stress first of all that industrial
production is naturally complex and normally takes time; nonetheless, all decisions on
production are transformed into reality in the daily market, through the purchasing and
hiring of factors, which is the only event observed for statistical purposes. In the
Marshallian approach production decision is primarily based upon the profit margin, both
expected and previously observed in the daily market period: the higher the profit, the
higher the total capital allocated to the branch, increasing production in the short run, and
capacity in the long run. This process may be identified with the notion of capital mobility.
In some daily market period the supply price could be such that the margin would be
"insufficient"; however, in a long run average the profit margin must be considered at least
as "acceptable": if the price is not "sufficient to cover in the long run a fair share of the
general costs of the business, production will gradually fall off" (page 313). The profit
margin is defined (page 313) as the surplus over direct costs; it is the return on the total
capital, and depends also on the turnover of floating capital (page 374). Among many
alternatives, the profit margin may be defined as the difference between the supply price P
and the cost of production W:
profit margin: Mt = (Pt - Wt)
(3)
Despite the fact that it is adequate for temporal analysis on the same industrial branch, for
empirical comparisons between different branches this definition may be misleading; in
this case it should be modified by information on the different fixed capital and on the
turnover observed in each branch. In theoretical terms it may be expected that factor
mobility, especially financial capital mobility, would prevent sectoral production
constraints: given a reserve fund, if capital is free to move, then all productive sectors have
the financial capital they consider appropriate for the running level of production, obtaining
thus an unconstrained, non-uniform, profit margin.
Additionally, Marshall states that production also depends upon inventories: a rise in stock
is perceived as a fall in demand, and thus each company, acting alone or in accordance with
its competitors, diminishes production in order to avoid excessive stockpiling and further
pressure of stock on price. This stems from Marshall's remark that in order to prevent the
inventory from becoming excessive, producers decide, "either from a regard to their own
interest or by formal or informal agreement with other producers, to suspend production for
fear of further spoiling the market" (page 311). On the contrary, if stocks fall producers
understand that demand has risen and then each company plans to invest and increase
production, trying to acquire for itself the largest possible share of the new demand. To
sum up, the production decision component of supply behaviour may be stated as a
function of the previously realized profit margin M and the stock E then available:
production decision: Qt = h (Mt-1, Et-1)
(4)
where the derivative in relation to profits (dQ/dM) is positive and (dQ/dE) is negative.
Besides Marshall's contribution, the existence and the importance of a relation between
inventory and production decision has been studied in many theoretical and empirical
works, under different approaches among which the "stock adjustment" by HICKS (1965)
and the production smoothing procedures must be remembered.
6
Therefore, the complete Marshallian daily market model has as many equations as
endogenous variables: producers set price P through the supply price equation which states
that price is a function of the exogenous variable cost, and of inventory E which has a
natural accounting equation associated with it; consumers decide on the amount demanded
D through the equation of the total demand; and finally producers decide the amount Q to
produce through the equation of the production decision, which is based on the profit
margin M defined, for example, by equation (3), and on inventory E. There is no supply
curve in the daily market; this would be a redundant equation.
2.2. Concluding Remarks on Marshall
The necessary and sufficient condition for equilibrium is market clearing: quantities
supplied and demanded must be equal. In contrast, Marshall assumes that in the real daily
market production and consumption never actually match. In the daily market there is no
clearing, which is the same as to say that in the daily market, when real transactions are
carried out, there is no equilibrium between supply and demand; accordingly, there is no
daily market supply curve. This distinction between non-clearing daily market and clearing
equilibrium market is important also because data on real transactions are observed and
collected for statistical and analytical purposes only in the daily market when there is no
equilibrium between supply and demand: real data are disequilibrium data.
Marshallian producers make decisions when the market is outside equilibrium; however, it
would be inappropriate to say that he assumes a disequilibrium approach: the lack of
equilibrium in his model is associated with actual transactions realized during the daily
market period, and this feature stems basically from the behaviour of the exogenous
variables, costs and demand, which are continuously varying. Marshall states that the
market is always moving towards equilibrium; it would reach this situation only if the
exogenous variables were constant during a certain minimal period of time. Marshallian
equilibrium is a theoretical construction, an abstraction; quoting Adam Smith "and other
economists" as he says, he points out that "the normal or natural value of a commodity is
that which economic forces tend to bring about in the long run (...) if the general conditions
of life were stationary for a run of time long enough" (page 289).
ROBINSON (1965) states that "The short period is here and now, with concrete stocks of
means of production in existence. Incompatibilities in the situation (...) will determine what
happens next. Long-period equilibrium is not at some date in the future; it is an imaginary
state of affairs in which there are no incompatibilities in the existing situation, here and
now" (page 101). In this line BOGGIO (1987) observes that, in classical terms, natural
rates and prices are centres of gravitation towards which actual endogenous variables tend
to move; in Marshall's words equilibrium positions are "centres about which the amount
and the price tend to oscillate" (page 289).
Marshall uses the image of a stone hanging by a string (page 288) to illustrate this
phenomenon: if the stone is shifted from its equilibrium position the force of gravity will
bring it back, after some oscillation. Considering that exogenous shocks induce
"movements partially rhythmical and partially arbitrary" (page 288), the conclusion is that
gravitation around equilibrium positions is a random phenomenon. Gravitation is thus a
component of economic variables which stems from the process of adjustment of producers
to ever-changing demand and cost conditions.
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3. AN ANALYTICAL APPROACH TO MICROECONOMICS
In a few words, the dynamics of the Marshallian decision-making model is as follows:
variations in the exogenous variables on the consumers' side, such as their income, lead to
shifts in the demand curve, then in consumption, and then in inventories. Variations in
inventories induce producers to change price and production simultaneously, each one
searching for the best profit allowed for him by the intensity of rivalry and the degree of
cooperation between them. Both price and production are thus connected to inventories,
and much research work has been conducted on one or other relation: price vs inventories,
or production vs inventories. In the literature of economics there is little analysis of the
simultaneous relations of inventories with price and production. However, this is not a new
strand; theoretical contributions are presented in DUMENIL & LEVY (1987), KIRMAN &
SOBEL (1974), and in HAY (1970).
Additionally, econometric works have been developed by MILLS (1962) and by his critics
STEUER & BUDD (1968). Particularly interesting are the empirical findings of
KAWASAKI, McMILLAN & ZIMMERMANN (1982), as their work is based upon a
statistical method which is similar to a reduced model, but is independent of any particular
structural market model. Their conclusion is that firms do react to any shift in the level of
inventories, setting new price and production values, in such a way that convergence to a
new equilibrium situation is assured. Based upon these principles, this section proposes
and develops the following
DYNAMIC ANALYTICAL MARKET MODEL
demand: Dt = ao - a1 Pt + a2 Ft
supply price: Pt = bo + b1 Wt - b2 Et-
production decision: Qt = ho + h1 Mt- - h2 Et-
where Mt = Pt - Wt is the profit margin; and
Et = Et-1 + Qt - Dt is the inventory.
There are five endogenous variables: D, P, Q, M, and E, and five corresponding equations.
The exogenous variables are income-related F and cost-related W. The main feature of the
model is the supply behaviour, which is a generalization of the Marshallian decisionmaking model on supply price (equation 1) and on production (equation 4). Considering, as
suggested by Marshall (page 281), that current values are consequences of previous
decisions, instead of basing their decisions only on their last realized profit and on their
available inventory, in this model producers consider a series of the past values of these
endogenous variables, represented by the lag structure given by ,  and . The lag
structure is a priori unknown, but it may be determined by econometrics of the model.
This is not a disequilibrium schedule, it is a dynamic model. Given a situation of
equilibrium, after an external shock in time t the model brings about the values of all
endogenous variables in time t+1, t+2, t+3, and so on. If the external shock was given only
once, then successive adjustments made by producers would make endogenous variables
follow a damped oscillatory trajectory in the direction of a new equilibrium situation.
8
However, considering that in the real world exogenous shocks are many and randomly
distributed, the trajectory is always disturbed, in such a way that the equilibrium is never
actually attained; actual values oscillate around the equilibrium positions. Special
equilibrium values for endogenous variables are neither expected nor assumed ad hoc by
this model; for example, inventory is in no circumstances presumed to be null.
3.1. Equilibrium and Gravitation
Considering that the equilibrium situation cannot be attained, it may only be imagined as a
theoretical construction; it could only be observable if and when all exogenous variables
have stopped varying. Then, after some time has elapsed, the effects of external shocks
over all endogenous variables would have vanished. The structural market model would
therefore be in a motionless position, which is the equilibrium status. The model has thus
one theoretical equilibrium position in time t which is associated with the values for the
exogenous variables in time t. Therefore, the model actually gravitates around theoretical
equilibrium positions.
Actually, observed economic values are always daily market values; long run equilibrium
values are abstractions from reality which must necessarily be based on those daily market
values. Long run equilibrium values are neither decided nor imposed by producers: they
must be theoretically deduced from daily observed values. The process by which actual
values of economic variables are kept away from their equilibrium status is the gravitation
phenomenon, which depends on how fast producers can and want to adjust production to
consumption. Measured by the spread between actual and long run equilibrium values,
gravitation is the link between reality and economic theory.
This process of adjustment of production is required as a consequence of exogenous shocks
given to the system, from both demand and cost sides. Considering that these shocks are
random, gravitation is also random and must have zero mean; it is a disturbance term. This
also means that gravitation adds to the behaviour of an economic endogenous variable a
trend component which may be isolated and eliminated because it is just a noise without
economic meaning. Moreover, gravitation is not tractable through time-series analysis
because it has a non-systematic, impredictable behaviour. As LIMA (1992b) proposes,
gravitation is an error component of economic variables, and consequently parameters
obtained by direct econometric estimation using actual series will probably be biased.
Alternatively, gravitation may be seen as an omitted varible, implying that there will
probably be autocorrelation in the residuals. Therefore, the econometric method should
eliminate the gravitational component of endogenous variables.
3.2. The Supply Curve
The main feature of the analytical decision-making model is supply behaviour which has
been divided into two separate equations which is associated with the short run: the supply
price and the production decision. However, price and production are mutually dependent,
via inventories, and when in the theoretical situation of equilibrium one is connected with
the other by a special, stable, theoretical relation which may be identified as the supply
curve. The short run supply behaviour is such that changes in the level of inventories
induce changes in both price and production, and in the same direction, because
coefficients have the same negative signal in the supply price equation and in the
production decision equation.
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Therefore, these two equations may be combined: focusing on the production decision, first
the stock E is replaced by its expression taken from the supply price equation. The
inventory will thus be eliminated in the production decision equation, which will become a
function of M, P and W. After that, the profit margin M is replaced by its definition, which
states that it is the difference between P and W. These substitutions lead eventually to one
expression where Q is a function of P and W, such as for example:
Q*t = Bo + B1 P*t - B2 Wt
(5)
where asterisks indicate equilibrium values. This equation is the line of simultaneous
theoretical equilibrium of price and production which may be defined as the supply curve:
it results from the behaviour of producers when deciding on price and production, which
means that it contains only price and production levels that producers consider interesting
for them. Differently from what neoclassical theory states, the supply curve is not a relation
of causality; this would happen only if firms were allowed to decide production based upon
a given price level, or vice versa. Instead, firms have some discricionary power over market
prices and can modify them by varying production, and vice versa. In any case, the final
theoretical equilibrium levels of price and production depend also upon consumers, via
their demand curve.
The supply curve is a theoretical construction connecting imaginary equilibrium levels of
price and production; it cannot actually be observed because real values are only those
computed from the daily market when there is no supply curve. This dynamic model can
therefore describe the daily (actual) and the long run equilibrium (theoretical) economic
behaviour. Considering that the supply curve is derived from its two components, the
supply price and the production equation, its slope depends upon the propensity to invest
and on the simultaneous reactions of all companies in relation to individual inventories
shifts. Formally:
(dQ/dP) = [(Q/M) x (M/P)] + [(Q/E) x (E/P)]
where (dQ/dP) is the long run supply slope. While the position (height) of the supply curve
depends on the technology of production and on input prices, represented by W in the
model, the slope is subject to some physical features, such as perishability, technology of
production and distribution, management, financial strength, and ultimately upon
businessmen's characteristics, such as proficiency, reactions to expectations formation,
selling eagerness, knowledge of the market, cash availability, and rivalry. Competition is in
turn conditioned by objective considerations such as the availability of funds, and the
notion that it makes no sense to an individual producer to carry the stock of the whole
industry. With the exception of the direct effect of profit on production, represented by the
first square brackets in the expression above, and the given physical restrictions, Marshall
condensed all those behavioural features which influence the supply slope into the single
notion of "not spoiling the market".
One important characteristic of those features is that they are non-separable ex post; it is
unfeasible to identify empirically the effect of any one of them, thus isolating it from the
others, because one cannot have statistical information on them: most of them are not
measurable, as BLINDER (1990) has already observed. Incidentally, neoclassical theory
adds to that list of behavioural features one more hypothesis: that the process of profit
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maximization can be described by differential calculus. Following this approach, modern
neoclassical analysis such as that developed in BRESNAHAN (1989) applies differential
calculus for maximization simultaneously condensing those behavioural features into
notions such as "index of competitiveness" or "conjectural variation". SCHMALENSEE
(1988), more specifically, states that besides maximization the supply slope "emerges from
what may be a complex pattern of behaviour" (page 650).
However, the fact that the individual effect of each of those features on the supply slope
cannot be identified remains untouched if one multiplies or not the composed effect by an
additional hypothesis - the profit maximization - about the behaviour of producers.
Ironically, this means that the neoclassical effort in developing economic theory may
possibly be reduced to a simple change in names, replacing "not spoiling" by "complex
pattern" without adding new information on supply behaviour. Except if game theory can
find a miraculous device to measure empirically how competitors interact, and not simply
state it as a hypothesis unsuited for any empirical test, it looks improbable that neoclassical
theory will someday elaborate a theory of supply behaviour.
To sum up, the supply curve is a synthetic tool, describing a set of possible equilibrium
points of the economy; a situation to which the economy would tend to run, if exogenous
variables have stopped varying. The slope is the core of the supply curve and arises from
the psychological behaviour of producers, which is constrained by some permanent and
temporary conditions imposed by institutions of real life. No special value, ad hoc defined,
is expected; the slope is a composition of parameters of the structural model and, like them,
it cannot be determined ex ante. The slope of the supply curve is a resultant of "a complex
pattern of behaviour"; instead of theoretically anticipated, it must and can be estimated by
econometrics.
4. AN EMPIRICAL APPLICATION
4.1. Main Results
In order to give empirical support to the analytical approach proposed here, this section
presents briefly the results obtained in a study on the Brazilian cement industry. The market
model is that presented in section 3, and the exogenous variables are: F, the Gross Fixed
Capital Formation, and W, the estimated direct cost of production. The econometric
method is that presented in LIMA (1992b). The reduced model is presented below, where
D1 refers to a dummy variable associated with the fact that during the first half of the
period of analysis production was constrained by available industrial capacity (“t” statistics
are in brackets):
ESTIMATED REDUCED MODEL
CONSUMPTION:
Dt = 9.896 - 0.312 Wt + 30.234 Ft-1 - 2.958 D1
(5.17) (-2.91)
(13.07)
(-3.76)
R2 = 0.98
DW = 1.90
F (3,12) = 162.48
PRICE:
11
Pt = 16.791 + 1.102 Wt-2 + 11.967 Ft-1
(6.33) (6.04)
(2.32)
R2 = 0.87
DW = 2.24
F (2,12) = 40.64
PRODUCTION:
Qt = 9.362 - 0.304 Wt + 31.048 Ft-1 - 2.960 D1
(4.69) (-2.72)
(12.87)
(-3.60)
R2 = 0.98
DW = 1.94
F (3,12) = 158.10
PROFIT MARGIN:
Mt = 8.910 + 0.908 Wt-2 + 16.337 Ft - 13.970 Ft-2
(2.62) (4.21)
(2.17)
(-2.08)
R2 = 0.71
DW = 2.24
F (3,11) = 9.16
INVENTORY:
Et = 0.310 + 0.076 Wt-1 - 1.618 Ft + 1.372 Ft-1 - 0.404 D1
(0.88) (4.56)
(-2.28) (1.93)
(-2.81)
R2 = 0.93
DW = 2.09
F (4,11) = 36.71
INVENTORY (NO INTERCEPT):
Et = 0.086 Wt-1 - 1.415 Ft + 1.378 Ft-1 - 0.296 D1
(7.13)
(-2.13)
(1.96)
(-3.92)
In the next step the reduced equilibrium model was calculated, supposing theoretically that
all exogenous variables were fixed at their levels in time t and that D1 is always zero.
Formally:
REDUCED EQUILIBRIUM MODEL
consumption: D*t = 9.896 - 0.312 Wt + 30.234 Ft
price: P*t = 16.791 + 1.102 Wt + 11.967 Ft
production: Q*t = 9.362 - 0.304 Wt + 31.048 Ft
profit margin: M*t = 8.910 + 0.908 Wt + 2.367 Ft
inventory: E*t =
0.086 Wt - 0.037 Ft
Considering that the demand equation and the supply price equation are just-identified,
their parameters could be derived directly from the coefficients of the reduced equilibrium
model following an indirect least squares procedure. Nonetheless, in this example the
equilibrium series, which are free of gravitation, were used in the second stage of the
econometric work to compute the structural relations between the endogenous variables of
the market model, then bringing about the estimates:
SUPPLY PRICE:
12
P*t = 18.00 + 15.82 Wt - 169.7 E*t
(15.9) (5.3)
(-4.9)
R2 = 0.97 DW = 2.03 F (2,12) = 224.3
PRODUCTION DECISION:
Q*t = - 33.89 + 2.57 M*t - 6.58 E*t
(-985) (1639)
(-754)
R2 = 1.00 DW = 2.51 F (2,12) > 10000
DEMAND CURVE:
D*t = 14.65 - 0.28 P*t + 33.62 Ft
(7241) (-4258) (13284)
R2 = 1.00 DW = 1.97 F (2,12) > 10000
Finally, the long run equilibrium supply curve (expression 5), which is theoretically
derived as a combination of the supply price and the production decision equations, may
also be seen as an outcome of an ILS procedure that brings about the expression below.
SUPPLY CURVE:
Q*t = - 34.6 + 2.61 P*t - 3.20 Wt
4.2. A Commentary on Price Stickiness
The cement industry has frequently been taken as a major example of oligopoly, and the
Brazilian industry cannot be seen as an exception to this rule. One could then model price
formation in this market as if firms follow the rigid mark up principle of the "orthodox"
post-Keynesian theory. In this situation price would be fully sticky in accordance with the
notion that price stickiness may be considered as a safe indication of the existence of a
cartel. Suppose thus that a particular model assumes price P to be a simple linear function
of production costs W. Using the same econometric method one could therefore obtain the
reduced equation for the price:
Pt = 17.328 + 0.803 Wt-1 + 0.691 Wt-2
(7.29) (2.66)
(2.45)
R2 = 0.88
DW = 2.02
F (2,12) = 45.10
In the next step one would derive the price rule:
Pt = 17.328 + 1.494 Wt
In this simplified model there would be no room for production decision: price is given for
consumers who decide how much to buy and consequently how much will be produced.
Therefore, the supply curve would be the same as the price rule. Apparently, actual data
does not allow for rejection of the Keynesian orthodox hypothesis that the mark up
principle prevails in the Brazilian cement market. This simple model takes as an
assumption that, at least in the short run, producers set prices without regard to demand.
13
However, by assuming price to be demand-insensitive this model just cannot test the
hypothesis whether demand influences prices or not. In contrast, the general approach
proposed here can do the thrick.
In fact, econometric results obtained from the general model reflect the market features one
could expect from this industrial branch: supply is quite elastic and Brazilian cement prices
are, if not fully, certainly "very" sticky. As estimated with the values of exogenous
variables for 1986, price elasticity of supply is 4,0 while the elasticity of price in relation to
demand variations is only 0.21. For an economic expansion as great as 10%, the cement
price would rise by only roughly 2%. Actual data gives support to the hypothesis that
demand do influences prices, but also reveals that this influence is low when compared
with production costs. The supply-and-demand model can deal with the notion of price
stickiness without assuming a rigid mark up pricing policy. Price rigidity can actually be
tested instead of assumed. Furthermore, the "historical conditions" which could explain
why short run mark up rates vary must necessarily be embodied in the levels of exogenous
variables of the general model, supposing of course that no relevant exogenous variable has
been ommitted. The supply-and-demand model, which is not a neoclasssical device, is
more general than the rigid mark up pricing policy.
5. A LINK BETWEEN MARSHALL AND KEYNES
This paper develops the Marshallian principles on the daily market, when real transactions
are made and real prices are observed, to build a dynamic model which may explain both
the theoretical imaginary equilibrium situation and the actual movements around it.
Furthermore, the model allows for the deduction of the theoretical supply curve, whose
slope depends on a complex behaviour of producers, thus reproducing the supply-anddemand model, independently of the hypotheses of profit and utility maximization. It is
demonstrated that supply-and-demand is not necessarily a neoclassical concern. This
approach is in line with the "anti-Say" Marshallian notion that the economy is pushed by
individual producers who adjust supply to demand, following a convergent decisionmaking process.
The connection with Keynes and macroeconomics may be briefly outlined, as follows, in
addition to the statement by Harcourt and the references to the Keynesian user cost and to
the Keynesian speculative reserve fund as a kind of inventory. Firstly, the analytical
approach to supply behaviour has given no ad hoc special equilibrium levels; it leads freely
to some theoretical equilibrium solution: a free "intrinsically economic" solution. This
means that the interaction of supply and demand will determine not only the theoretical
equilibrium levels of price, production and inventory, but also the actual industrial capacity
utilization rate, the level of the reserve fund, the employment level and so on.
The analytical approach assures that, given the economic policies at the micro and
macroeconomic levels, there will always be some theoretical "market solution". This
solution cannot ensure full-employment as a principle. Instead, such as the involuntary
inventory of finished goods, the involuntary industrial idleness and the involuntary stock of
the speculative fund, the involuntary unemployment - the Keynesian unemployment - may
be expected to be the rule and may be determined empirically. This approach looks like a
legitimate out-of-equilibrium Keynesian feature. It is not an equilibrating device, in the
sense that a situation with some kind of "justice" would eventually emerge. It allows for a
14
super-aggregate analysis in which historical circumstances - captured by the model through
the levels of the exogenous variables - do matter.
Secondly, the formal link with macroeconomics will be given by the production
(investment) decision equation, which is in fact a factors demand equation, financial capital
certainly being the most important of them. Investment is a function of the profit rate and
depends on the mobility of financial capital: given a speculative reserve fund, if financial
capital is free to move, then all productive sectors may generally have the financial capital
they are worth of. Further discussion on the theme and an empirical application of this
supply-and-demand approach may be found in LIMA (1993), where special emphasis is
given to the analysis of the Brazilian inflationary process. To sum up, mobility of capital is
the interface between the real industrial productive sector and the monetary Keynesian
reserve fund, between the real and the monetary sides of economics. Capital mobility
provides the link between Marshallian microeconomics and Keynesian macroeconomics.
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