The Marginal “Revolution”:
Jevons
Menger
Walras
History of Economic Thought
Boise State University
Fall 2015
Prof. D. Allen Dalton
William Stanley Jevons (1835-1882)
– born Liverpool, merchant
– undergrad work at University College,
London in chemistry and metallurgy
– 1854, leaves school to become assayer at
Sydney (Australia) mint
– private research meteorology, railroads,
economics, national statistics
– 1859, returns to London to finish
university education
– 1863, tutor at Owens College, Manchester
– 1866, professor of political economy at
Owens
– 1876, professor University College,
London
– 1880, retires due to ill health
Jevons’ Minor Works
• “Notice of a General Mathematical Theory of Political
Economy” (1862)
– sketch of ideas to be later fleshed out in Theory of Political
Economy, paradoxically without any mathematics
• (pamphlet) A Serious Fall in the Value of Gold
Ascertained and its Social Effects set forth (1863)
– pioneering methodological and empirical contribution to
index numbers, showing gold discoveries were source of
commodity price rises
• The Coal Question (1865)
– alarmist argument that coal was being exhausted and would
limit British economic growth
– bestseller, widely debated, brought him instant fame
• Investigations in Currency and Finance (1884)
– exogenous business cycle theory (“sunspot cycle”)
Jevons’ Contributions
• The Theory of Political Economy (1871)
• Value and Exchange; Capital and Interest
• Value and Exchange
– starting point: “to maximize pleasure is the problem
of economics”
– utility is function of quantity of goods consumed,
u = u(x); disutility a function of “discommodities”
• (x) = du/dx = u’(x) is defined as degree of utility
• the “degree of utility” of the last increment consumed is
termed the final degree of utility (marginal utility)
– degree of utility diminishes as quantity increases
– for good with alternate uses, optimal allocation
occurs when same final degree of utility occurs in
all uses (weak form of Gossen’s Second Law)
Jevons’ Contributions
• Utility maximization is basis of theory of exchange
– relative price () defined as ratio in which small
quantities of goods exchanged against one another; 
= px/py = dy/dx
– for homogenous goods in well-functioning markets,
one price will prevail - Jevons’ Law of Indifference
(Law of One Price)
– implies that total quantities exchanged by given trader
stand in same ratio as any small quantities; y/x=dy/dx
= .
– Thus, “the ratio of exchange of any two commodities
will be the reciprocal of the ratio of the final degrees of
utility of the quantities of commodity available for
consumption after the exchange is completed”
Jevons’ Contributions
(x)
 (y)
R = a + b/
(x)/(y) =  = px/py
• Let  be given, as well as
quantities of x and y (a and
b, respectively).
• If b expressed in terms of
a, total resources are R = a
+ b/.
• Blue curve represents MU
of x; Black curve
represents utility of
marginal unit of x
exchanged for Y (and
exchange occurs at ratio )
• Optimality requires (x) = 
(y), or (x)/(y) = , and 
= px/py, so...
Jevons’ Contributions
• but this is true for every individual, so the price ratio
between commodities equals the ratio of marginal utility
between those commodities for all individuals
(x)1/(y)1 =  = px/py = (x)2/(y)2
• Capital and Interest
– capital regarded as stock of goods waiting to be
consumed (directly or indirectly-machines)
– essential function of capital is to allow an interval
between labor input and final consumption
– “capital is concerned with time”
– to measure the interval Jevons introduces concept of
“average interval of investment”
• anticipates Bohm-Bawerk’s “average period of
production”
Jevons’ Contributions
• Capital and Interest
MPK
Labor
income
i
Capital
income
K
K
Slope equals i
Value
of
output
Time
– output increasing function of
interval of investment [Q = F(t),
where F’(t) > 0]and the interest
rate is equal to the increment in
output obtainable from the last
increment in time, divided by
output [ i = F’(t)/F(t)]
– given the length of production
time, the market rate of interest
will equal the rate of growth of
output from waiting
– marginal productivity principle
and Jevonian Triangles
Jevons’ Contributions
• The Principles of Science - a Treatise on
Logic and Scientific Method (1874)
– laws of science begin from creative act of
inventing hypothesis from which logical
implications are deduced and tested
against observation
– certainty of science can never be attained;
probability plays a crucial role
– reads like early Popper
Carl Menger (1840-1921)
– born Galicia (Poland)
– studied law at Vienna and
Prague, obtained doctorate at
Cracow
– financial journalist, civil servant
– 1873, professor extraordinary in
Faculty of Law at Vienna
– 1876, tutor to Crown Prince
Rudolph
– 1879, chair of political economy
at Vienna
– 1903, retires
• controversy over reasons for
retirement
Menger’s Contributions
• Principles of Economics (1871) - Grundsatze
– first volume in planned four volume work, others
never written
• Investigations on the Method of the Social
Sciences (1883)
– response to Schmoller’s unkind review of the
Grundsatze which argued theory had no place in
political economy
• founder of the Austrian School
– emphasis on causal-genetic explanations
– centrality of subjective utility, uncertainty,
adjustments in disequilibrium, and time
Menger’s Contributions
• Principles of Economics (1871)
– Chapter 1: “The General Theory of the
Good”
• characteristics of goods in general
– need, property of satisfaction, knowledge, access
• first-order (consumer) goods v. higher-order
(producer) goods
• value of higher orders derived from first-order
goods
• necessary complementarity in time-consuming
production process
Menger’s Contributions
• Principles of Economics (1871)
– Chapter 3: “The Theory of Value”
• extensive discussion of subjectivity of utility
• analysis of economizing by single individual of
lumpy alternatives of equal-expenditure
bundles of alternative goods
• value of any good in comparison with another
is determined by its least dependent use
• extended discussion of uncertainty, error and
changes in knowledge upon economizing
process
Menger’s Contributions
• Principles of Economics (1871)
– Chapter 4: “The Theory of Exchange”
• purpose of exchange; mutual beneficence of
exchange
• exchange as result of inverted subjective
evaluations
– Chapter 5: “The Theory of Price”
• analysis of price formation, progressing from
monopoly to competition
– Chapter 6: “Use Value and Exchange
Value”
• reemphasis of difference between subjective
utility and objective exchange ratio
Menger’s Contributions
• Principles of Economics (1871)
– Chapter 7: “The Theory of the Commodity”
• commodities are goods intended for sale
• extensive discussion of marketability
– Chapter 8: “The Theory of Money”
• money arises on the market as a commodity
• the commodity money arises as a
consequence of its being the most marketable
of all commodities
Léon Walras (1834-1910)
– father, Auguste Walras, disappointing
career as teacher and economic writer
• father championed notion that price
reflects relative scarcity
– rejected by Ecole Polytechnique, enrolls
in Ecole des Mines but neglects studies
and does not graduate
– 1858 conversation with father leads to
interest in economic matters
– 1860, wins fourth prize in essay contest
at International Tax Congress in
Lausanne
– 1870, appointed professor of political
economy in law faculty at Lausanne
– 1892 retires; Pareto succeeds him
Walras’ Contributions
• Elements of Pure Political Economy (1874,
1877)
– first volume in planned three volume work,
dealing with pure, applied, and social economics;
latter two never written
– Minor Works: Etudes d’économie sociale (1896)
and Etudes d’économie politique appliqué (1898)
• develop views of ideal society, role of government and
private property
• favored land nationalization; government to provide
public goods and control natural monopolies from land
rent; abolition of taxes; abolition of paper currency and
institution of managed gold standard (stabilize prices via
changing supply of overvalued silver coins); otherwise
free competition.
Walras’ Contributions
• Elements of Pure Political Economy (1874,
1877)
• General Equilibrium Analysis
– begins with analysis of exchange under partial
equilibrium (two goods); arrives at Gossens’ Second
Law, allowing him to explain why prices are
determined by scarcity (solving his father’s problem)
– generalization from two goods to n goods; explicit
analysis of general equilibrium
– view of money as numeraire good
– derivation of demand from utility maximization
– general equilibrium defined as zero excess demand in
all market simultaneously
Walras’ Contributions
• General Equilibrium Analysis
– Tâtonnement process
• iterative process to solve simultaneous equations;
disallows false trading (exchange at nonequilibrium
prices) by use of auctioneer who changes prices due to
excess demand conditions
• stability questions understood but not analyzed
– Extension of model to production
• assumed fixed coefficients of production
• profits and losses are signal for expansion or
contraction of input usage and output production
• households endowed with factors that produce
incomes
• incomes replace endowments on demand for
output side
Walras’ Contributions
• General Equilibrium Analysis
– Extends model to account for growth through
investment and saving
• investment defined as value of new capital goods; price
of each capital good is capitalized value of rental income
it provides (therefore inverse relation between
investment and interest rate)
• saving is income not consumed, determined by marginal
equality of present consumption foregone and future
income gained
– Treats money as an asset held as inventory to
accomplish function of exchange over a time
period
• demand for cash balance is diminishing function of
interest rate
Influences/Differences
• Influence
– Menger had greatest initial influence in spreading
“marginalist” ideas
– Walras and Jevons mathematical versions
eventually became more widespread and influential
– Walras had greatest impact on mainstream modern
economist’s toolkit
• Differences
– Menger’s emphasis on causality in time differs from
simultaneous equations approach of Walras
– Menger emphasizes uncertainty, error and
processes rather than Jevons’ and Walras’
emphasis upon equilibrium
Additional Contributions
• Friedrich von Wieser
– cost is marginal utility foregone from
application of unit of input to produce
one good rather than another
– imputation problem; expected prices of
first-order goods determine the prices
of higher order goods
• John Bates Clark
– extension of emphasis on marginal
productivity theory of distribution as
applied to all factors of production
– argued marginal productivity pricing of
factors was just
Additional Contributions
• Philip Wicksteed
– mathematical presentation of marginal
productivity theory
– used Euler’s Theorem to show that in
equilibrium, when production function
is homogeneous and linear, that
shares to wages, rent, and interest
exhaust the revenue of the firm
• Francis Ysidro Edgeworth
– extension of exchange analysis to note
multiplicity of possible equilibria from
original endowments; contract curve