Anticipations of Marginalism
History of Economic Thought
Boise State University
Fall 2015
Prof. D. Allen Dalton
Background
• Throughout history there exists a strong
subjective utility theory of value
– Olivi and San Bernardino
– Late Spanish Scholastics
– Galiani and Turgot
– French School
– British Oxford-Dublin School
• This view is buried under the Smith-RicardoJ.S. Mill onslaught that propounds a labor
theory/cost-of-production theory of value
Background
• The height of this older subjective theory
found in the French “Engineers,” most
prominently, Jules Dupuit
• Also during the Classical period, a few lonely
voices appear (von Thünen, Cournot, and
Gossen) that are generally viewed as
anticipators of the Marginalist “Revolution”
and the transformation of economics from a
concentration on economic growth to an
emphasis upon resource allocation
– these latter contributions might be viewed as
“Marginalism without the name”
Johann Heinrich von Thünen
• Johann von Thünen (1783-1850)
– born into landowning family, took
over deceased father’s two estates at
age 16
– studies agronomy at Celle under
Albrecht Thaer, father of rational
agriculture; critical of Thaer’s
economics, studies economics at
University of Göttingen
– Returns to agriculture, purchasing
large estate from brother-in-law
– Becomes internationally recognized
authority on agriculture
von Thünen’s Contributions
• The Isolated State with Respect to
Agriculture and National Economy (1826,
1850)
– works out central idea first conceived in 1803:
that net prices obtained by farmer decline with
increasing distance from market; that relative
prices will influence choice of crops and
techniques at differing distances from the market
– Constructed his theory from scratch
– Derived economic propositions from explicit
optimization, though book does not use
differential calculus
– Pioneer in mathematical economics
von Thünen’s Contributions
• Theory of Rent, Location and Resource
Allocation
– product sold at fixed price (p)
– transportation costs (t) rise with
increasing distance (s)
– output per acre (q) increases with labor
input per acre (a) at a diminishing rate:
q’(a) negatively sloped with respect to a
– at each p, farmer chooses production
method such that MP of labor, evaluated at
p, equals the wage rate (w)
von Thünen’s Contributions
p
t
pq’(a)=w
q’(a)
s
Labor
intensity
a
• As distance (s) from
market increases,
producer price
declines, marginal
product of labor
rises, labor intensity
falls and rent falls.
• Generalized to
multiple crops to
predict spatial
pattern of crop
production
von Thünen’s Contributions
Rent
Vegetables
Forest
Rye
s
• Farmers seek to
maximize rent; at
margin, respective
products yield same rent
• Extends model to
account for how
changes in conditions
affect location of
production, intensity of
factor use and rents
(transportation costs,
technology, etc.)
von Thünen’s Contributions
• Marginal Productivity Theory of Distribution
– second part of The Isolated State (1850)
– “effectiveness” of capital and labor both
measured by the increment in the output due to
the increase in the quantity of the factor
– both labor and capital are increased up to the
margin “where the value of the incremental output
of the last worker (or “last particle of capital”) is
absorbed by the wage received (or “payment to
capital”)
• The “Natural Wage”
– attempt to determine the wage (when savings are
excess over subsistence) that will maximize the
return on savings (why?)….. w* = pa
von Thünen’s Influence
• Universally acclaimed, his book had immediate
success
• Most of success due to “natural wage”
• Other aspects lay largely dormant
• Presented analysis idiosyncratically; weighed
down with numerous tedious numerical examples,
digressions and repetitions
• If presented succinctly and translated into plain
language, he might have inaugurated the Marginal
“Revolution”
• Marshall reads him circa 1869, later credits von
Thünen with teaching him economics
Antoine-Augustin Cournot
• Antoine A. Cournot (1801-1877)
– 1823, math degree from Sorbonne
– private secretary to French marshal
(1823-1833)
• wrote doctoral dissertation in
mechanics and secondary thesis in
astronomy, obtained law degree,
published numerous articles
– 1834, Poisson obtains for him a
professorship at University of Lyon
– 1835, elected rector at University of
Grenoble; distinguished career as
university administrator till
retirement
Cournot’s Contributions
• Researches into the Mathematical Principles
of the Theory of Wealth (1838)
– pioneering, systematic analysis of profit
maximization by firm
– presented by use of differential calculus
– unreviewed, Cournot retreats from
economics, and not until 1863 did he write
on economics again, presenting his theory
stripped of mathematics
• “Hamlet without the prince of Denmark..for his one
original contribution was precisely the use of calculus to
solve problems of constrained optimization”
Cournot’s Contributions
• Researches into the Mathematical Principles of
the Theory of Wealth (1838)
– begins with market demand, where q = F(p)
• first demand function and demand curve
– Firm revenue, R = pF(p)
• maximized at dR/dp = F(p) + pF’(p) = 0
– Begins with monopoly, works towards
competition
– Production costs depend on quantity
• C = Φ(q) = Φ[F(p)]
– Profit maximization; Π = R - C = pF(p) - Φ[F(p)]
• dΠ/dp = F(p) + pF’(p) - Φ’(q)F’(p) = 0
Cournot’s Contributions
• Researches into the Mathematical Principles of
the Theory of Wealth (1838)
– analysis of effects of changes in marginal cost
– analysis of effects of taxes (notes excise tax is
equivalent to shift in demand or cost curve)
– Duopoly Theory
• homogeneous product, ignores costs
• q = q1 + q2 = F(p)
• Cournot assumption: each firm expects the
other’s output to be independent of resulting
market price and optimizes output accordingly
Cournot’s Contributions
• Duopoly Theory
– reaction curves:
q2
r1
B
C
r2
A
q1
• q1 = r1(q2)
• q2 = r2(q1)
– at A, firm 2 finds firm 1 has
produced less than
expected, expands output
to B; firm 1 then finds firm
2 has produced more than
expected….
– if r2 is steeper than r1 then
outcome is unstable
• first time that stability
requirement used
Cournot’s Contributions
• Researches into the Mathematical Principles of
the Theory of Wealth (1838)
– Pure Competition
• as number of firms expands, price become
parameter for each firm so that each firm
supplies according to parametric price
– qi = qi(p)
• Market price determined by aggregate
supply equaling aggregate demand
– Σ qi(p) = F(p)
Cournot’s Influence
• Developed and applied tools of constrained
optimization - in one stroke, the theory of the firm
had been created
• Introduction of calculus into economist’s toolkit
• Immediate influence negligible; economists did not
understand calculus - contributions neglected until
later
• Influenced following generation of Jevons and
Walras
• Marshall reported that he learned his method from
Cournot (remember he said he learned his
economics from Thünen)
Hermann Heinrich Gossen
“He was a man of one idea; but that was an
immortal one.”
- F.Y. Edgeworth, Palgrave’s Dictionary of Political Economy
• Hermann Heinrich Gossen (1810-1858)
– father tax collector under Napoleon
– changed schools several times before dropping
out, gaining diploma through independent study
– university studies concentrated on law and
government
– entered civil service in 1834, forced to resign in
1847 due to poor performance
– entered insurance business briefly, then set about
developing his ideas
Gossen’s Contributions
• Entwickelung der Gesetze des menschlichen
Verkehrs (1854) (translated in 1963 as The
Laws of Human Relations and the Rules of
Human Action Derived Therefrom)
– published at Gossens’ expense
– few copies sold, Gossen withdrew it from circulation
– first noted and understood by Robert Adamson, who
had found an obscure reference to it, obtained one of
few circulating copies, and reported content to
Jevons
– Jevons devotes 6 pages of 2nd edition of his The
Theory of Political Economy to a tribute to Gossen’s
originality
Gossen’s Contributions
• Analysis starts with optimal allocation of time
• Gossen’s First Law
– “The magnitude of a given pleasure decreases
continuously if we continue to satisfy this
pleasure without interruption until satiety is
ultimately reached”
– marginal utility curves drawn for marginal unit of
resources (time) applied
• Gossen’s Second Law
– “The magnitude of each single pleasure at the
moment when its enjoyment is broken off shall be
the same for all pleasures.”
– principle claim to fame
Gossen’s Contributions
• Application of
Gossen’s Second
Law
u
v(e)
u*
E
E
– Allocation of
resources (ei)to
activities yielding
pleasure u(e)
- Production: activities
reinterpreted as
products and
resources as effort,
where effort is disutility
- v(e)
Gossen’s Contributions
• Application of Gossen’s Second Law
– Exchange
• perceives indeterminateness of bilateral exchange
• he postulates that marginal utilities must be
equalized between individual’s for each product
(presumes cardinality and interpersonal
comparability) but foreshadows equality of MRS
– Market Exchange
• parametric prices; E reinterpreted as income and
product curves reinterpreted as marginal utility per
currency unit spent and v(e) interpreted as disutility
of earning income at current prices
• conclusion: “the last atom of money creates the
same pleasure in each pleasurable use”
Gossen’s Philosophy
• Second part of The Laws of Human
Relations is a passionate defense of
free markets
– free trade, private property, antimonopoly, liberal education, metallic
currency, abolition of paper money
– did see sources of inefficiency in land
ownership; proposed government buy
land and then lease to highest bidder
– talked of competitive markets as if they
were the revealed perfection of a
benevolent God
Francesco Ferrara
• Francesco Ferrara (1810-1900)
– Self-taught economist
– Leading Sicilian liberal during
period of reform and revolution
– Professor of political economy,
University of Turin (Italy)
– Two-volume History of thought
(Esame storico-critico di
economisti e dottrine
economiche, 1889-92) gives
special place to Say, Dunoyer, and
Bastiat
Ferrara’s Contributions
• Analyzes human choice in the context of
utility and “cost of reproduction”
– Both ideas are subjective; “cost of
reproduction” close to the opportunity cost
concept
– Viewed utility as declining and “cost of
reproduction” rising as an activity is extended
– Exchange value and price arise from the
foundations of choices undertaken by
comparing utility and “reproduction cost”
– influences Vilfredo Pareto, Maffeo Pantaleoni
(first Italian marginalist), Luigi Einaudi
Supply and Demand Geometry
• Supply and Demand analytics are the
most frequently used tool of
microeconomics.
• The economists who anticipated the
“marginal revolution” were involved in
the development of these tools.
• Cournot, Karl Rau, Jules Dupuit, Hans
von Mangoldt, and Fleeming Jenkin
contributed to the development of
demand/supply analytics from 18381870.
Supply and Demand Geometry
• By 1870, supply and demand had been utilized to:
(1) depict equilibrium,
(2) show how price/quantity adjustments ensure
equilibrium,
(3) examine price elasticity,
(4) show how shifts in demand/supply alter
equilibrium,
(5) analyze the incidence of taxation,
(6) examine the welfare effects of taxation,
(7) analyze price discrimination,
(8) distinguish between market period and long-run
equilibrium,
(9) analyze the pricing of joint products.
Supply and Demand Geometry
Antoine Augustin Cournot in his
Researches (1838):
(1) First to draw a market demand
curve, showing the demand function as
a function of sales at different prices.
(2) In identifying the revenuemaximizing price as that which occurs
when dD/dp = D/p, and that revenue
rises or falls as dD/dp is less than or
greater than D/p, he discovered the
concept of price-elasticity of demand.
Supply and Demand Geometry
Cournot:
(1) Introduced the first supply curve as a
positive function of price, arguing that
marginal cost rose as a function of
output;
(2) identify the competitive equilibrium as
occuring where the curves intersected;
(3) show the effect of a per-unit tax on the
competitive equilibrium, noting that price
rose by less than the tax so long as
demand was negatively –sloped;
(4) and, noted that the portion of the tax
shifted to buyers varies inversely with the
price-elasticity of demand.
Karl Heinrich Rau
• Karl Heinrich Rau (1792-1870)
– Born in Erlangen, Bavaria.
– Studies at University of Erlangen (1808-1812),
becomes Privatdozent and then professor in
1818.
– Becomes Chair of Political Economy at
University of Heidelberg in 1822 and remains
there till his death.
– Author of leading textbook from 1826-1854,
Grundsätze der Volkswirthschaftslehre
(Principles of Political Economy).
– Maintained all prices should be treated within
demand-supply framework.
Supply and Demand Geometry
Karl Heinrich Rau was the first
economist to use the supply-demand
diagram to investigate the stability of
market equilibrium and show the
forces that restore equilibrium when
disturbed.
In the 4th edition (1841) of his
Grundsätze, he argued that if price is
other than at equilibrium, an excess
demand or excess supply arises that
leads to sellers to alter the price they
are charging, until equilibrium is
restored
Jules Dupuit
• Jules Dupuit (1804-1866)
– French civil engineer
– Educated at Ecole Polytechnique
(Paris)
– 1824, entered service of
Administration of Bridges and
Highways, eventually rising to chief
engineer in charge of Paris
municipal services
– Most of books on engineering
subjects, second half of life became
interested in economic problems
Dupuit’s Contributions
• Most important economic contributions
– “On the Measurement of the Utility of Public
Works” (1844)
– “On Tolls and Transport Charges” (1849)
• How should public works investments be
valued?
• Three fallacies
– utility of public work isn’t measured by its cost
– utility isn’t measured by saving in transportation
costs allowed (increase in Q, increase TC)
– utility isn’t measured by increase in quantity
transported valued at constant price (because
value declines with increased quantity)
Dupuit’s Contributions
• The “Two Laws of Demand”
– First Law : demand curves slope
downward with respect to price constructs demand curve based
on “maximum sacrifice willing to
be made to acquire given
quantity” - negatively sloped
because extra quantities of a good
add less to total satisfaction.
– Second Law : the demand curve is
convex because of the “pyramid
of income distribution”
Dupuit’s Contributions
• Distinguishes between
“absolute utility” (total) and
“relative utility” (consumer
surplus)
• The price op measures the
utility of only the last unit
purchased.
• The trapezoid oPnr measures
“absolute utility”, the
rectangle opnr measures the
total expenditure on the good,
and the triangle pPn
measures “relative utility.”
Dupuit’s Contributions
• The triangle nNr is the utility
lost due to price constraint –
under competitive conditions
when resources are scarce,
the units rN are worth less
than the price necessary to
have them produced.
• If this depicts a costless
monopoly charging oP,
however, then nNr is the
value of goods consumers
artificially lose (the first
diagram to depict deadweight
loss of monopoly).
Dupuit’s Contributions
• Welfare effects of a
per-unit tax.
– the imposition of a tax
results in a loss of
consumer surplus that
exceeds the yield of the tax.
Consumers lose “relative
utility” (consumer surplus)
that is not offset by any
gain.
Dupuit’s Contributions
• Pricing policy for
utilities
– Notes that
discriminatory pricing
reduces dead-weight
losses and notes classpricing for railroads
achieves such a goal
Hans von Mangoldt
• Hans von Mangoldt
(1824-1868)
– Text, Grundriss der
Volkswirthschaftslehre
(1863) (Outline of Political
Economy).
– Explicitly references Rau,
and his stability analysis,
like Rau’s, highlights the
price-equilibrating role of
excess demand and
excess supply.
Supply and Demand Geometry
- Relates the height
of the demand curve
to marginal utility
and the downwardsloping nature to
diminishing
marginal utility
- Identifies changes that can shift the demand
curve: population, tastes, knowledge, income and
wealth
- Identifies exceptions to law of demand –
conspicuous consumption and price expectations
Supply and Demand Geometry
Identified different shaped
supply curves with the
behavior of costs of
production
(a) constant cost; (b)
constant cost up to a fixed
capacity; (c) constant costs
that yield to increasing
costs and then fixed
capacity; and, (d)
decreasing costs due to
economies of scale followed
by increasing costs due to
diseconomies of scale.
Supply and Demand Geometry
First extended comparative
statics exercises, and posits a
three-step adjustment
process for unanticipated
shifts in curves:
(1) a shift in the curve, which
(2) produces a gap between
supply price and demand
price at existing output that
alters profits, which
(3) induces a change in the
quantity supplied to restore
equilibrium.
Supply and Demand Geometry
Extended analysis of joint product
cases: “joint demand,” “joint supply,”
“composite demand” and “composite
supply.”
• Joint demand - purchased in fixed proportions;
joint supply - produced in fixed proportions;
composite demand –two competing uses for a
fixed input; composite supply – two substitute
goods supply a single need.
Exceeds J.S. Mill’s statement
concerning the necessary conditions
that must hold for the profitable
production of jointly supplied goods to
an analysis of the demand and supply
adjustments necessary to bring the
conditions into fruition.
Fleeming Jenkin
• Fleeming Jenkin (1833-1885)
– Born Dungeness, Kent, England
– Educated in Scotland, Frankfurt, Paris and
Genoa, learned engineering at the University of
Genoa
– Professor of Engineering, University of
Edinburgh from 1868
– Inventor of telpherage (aerial tramway),
electrician, cable engineer, linguist, critic, actor,
dramatist, artist
– Memorialized by his student Robert Louis
Stevenson in Memoir of Fleeming Jenkin
Supply and Demand Geometry
In three papers published in
1868, 1870, and 1872 Jenkin
presented demand-supply
analysis in application to
labor, trade unions, and the
incidence of taxes.
Differentiated between
market period and long-run,
introduced idea of
reservation prices of
suppliers during market
period based on future
price expectations.
Supply and Demand Geometry
Analyzed comparative
statics due to demand
curve shifts (whims,
tates,expectations,
income) and supply
curve shirts (size of
stock on hand and
expectations) in market
period and due to
changes in cost of
production in long-run.
Supply and Demand Geometry
Analyzed tax incidence
on the basis of the slopes
of demand and supply
curves, derived the
concepts of consumer
surplus (priority to
Dupuit) and producer
surplus and noted that
the welfare loss to
consumers and
producers always exceed
the tax they pay.