The Beginning of
Microeconomics
Different Paths
Several Paths
 Mathematical
• Partial Equilibrium
– Alfred Marshall
• General Equilibrium
– Leon Walras
• Distribution
– Wilfredo Pareto
Several Paths (cont.)
 Non-Mathematical
• Laissez-faire
– Austrian Economics
• Institutional
– Thorstein Veblen
Mathematical
Mathematics and Microeconomics
Anotoine
Augustin
Cournot
Alfred Marshall
Leon Walras
Wilfredo Pareto
Antoine-Augustin Cournot
1801-1877
Antoine-Augustin Cournot (cont.)
 Ecole
Normal de Paris (studied
mathematics)
 Work as assistant to Marshall Gouvin SaintCyr (Napoleon’s general)
 Doctorate from the University of Paris
 His work attracted the attention of Poisson
who help him find a teaching job at Lyons
in 1834
Antoine-Augustin Cournot (cont.)
 He
was also Inspector General Education
(succeeding Ampere)
 In addition he was superintendent to
Grenoble and Dijon Academy
 Became blind and finally retired in 1862
Antoine-Augustin Cournot (cont.)
 Major
Works:
• Exposition of the Theory of Chance and
Probability
• Research Into the Mathematical Principles of
the Theory of Wealth
 Other
later works do no include
mathematics
Antoine-Augustin Cournot (cont.)

There are authors, like Smith and Say, who, in writing on
Political Economy, have preserved all the beauties of
purely literary style; but there are others, like Ricardo,
who, when treating the most abstract questions, or when
seeking great accuracy, have not bee able to avoid algebra,
an have only disguised it under arithmetical calculations of
tiresome length. Any one who understands algebraic
notation, reads at a glance in an equation results reached
arithmetically only with great labor and pains
(Mathematical Principles, p.4)
Antoine-Augustin Cournot (cont.)
 First
to place Law of Demand Mathematical
terms
• D = f(P) where dD/dP < 0
 First
to show the rule to maximize profits
•  = P*D - (D)
•d/dP = dD/dP*P + D - d/D*dP/P = 0
•dD/dP*P + D = d/D*dP/P
•MR = MC
Antotine-Augustin Cournot (cont.)
Graphically
Price, Costs
MC
AR = Demand
Quantity
MR
Costs, Revenues, Profits
TR
TC
Quantity

Antoine-Augustin Cournot (cont.)
 Duopoly Analysis
• IMPORTANCE:
– Interdependence of firm’s output
– Uncertainty
• LEAD TO
– Monopolistic Competition
– Game Theory
Antoine-Augustin Cournot (cont.)
 ASSUMPTIONS
•
•
•
•
•
Two sellers
Know the total demand
Ignore the output each is to produce
Costless production
Zero Output Conjectural variation
– i.e. a conjecture that firm B will have no output
reaction to firm’s A actions
Anontoine-Augustin Cournot (cont.)
Reaction Functions
Output of firm A
A’s reaction function
a0
a1
Output of firm B
b0
b1
Anontoine-Augustin Cournot (cont.)
Reaction Function
Output of firm A
J
a0
B’s reaction function
a1
aE
E
A’s reaction function
Output of firm B
b0
bE
Léon WALRAS (1834-1910)
General Equilibrium
Biography
 His
father, Auguste Walras, was a classmate
of Cournot.
 While not to the extent of young Mill,
Auguste was the teacher of Léon.
 Not a brilliant student, in fact he flunked the
math portion of the admission exam to the
École Polytechnique
General Equilibrium
 Basic
Premise:
• Demand and Supply are functions of several
variables all of which are constantly being
adjusted directly or indirectly
 Consequently:
• Rather than looking for individual impact of the
specific variable we look for general
equilibrium as direct adjustments of the
variables occur
General Equilibrium
 Equations:
• T, T’, T’’ different kinds of land (classical rent
notion)
• P,P’,P’’ different kinds of labor (unlike modern
marginal product notion)
• K,K’,K’’ different kinds of capital
General Equilibrium
 Additional
•
•
•
•
•
Notation:
m final goods: a,b,c,….
marginal utility function for individual r = q
Price of final goods pb, pc, pd,….
Price of factor of Production pt, pp, pk, ….
Household starts with given factors of
production qt, qp, qk, ….
General Equilibrium
 Additional
Notation (cont..):
• Quantity of factors of production offered by
household: ot, op, ok, …. where on > 0 if
household is offering factor and on < 0 if
household is demanding factor (for n = t, p,
k,…)
• Finally, household demand for final goods is db,
dc, dd,….
General Equilibrium
 Since
there is no money the system uses a
numeraire. For simplicity allow numeraire
to be a. Thus, Pa = 1.
 Allowing for equilibrium in the household
sector 
• otpt + oppp+ okpk + …. = da + dbpb+ dcpc + ….
 since
there are m commodities and n factors
there are m+n unknowns
General Equilibrium
 To
maximize utility:
• a) Marginal utility of factors held must be
proportional to their price
 t(qt - ot) = pt a(da)
 p(qp - op) = pp a(da)
 k(qk - ok) = pk a(da)
• where there are n of these equations.
General Equilibrium
 To
maximize utility:
• b) Marginal utility of commodities consumed
must be proportional to their price
 b(dt) = pb a(da)
 c(dp) = pc a(da)
 d(dk) = pd a(da)
• where there are m-1 of these equations.
General Equilibrium
 Demand
functions are (m-1):
• db = fb(pt, pp, pk, …, pb, pc, pd,…)
• dc = fc(pt, pp, pk, …, pb, pc, pd,…)
 Supply
functions are (n):
• ot = ft(pt, pp, pk, …, pb, pc, pd,…)
• op = fp(pt, pp, pk, …, pb, pc, pd,…)
General Equilibrium
 Recall
that this was at the individual level.
At the “macro” level then with the
assumption of summation we would get:
• Dn = Sdn where n= a,b,c,…. and
• On = Son where n= t,p,k,….
 This
gives us a total of 2m+2n-1 unknowns.
Vilfredo Pareto
July 15, 1848-August 19, 1923
 Son
of a Genoese father and a French
mother was trained as an engineer
 He left business at the age of 45 and
accepted the chair of Lausanne vacated by
the retirement of Walras
 Bad health and a sizable inheritance
allowed him an earlier retirement
Vilfredo Pareto
 He
went to live to Celigny on the Lake of
Geneva
 He grew to be known as the “lone thinker of
Celigny”
 Lived in a house with many cats named
“Villa Angora”
 Know as both a sociologist and an
economist
Vilfredo Pareto

Pareto married in 1889. His new spouse Dina
Bakunin, a Russian, apparently loved an active
social life, which was rather in conflict with
Pareto's own love of privacy and solitude. After
twelve years of marriage Dina abandoned her
husband. His second wife, Jane Regis, joined him
shortly after the collapse of his marriage and the
two remained devoted to one another throughout
the remainder of Pareto's life.
Vilfredo Pareto
 He
spend some time helping out political
exiles from Italy
 He was very much against Marxian
economics
 He strongly believed people well selfserving as Adam Smith had portrayed
Vilfredo Pareto
 Furthermore,
in his work in sociology he
strongly advocated the rule of the elite
 Because of this, some considered him to be
a fascist
 This believe isolated him even further
Vilfredo Pareto
 First
person to conceive of the distribution
of income in terms of a statistical
distribution
 He argued that if 100 persons were left in an
island with equal amount of income
 A year later, thru deceit, treachery, and other
methods only a small portion of the
population would have largest amount of
income
Income Distribution
Individuals
Uniform Income Distribution
at the beginning of the year
Income
Income Distribution
Individuals
Weak Pareto Law
Income