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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.

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Several Paths

  • Mathematical

    • Partial Equilibrium

      • Alfred Marshall

    • General Equilibrium

      • Leon Walras

    • Distribution

      • Wilfredo Pareto


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Several Paths (cont.)

  • Non-Mathematical

    • Laissez-faire

      • Austrian Economics

    • Institutional

      • Thorstein Veblen




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Antoine-Augustin Cournot (cont.)

  • Ecole Normal de Paris (studied mathematics)

  • Work as assistant to Marshall Gouvin Saint-Cyr (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


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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


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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


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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)


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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


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Antotine-Augustin Cournot (cont.)Graphically

Price, Costs

MC

AR = Demand

Quantity

MR

Costs, Revenues, Profits

TR

TC

Quantity


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Antoine-Augustin Cournot (cont.)

  • Duopoly Analysis

    • IMPORTANCE:

      • Interdependence of firm’s output

      • Uncertainty

    • LEAD TO

      • Monopolistic Competition

      • Game Theory


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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


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Anontoine-Augustin Cournot (cont.)Reaction Functions

Output of firm A

A’s reaction function

a0

a1

Output of firm B

b0

b1


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Anontoine-Augustin Cournot (cont.)Reaction Function

Output of firm A

J

B’s reaction function

a0

a1

aE

E

A’s reaction function

Output of firm B

b0

bE


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Léon WALRAS (1834-1910)

General Equilibrium


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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


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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


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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


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General Equilibrium

  • Additional Notation:

    • m final goods: a,b,c,….

    • marginal utility function for individual r = fq

    • 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, ….


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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,….


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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 Þ

    • otpt + oppp+ okpk + …. = da + dbpb+ dcpc + ….

  • since there are m commodities and n factors there are m+n unknowns


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General Equilibrium

  • To maximize utility:

    • a) Marginal utility of factors held must be proportional to their price

    • ft(qt - ot) = pt fa(da)

    • fp(qp - op) = ppfa(da)

    • fk(qk - ok) = pkfa(da)

    • where there are n of these equations.


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General Equilibrium

  • To maximize utility:

    • b) Marginal utility of commodities consumed must be proportional to their price

    • fb(dt) = pb fa(da)

    • fc(dp) = pcfa(da)

    • fd(dk) = pdfa(da)

    • where there are m-1 of these equations.


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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,…)


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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 onwhere n = t,p,k,….

  • This gives us a total of 2m+2n-1 unknowns.


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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


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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


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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.


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Vilfredo Pareto

  • He spend some time helping out political exiles from Italy

  • He was very much against Marxian economics

  • He strongly believed people well self-serving as Adam Smith had portrayed


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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


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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


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Income Distribution

Individuals

Uniform Income Distribution at the beginning of the year

Income


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Income Distribution

Individuals

Weak Pareto Law

Income