The Beginning of Microeconomics

1
The Beginning of Microeconomics

• Different Paths

2
Several Paths

• Mathematical
• Partial Equilibrium
• Alfred Marshall
• General Equilibrium
• Leon Walras
• Distribution
• Wilfredo Pareto

3
Several Paths (cont.)

• Non-Mathematical
• Laissez-faire
• Austrian Economics
• Institutional
• Thorstein Veblen

4
Mathematical
5
Antoine-Augustin Cournot

• 1801-1877

6
Antoine-Augustin Cournot (cont.)

• Ecole Normal de Paris (studied mathematics)
• Work as assistant to Marshall Gouvin Saint-Cyr
  (Napoleons 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

7
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

8
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

9
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)

10
Antoine-Augustin Cournot (cont.)

• First to place Law of Demand Mathematical terms
• D f(P) where dD/dP lt 0
• First to show the rule to maximize profits
• ? PD - ?(D)
• d?/dP dD/dPP D - d?/DdP/P 0
• dD/dPP D d?/DdP/P
• MR MC

11
Antotine-Augustin Cournot (cont.)Graphically
Price, Costs
MC
AR Demand
Quantity
MR
Costs, Revenues, Profits
TR
TC
Quantity
?
12
Antoine-Augustin Cournot (cont.)

• Duopoly Analysis
• IMPORTANCE
• Interdependence of firms output
• Uncertainty
• LEAD TO
• Monopolistic Competition
• Game Theory

13
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 firms A actions

14
Anontoine-Augustin Cournot (cont.)Reaction
Functions
Output of firm A
As reaction function
a0
a1
Output of firm B
b0
b1
15
Anontoine-Augustin Cournot (cont.)Reaction
Function
Output of firm A
Bs reaction function
J
a0
a1
E
aE
As reaction function
Output of firm B
b0
bE
16
Léon WALRAS (1834-1910)

• General Equilibrium

17
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

18
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

19
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

20
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, .

21
General Equilibrium

• Additional Notation (cont..)
• Quantity of factors of production offered by
  household ot, op, ok, . where on gt 0 if
  household is offering factor and on lt 0 if
  household is demanding factor (for n t, p, k,)
• Finally, household demand for final goods is db,
  dc, dd,.

22
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 mn unknowns

23
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) pp fa(da)
• fk(qk - ok) pk fa(da)
• where there are n of these equations.

24
General Equilibrium

• To maximize utility
• b) Marginal utility of commodities consumed must
  be proportional to their price
• fb(dt) pb fa(da)
• fc(dp) pc fa(da)
• fd(dk) pd fa(da)
• where there are m-1 of these equations.

25
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,)

26
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 2m2n-1 unknowns.

27
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

28
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

29
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.

30
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

31
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

32
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

33
Income Distribution
Individuals
Uniform Income Distribution at the beginning of
the year
Income
34
Income Distribution
Individuals
Weak Pareto Law
Income