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Week 11General Equilibrium
(Jehle and Reny, Ch.5)
Serçin �ahin
Y�ld�z Technical University
4 December 2012
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 1 / 26
Is there one particular state towards which the system will tend?
or are there may such states?
Are these fragile things that can be easily disrupted or are they robust?
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 2 / 26
Equilibrium in Exchange
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 3 / 26
Equilibrium in Exchange
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 4 / 26
Equilibrium in Exchange
Consider now the case of many consumers and many goods.Let
I = {1, ..., I}index the set of consumers, and suppose there are n goods.
Each consumer i ∈ I has a preference relation, �i
and is endowed with a non-negative vector of the n goods,
ei = (e i1, ..., ein).
Altogether, the collection ε =(�i , ei
)i∈I de�nes an exchange
economy.
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 5 / 26
Equilibrium in Exchange
Let e ≡(e1, ..., eI
)denote the economy's endowment vector, and
de�ne an allocation as a vector x ≡(x1, ..., xI
), where xi ≡
(x i1, ..., x
in
)denotes consumer i 's bundle according to the allocation.
The set of feasible allocations in this economy is given by
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 6 / 26
Equilibrium in Exchange
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 7 / 26
Equilibrium in Exchange
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 8 / 26
Equilibrium in Exchange
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 9 / 26
Equilibrium in Competitive Market Systems
In a perfectly competitive market system, all transactions between
individuals are mediated by impersonal markets.
A noteworthy feature of the competitive model is its decentralized
nature.
It is essential that prices are able to clear all markets simultaneously.
The interdependence of markets renders the existence of an
equilibrium price vector a subtle issue.
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 10 / 26
Equilibrium in Competitive Market Systems Existence of Equilibrium
Again let I = {1, .., I} index the set of consumers and assume that
each is endowed with a non-negative vector ei of n goods.
Further, suppose each consumer's preferences on the consumption set
Rn+ can be represented by a utility function ui satisfying the following
assumption.
Assumption 5.1: Utility is continuous, strongly increasing, and
strictly quasiconcave on Rn+.
If p ≡ (p1, ..., pn)� 0 is the vector of market prices, then each
consumer solves
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 11 / 26
Equilibrium in Competitive Market Systems Existence of Equilibrium
The solution xi (p,p.ei ) is the consumer's demanded bundle, which
depends on market prices and the consumer's endowment income.
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 12 / 26
Equilibrium in Competitive Market Systems Existence of Equilibrium
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 13 / 26
Equilibrium in Competitive Market Systems Existence of Equilibrium
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 14 / 26
Equilibrium in Competitive Market Systems Existence of Equilibrium
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 15 / 26
Equilibrium in Competitive Market Systems Existence of Equilibrium
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 16 / 26
Equilibrium in Competitive Market Systems Existence of Equilibrium
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 17 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 18 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 19 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 20 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 21 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 22 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 23 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 24 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 25 / 26
Equilibrium in Competitive Market Systems E�ciency
Serçin �ahin (Y�ld�z Technical University)Week 11 General Equilibrium (Jehle and Reny, Ch.5)4 December 2012 26 / 26