Week 11 General Equilibrium (Jehle and Reny,...

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?

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.

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

)denotes consumer i 's bundle according to the allocation.

The set of feasible allocations in this economy is given by

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.

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

The solution xi (p,p.ei ) is the consumer's demanded bundle, which

depends on market prices and the consumer's endowment income.

Equilibrium in Competitive Market Systems E�ciency

Week 11 General Equilibrium (Jehle and Reny,...

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