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# lecture10 - Lecture 10 Complete Markets States of the World...

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Lecture 10 Complete Markets

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ECN/APEC 7240 X - 2 States of the World Consider an infinite-horizon model where in each period t the state of the world is described by a stochastic variable s t S . • Let s t denote the history ( s 0 , . . . , s t ). The probability of realizing s t is π t ( s t ). – We normalize π 0 ( s 0 ) = 1. The probability of s t conditional on s τ is . ) ( ) ( ) | ( τ τ τ π π π s s s s t t t t =
ECN/APEC 7240 X - 3 Complete Markets Consumption is the only physical good. We view consumption in different states of the world as different goods. If markets are complete, we can buy and sell consumption in all possible states of the world in competitive markets.

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ECN/APEC 7240 X - 4 Preferences and Endowments There are I agents. In period t , agent i has an endowment y i t ( s t ) of consumption if s t is the state of the world. • If i has the consumption plan c i = { c i t ( s t )} t =0 , he values the plan by [ ] = = 0 ) ~ ( ) ( t t t i t i s c u E c U β [ ] ∑ ∑ = + = 0 1 ). ( ) ( t S s t t t t i t t t s s c u π β
ECN/APEC 7240 X - 5 Utility u is a strictly increasing, twice continuously differentiable, strictly concave function. u satisfies the Inada condition . ) ( ' lim 0 = c u c

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ECN/APEC 7240 X - 6 Allocations An allocation is a set of plans ( c 1 , . . . , c I ). An allocation is feasible iff for all t 0 and for all s t S t +1 , . ) ( ) ( 1 1 = = I i t t i I i t t i s y s c
ECN/APEC 7240 X - 7 Arrow-Debreu Markets For all t 0 and for all s t S t +1 , there is a market for consumption at s t .

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lecture10 - Lecture 10 Complete Markets States of the World...

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