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Unformatted text preview: Paul Milgrom and Nancy Stokey Journal of Economic Thoery,1982 Motivation Model I Model II There are L commodities in each state of the world. Assume consumption set is R L + . Each trader i is described by: his endowment, e i : ϴ R L + his utility function, U i : ϴ x R L + R his (subjective) prior beliefs about ω, p i (.) and his (prior) informational partition, P i Utility Assumed that U i ( ϴ , .): R L + R is increasing for all i, ϴ . If U i ( ϴ , .) is concave for all ϴ , trader i is said to be weakly risk averse. If strictly concave, then strictly riskaverse. Model III Trades A trade , t = (t 1 , …, t n ) is a function from Ω to R nL , where t i (ω) describes trader i’s net trade of physical commodities in state ω. If a trade can be described as a function from ϴ to R nL , it is called a ϴcontingent trade . E.g. a bet: I’ll bet you $100 it doesn’t rain tomorrow. A trade is feasible if: Beliefs Assume p i (ω) > 0 for all ω and every i. Let E i [.] denote i’s expectation under p i . Say that beliefs are concordant if: Theorem I The idea of the proof: traders are at an ex ante paretooptimal allocation. Thus, in order for a trader to wish to trade, he must allocation....
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This document was uploaded on 01/05/2012.
 Fall '09

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