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Unformatted text preview: Economics 201BSecond Half Lecture 15 GEI Model (Continued) Saw in Lecture 14 that Equilibrium need not be Pareto Opti mal. Model V(b): Either 2 periods, L > 1, securities pay off in goods; or more than 2 periods with L = 1. Two situations work much the same way. Natural Conjecture : In the GEI model, Walrasian Equi librium is constrained Pareto Optimal, i.e. there is no allo cation achievable by the given markets that Pareto domi nates the Equilibrium allocation. Note that the conjecture is ambiguous, since the allocations achievable by the given markets depend on the prices. Under any reasonable interpretation, the conjecture is false . Hart Example (19.F.2 in MWG, but with different spin). I = 2, L = 2, S = 2. There are no securities, so you cant trade consumption across states. States s = 1 and s = 2 have identical Edgeworth boxes. Each Edgeworth box has three Equilibrium prices; let p and p be two of them. Within each Edgeworth box, agent 1 prefers p to p , agent 2 prefers p to p 1 Fix utility functions v 1 , v 2 realizing the preferences of agents 1,2 in the common Edgeworth box. x `si denotes the consumption of good ` by agent i in state s . Let u 1 ( x 111 , x 211 , x 121 , x 221 ) = 100 v 1 ( x 111 , x 211 ) + v 1 ( x 121 , x 221 ) u 2 ( x 112 , x 212 , x 122 , x 222 ) = v 2 (...
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This note was uploaded on 08/01/2008 for the course ECON 201B taught by Professor Anderson during the Spring '06 term at University of California, Berkeley.
 Spring '06
 ANDERSON
 Economics

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