201Lecture152006 - Economics 201BSecond Half Lecture 15 GEI...

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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.

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201Lecture152006 - Economics 201BSecond Half Lecture 15 GEI...

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