201Lecture142006 - Economics 201BSecond Half Lecture 14...

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Economics 201B–Second Half Lecture 14 Uncertainty, including GEI Model GEI (General Equilibrium, Incomplete Markets) Model studies situations in which markets are incomplete: there are restric- tions on the allowed trades Six Models V(a): DC V(b): DI -↑ III :REE IV :GEI -% II: A I: A-D A-D: Arrow-Debreu complete contingent claims A: Arrow securities REE: Rational Expectations Equilibrium GEI: General Equilibrium, Incomplete Markets DC: Dynamic Completeness DI: Dynamic Incompleteness Model I: Complete Set of Arrow-Debreu Contingent Claims L physical goods (umbrellas, houses) States s =1 ,...,S States reflect the set of possible situations (rainy, sunny, my house burns, doesn’t burn) 1
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At time 0, don’t know which state s will prevail at time 1, but do know the set of states and the probability dis- tribution over the states. Trade “contingent commodities” (an umbrella if it rains, a house if my house burns). You buy a piece of paper (security) which you can turn in for an umbrella if it rains, and is worthless otherwise. At time 1, the state s is revealed. You turn in your state s securities for goods, the securities for the other states are worthless, there is no trade, consumption occurs. Formally, a state-contingent commodity bundle is ( x 11 ,...,x L 1 ,x 12 ,...,x L 2 ,...,x 1 S ,...,x LS ) R LS + where ( x 1 s ,...,x Ls ) is the consumption if state s occurs. Point: Create LS goods, just like an economy with no un- certainty. The Existence and Welfare Theorems and their proofs hold verbatim provided There is a market for each of the LS state-contingent commodities; and Either · Everyone knows the true probability distribution over
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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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201Lecture142006 - Economics 201BSecond Half Lecture 14...

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