pr6ec70204

# Pr6ec70204 - an endowment of 1 unit of the good The agent’s utility function is u c = log c(1 1 Deﬁne and compute the Arrow-Debreu equilibrium

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Problem Set 6 Econ 702, Spring 2004 March 4, 2004 Problem 1 (ADE in a stochastic RA-NGM) In the beginning of the semester, we deﬁned certain objects in the deterministic AD environment, i.e. the com- modity space, consumption possibility set, production possibility set, etc. Then we wrote the growth model in the AD language with the purpose of applying the welfare theorems to the growth model. Now we want to do the same for the stochastic growth model. 1. Deﬁne the consumption possibility set, X , for the stochastic growth model. 2. Deﬁne the production possibility set, Y , for the stochastic growth model. Problem 2 Consider an economy with two periods. There are two states of nature: The good state and the bad state. The good state has probability 0.9 and the bad state has probability 0.1. There is only one agent in the economy. At t=0, the agent has one unit of the good. At t=1, in the ’good’ state, he will have an endowment of 2 units of the good, and in the ’bad’ state he will have

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Unformatted text preview: an endowment of 1 unit of the good. The agent’s utility function is: u ( c ) = log c (1) 1. Deﬁne and compute the Arrow-Debreu equilibrium for this economy. 2. Deﬁne Sequence of Markets equilibrium for this economy and show that it’s the same with the ADE allocation. Problem 3 Consider the economy described in Problem 2, but with two goods per period, say coconuts and scallops. At t=0, the agent is endowed with 1 coconut and 1 scallop. At t=1, in the good state, he’s endowed with 2 coconuts and 1 scallop; and in the bad state, he’s endowed with 1 coconut and 2 scallops. The agent’s utility function is: u ( c ) = log s + log c (2) 1 1. Deﬁne and compute the Arrow-Debreu equilibrium for this economy. 2. Deﬁne Sequence of Markets equilibrium for this economy and show that it’s the same with the ADE allocation. 2...
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## This note was uploaded on 11/12/2010 for the course ECON 8108 taught by Professor Staff during the Spring '08 term at Minnesota.

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Pr6ec70204 - an endowment of 1 unit of the good The agent’s utility function is u c = log c(1 1 Deﬁne and compute the Arrow-Debreu equilibrium

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