solpr9ec70204

solpr9ec70204 - Problem Set 9 Econ 702, Spring 2004 April...

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Unformatted text preview: Problem Set 9 Econ 702, Spring 2004 April 8, 2004 Keep in mind that so far we looked at the following models of heteroge- nous agents economies and in the first four questions, we will look at the stationary equilibria of these economies. 1. Heterogenous agents economy with no trade: Archipelago with a con- tinuum of islands where fishermen cannot swim. 2. Economy with heterogenous agents and trade: Huggett Economy. 3. Economy with heterogenous agents and production: Aiyagari Economy. Problem 1 (Fishermen Economy) Solution: Given B F , B a and B e are fixed, The agent decision rule, g ( e,a ) must be in the asset space so that g ( e,a ) A ( e,a ) ( E A ). Since B a A , we know that g(e,a) is either in B a or not in B a . Then 1 g ( e,a ) B a = 1 or 0. is a transition matrix for Markov chain, so that ee is measurable. Then e B e ee is measurable as well. e B e ee multiplied by 1 or 0 is measurable as well. Then Q ( ., B is measurable. Problem 2 (Heterogenous Agents Economy with Trade) Solution: A stationary recursive competitive equilibrium in the loan economy is { q * ,g ( s,a ; q * ) ,V ( s,a ; q * ) ,x * ( q * ) ,Q ( s,a,B ; q * ) } such that, 1 1. (Agents optimize) Given q * , { g ( s,a ; q * ) ,V ( s,a ; q * ) } solve the agents problem. 2. (Consistency) Q ( s,a,B ; q * ) is a transition function associated with ss and g ( s,a ; q * ), Q ( s,a,B ; q * ) = 1 [ g ( s,a ; q * ) B a ] X s B s ss (1) 3. (Stationarity) x * is the unique stationary distribution associated with Q ( s,a,B ; q * ), x * ( B ) = Z ( S...
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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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solpr9ec70204 - Problem Set 9 Econ 702, Spring 2004 April...

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