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solpr9ec70204

# solpr9ec70204 - Problem Set 9 Econ 702 Spring 2004 April 8...

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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. Γ is a transition matrix for Markov chain, so that Γ ee is measurable. Then e B e Γ ee is measurable as well. e B e Γ 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

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1. (Agents optimize) Given q * , { g ( s, a ; q * ) , V ( s, a ; q * ) } solve the agent’s problem. 2. (Consistency) Q ( s, a, B ; q * ) is a transition function associated with Γ ss and g ( s, a ; q * ), Q ( s, a, B ; q * ) = 1 [ g ( s,a ; q * ) B a ] s B s Γ ss (1) 3. (Stationarity) x * is the unique stationary distribution associated with Q ( s, a, B ; q * ), x * ( B ) = ( S × A ) Q ( s, a, B ; q * ) dx * ( B ) B (2) 4. (Markets Clear)
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solpr9ec70204 - Problem Set 9 Econ 702 Spring 2004 April 8...

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