pr9ec70204 - Problem Set 9 Econ 702, Spring 2004 April 8,...

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Unformatted text preview: Problem Set 9 Econ 702, Spring 2004 April 8, 2004 Problem 1 (Fishermen Economy) Consider the fishermen economy that was introduced in class, with an Archipelago with a continuum of islands. There is a fisherman on each island (and the fisherman cannot swim). Every period the fisherman wakes up and receives his endowment of fish, e, which follows a Markov process with transition matrix Γ ee . There is a storage technology and if the farmer saves q units of fish today, he gets 1 unit of fish tomorrow. His savings are denoted by a . ( e,a ) is the type of the fisherman and the set consisting of such pairs is: E × A = { e 1 ,e 2 ,...,e n } × [0 , ¯ a ] Let F denote the σ-algebra defined on the set ( E × A ). We are interested in the transition function which tells us the probability that a fisherman with ( e,a ) today ends up in some ( e ,a ) ∈ B ∈ F , where B = ( B e × B a ). Using the fisherman’s decision rule a = g ( e,a ) and the transition matrix for the endowment process Γ ee , the transition function can be constructed as follows: Q ( e,a,B ) = 1 [ g ( e,a ) ∈ B a ] X e ∈ B e Γ ee (1) Show that given ¯ B ∈ F , Q ( ., ¯ B ) : ( E × A ) → R is measurable with respect to F...
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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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pr9ec70204 - Problem Set 9 Econ 702, Spring 2004 April 8,...

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