solpr7ec70204

Solpr7ec70204 - Solutions to Problem Set 7 Econ 702 Spring 2004 Prepared by Ahu Gemici Problem 1(Lucas Tree Model Solution From the First Order

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Solutions to Problem Set 7 Econ 702, Spring 2004 Prepared by Ahu Gemici March 24, 2004 Problem 1 (Lucas Tree Model) Solution: From the First Order Conditions we get: q i = β X j u c ( c 0 ) u c ( c ) Γ ij [ q j + z j ] i (1) In equilibrium, c=z, q i = β X j u c ( z j ) u c ( z i ) Γ ij [ q j + z j ] i (2) The above system of equations characterizes the prices of the tree at each state { q i } I i =1 . Now we will write this system of equations in the matrix form: q 1 .. .. q I = β Γ 11 u 0 ( z 1 ) u 0 ( z 1 ) β Γ 12 u 0 ( z 2 ) u 0 ( z 1 ) .. β Γ 1 J u 0 ( z J ) u 0 ( z 1 ) .. β Γ 22 u 0 ( z 2 ) u 0 ( z 2 ) .. .. .. .. .. .. β Γ I 1 u 0 ( z 1 ) u 0 ( z I ) .. .. β Γ IJ u 0 ( z J ) u 0 ( z I ) q 1 .. .. q I + z 1 .. .. z I Let q= q 1 .. .. q
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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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Solpr7ec70204 - Solutions to Problem Set 7 Econ 702 Spring 2004 Prepared by Ahu Gemici Problem 1(Lucas Tree Model Solution From the First Order

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