homework8 2010 solutions

homework8 2010 solutions - ECN/APEC 7240 Spring 2010...

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Unformatted text preview: ECN/APEC 7240 Spring 2010 Homework 8 Solutions 1) Consider a model where members of the labor force maximize , ~ = T t t t y E where y t is the income received at t and (0, 1). In each period, labor force members are either employed with wage w or unemployed, in which case they receive unemployment compensation c (0, B ), where B > 0. Every period, an employed worker has a probability (0, 1) of being fired, in which case he receives c instead of w . Meanwhile, a member of the labor force who starts the period unemployed receives in each period a job offer with a wage w drawn from a distribution with cdf F on the interval [0, B ]. a) The Bellman equation for this model is . ) ' ( ) ' ( , ) ' ( ) ' ( ) ( ) 1 ( max ) ( + + +- + = B B w dF w v c w dF w v c w v w w v Let us suppose that - + = w w w w H E w w E w v ) ( ) ( where E , H , and w have to be determined. Since the second entry in the Bellman equation is independent of w and the first entry is not, w is the reservation wage above which the consumer accepts the offer and below which he does not. Then we must have + = + +- + = B B w dF w v c w dF w v c w v w w v ) ' ( ) ' ( ) ' ( ) ' ( ) ( ) 1 ( ) ( ) ( ) ( w v w v w = + Thus . 1 ) ( - = = w w v E If w > , w ECN/APEC 7240 Spring 2010 [ ] . ) ( ) 1 ( )) ( )( 1 ( ) ( E w w H w E w w H E w w w H E +-- + = +- +- + =- + Equating coefficients, H H ) 1 ( 1 - + = E w H w H E +-- =- ) 1 ( . Solving these, we obtain . ) 1 ( 1 1 -- = H [ ] ....
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.

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homework8 2010 solutions - ECN/APEC 7240 Spring 2010...

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