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ps5macro2sp08 - Econ 387L Macro II Spring 2008 University...

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Econ 387L: Macro II Spring 2008, University of Texas Instructor: Dean Corbae Problem Set #5- Due 2/26/08 1. Consider the following search model. A worker who is employed begins each period with a wage w. The worker can either work at that wage or search and receive unemployment bene fi ts b in the current period. If the worker chooses to work, he is employed at wage w in the following period with probability δ and unemployed with probability 1 δ. An unemployed worker who searches receives a wage offer from a distribution F ( w ) at the end of the period (so that if he accepts a particular offer e w , he would begin the next period employed at wage w 0 = e w ) . Wage offers are i.i.d. over time. The worker’s preferences are P t =0 β t u ( c t ) where c t denotes consumption, u ( · ) is an increasing function, and β < 1 . Assume no borrowing or lending. a. Set up the worker’s decision problem as a dynamic program. b. Show that the solution to the worker’s problem is of the reservation wage form (i.e. that there exists a wage w such that for all draws w w the worker accepts and continues to search otherwise). Characterize the reservation wage. In particular, prove that
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