ps5_ans_sp08_part1 - Econ 387L: Macro II Spring 2008,...

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Econ 387L: Macro II Spring 2008, University of Texas Instructor: Dean Corbae Problem Set #5- Answers Part 1 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 f 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 o f er from a distribution F ( w ) at the end of the period (so that if he accepts a particular o f er e w , he would begin the next period employed at wage w 0 = e w ) . Wage o f ers 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. Answer: Since search is costless, the unemployed will always search. Upon searching she’ll receive a wage o f er w 0 from a distribution F ( w 0 ) and she will decide whether to stay unemployed and wait for a better job o f er or to accept the o f er and become employed at wage w 0 . Note that the option value of waiting for one more period is positive, because an employed agent cannot receive any job o f er. So, the unemployed has to compare the gain from searching for one more period (we can call it as the marginal bene f t of search), which is positive, and the gain from accepting the job o f erandno
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ps5_ans_sp08_part1 - Econ 387L: Macro II Spring 2008,...

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