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Grad school Macroeconomics hw: Please see attached document for the full assignment

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Grad school Macroeconomics hw: Please see attached document for the full assignment. Consider the following efficiency wage model where EV is the value of being employed without shirking, SV is the value of being employed with shirking and UV is the value of being unemployed. ρ is the discount rate of the representative worker, b is the rate at which jobs break, q is the detection rate of shirking workers and a is the rate at which unemployed workers find a job. The number firms in the economy is N, L is the number of workers, is the number workers per firm, w is the real wage and e is the full (non-shirking) effort level.The following three equations describe the relation between the values of being in different states as a worker in the above described Shapiro-Stiglitz model:a. Derive the value function relation for the shirking worker.b. Assume ̅=1, =100 and =10. Also assume = = =0.1. Derive and solve for equilibrium wage, employment and unemployment.c. If the cost of full effort doubles ( ̅=2) in this economy (think education cost and quality), how would that affect wage and employment?
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