grad school

1. Consider the following efficiency wage model where I, is the value of being employed without shirking, I, is the value of being employed with shirking and V is the value of being unemployed. p 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, L 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: PV= = (w-e)-b(V - V.) PV's = w-(b+9)(Vs -V.) plu = a (V - Vu) The production function is Y(t) = (e * L(t)) 0.5. a. Derive the value function relation for the shirking worker. b. Assume e = 1, L = 10 and N = 100. Also assume p = b = 0.1, q = 0.05. Derive and