2 The labor search model (25 points)
Assume the workers in the model are all in the labor force. That is, the workers are either employedor unemployed, with U denoting the fractions of workers who are unemployed, and (1 - U) thefraction who are employed. The jobs of the employed differ according to the wage that they arepaid. Each period, there is a probability p that the unemployed worker can draw one job offer fromthe wage distribution,

. The worker has the option to reject the offer, in whichcase, he or she receives unemployment compensation. Alternatively, the worker can accept the offerto work at w, in which case, he or she receives w each period. Let 

  denote the expected valuefor a worker who has offer with wage w in hand.

is an increasing and concave function ofwage, u. In addition, Vu denotes the value of the unemployed worker, which is assunned to equal b.In the model, there will be fows between the pool of employed workers and the pool of unemployedworker. Some employed workers will be separated from their jobs and become unemployed, whilesome nnemployed workers will receive job offers that are suficiently attractive to accept.1 (5 points) Let the reservation wage be defined as the wage such that the worker is indifferentbetween accepting and rejecting an offer. Please write down the equation that pins down thereservation wage in the model. Use the reservation wage to characterize the decision regardingaccepting the job offer or not.