Formulate the problem in Section 16.5.2 as one of an unemployed worker sampling wages from an exogenously given stationary wage distribution H (w). The objective of the worker is to maximize the net present discounted value of his income stream. Assume that once the worker accepts a job he can work at that wage forever.

(a) Formulate the dynamic maximization problem of the worker recursively, assuming that once the worker finds a job he never quits.

(b) Prove that the worker never quits a job that he has accepted.

(c) Prove that the worker uses a reservation wage R.

(d) Calculate the expected duration of unemployment for the worker.

(e) Show that if the wages in the distribution H (w) are offered by firms and all workers are identical, the wage offers of all firms other than those offering w = R are not profit maximizing. What does this observation imply about the McCall search model?