Exercise 16.12. Formulate the problem in subsection 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. (1) Formulate the dynamic maximization problem of the worker recursively assuming that once the worker finds a job he will never quit. (2) Prove that the worker will never quit a job that he has accepted. (3) Prove that the worker will use the reservation wage R for deciding what job to accept. (4) Calculate the expected duration of unemployment for the worker.

(5) Show that if the wages in the wage 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?