4332

Consider an unemployed worker who each period can draw two independently and identically distributed wage offers from the cumulative probability distribution function F(w). The worker will work forever at the same wage after having once accepted an offer. In the event of unemployment during a period, the worker receives unemployment compensation c. The worker derives a decision rule to maximize where yt = w or yt = c, depending on whether she is employed or unemployed. Let v(w) be the value of for a currently unemployed worker who has best offer w in hand.

a. Formulate the Bellman equation for the worker’s problem.

b. Prove that the worker’s reservation wage is higher than it would be had the worker faced the same c and been drawing only one offer from the same distribution F(w) each period.