Consider an agent who lives two periods. He is unemployed at the beginning of the first period and has a wage offer of w. If he accepts the wage offer w, he will work forever at that wage. If he rejects the offer, he receives an unemployment benefit of 4 dollars this period and he gets to draw a new offer next period. There are only two possible offers with equal probability next period: one wage offer of 8 dollars, and another offer of 24 dollars. The worker's objective is to maximize the sum of expected discounted earnings. The discount factor ? is 0.5.
(a) Set up this worker's problem and find his reservation wage.
(b) What happens to his reservation wage as the unemployment benefit increases?