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...

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 at that wage in both periods. If he rejects the o§er, he receives

unemployment benefit of $4 this period and he gets to draw a new wage offer

next period. There are only two possible offers with equal probability next

period: one wage offer at $8, and another offer at $24. The worker's objective

is to maximize the sum of expected discounted earnings. The discount factor is

r=.5.

(a) How much would the agent value today a dollar tomorrow?

(b) What is the expected value of the potential o§ers?

(c) What is the value for the worker if he accepts the current offer?

(d) What is the value for the worker if he rejects the current offer?

(e) What is the lowest value for w for the worker to accept the offer?

(f) Suppose the government increases the unemployment benefit to $6. How

is your answer in (e) affected?