A simple model of search. Consider an agent who lives two periods. He is unemplo

Question

A simple model of search. 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) How much would the agent value today a dollar tomorrow? (Hint: use the concept of discount factor).

(b) What is the expected value of the potential offers?

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

(e) What is his reservation wage?

Explanation / Answer

As the discount factor is 0.5 or 50% the agent would value today a dollar 1.5 times a dollar tomorrow.

Expected value of the potential offers = 8 x 0.5 + 24 x 0.5 = $16

The value for the worker if he accepts the current offer w will be w itself. And the value for the worker if he rejects the current offer w will be $4.

His reservation wage will be the minimum wage that he is willing to work on. If he accepts the initial offer it will be w or else it will be $8.

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