1. Phil has two periods of work remaining prior to retirement. Assume that Phil maximizes the present value of his expected lifetime earnings and his discount rate is 10 percent. He is currently employed in a firm that pays him the value of his marginal product, $62,000 per period. There is one other firm that Phil could potentially work for. There is an 80 percent chance of Phil being a good match for the other firm and a 20 percent chance of him being a bad match. If he is a good match, his VMP at the new firm will be $65,000 per period. If he is a bad match, his VMP at the new firm will be $40,000 per period.
a. Suppose it takes a full period to discover whether Phil is a good or bad match with the new firm. Thus, when the firm is making Phil's initial offer, the managers do not know what his productivity will be, though they do know the distribution of possible outcomes described above. What wage will the firm offer in this initial period?
b. After the value of the match is determined, Phil will then be offered a wage equal to the realized value of his marginal product in the firm. When offered that wage, Phil is free to (a) accept or (b) return to his original firm and his original wage. He can do this immediately, so that if he gets a low wage offer from the new firm, he can go back to his original firm and earn his original wage in the second period.