A risk-neutral agent's working life has two periods. In each period, the agent can provide high effort (at personal cost $2,000) or low effort (at zero personal cost). In a given period, a high effort worker contributes $X to the company's revenues, a low effort worker contributes $10,000.
If the worker chooses low effort in the first period, then with probability 0.1 she is detected by her supervisor and fired at the end of the period without any compensation. In such a case, the firm hires a new (identical) worker for the second period. If fired, the worker goes to her alternative employment, where she can earn $5,000 in the second period without providing high effort. In the second period, the firm pays $5,000 (to either the retained worker or the replacement worker), regardless of the worker's level of effort. At the end of the second period, the firm dissolves.
(a) What is the lowest efficiency wage that would induce the worker to provide high effort in the first period?
(b) What is the lowest value of X for which the firm is willing to pay the above efficiency wage?
(c) What is the worker's net utility under the efficiency wage scheme? Is the worker better off than if she were simply paid $5,000 in each period and provided low effort? Explain briefly.