Ralph owns a production function. Randomness in the environment plus labor input from a

manager combine to produce output. The output can be one of two quantities: 1 2x x ?. The

managers input can be one of two quantities, H L ?. Ralph is risk neutral. The probabilities

are given below, and you should assume the higher output is sufficiently attractive that Ralph

wants supply of input Hin all that follows.

Ralphs manager is risk averse and also incurs an unobservable personal cost in supplying

the labor input. We model this in the usual way. The managers utility for wealth is as given in

(13.2), with ? 5,000Hc, 0 ?Lcand ?? 0.0001. Also, the managers opportunity cost of

working for Ralph is a certainty equivalent of M ? 10,000.

(a) Suppose the manager is trustworthy and will honor any agreement (or, equivalently,

serious penalties are feasible and the managers input can be observed). What is the

cost to Ralph of acquiring input H?

(b) Suppose the only observable for contracting purposes is the managers output.

Determine the optimal pay-for-performance arrangement. What is the cost to Ralph of

acquiring input H? What is the managers certainty equivalent for the payment

lottery that is faced?

(c) Why, in your solution to part (b) above, is the manager paid more when the largest

feasible output (i.e., 2x) is observed?