Ralph owns a production function. Randomness in the environment plus labor input from a manager combine to
Question:
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?
International Marketing And Export Management
ISBN: 9781292016924
8th Edition
Authors: Gerald Albaum , Alexander Josiassen , Edwin Duerr