Design of the Optimal Incentive Contract When Employee ls Work-Averse Helmut Paris, the owner of a small fanning operation is pondering the current employment contract between himself and his sole employee, Gary Drumbo.

Gary operates a small farm owned by Helmut. The farm is located some distance from Helmut, who, therefore, has no opportunity to_ observe Gary's activities. The farm's total output, X, is a function of Gary's level of effort,

a, and a combination of outside, uncertain events, (), such as sun, rain, and pests, over which Gary has no control.

Helmut and Gary have studied the production function and found that it has the farm:

X = a + b where (J is thought to take on values lying between zero and b.

Helmut makes decisions using the expected value decision-making criterion, whereas Gary is both risk- and effort-averse. That is, Gary suffers a personal cost when exerting effort.

This admission has prompted Helmut to offer Gary a share in output "to motivate Gary to provide higher effort." After some haggling, Gary has agreed to provide 100 units of effort in exchange for a satisfy of $1,000 and 10% of the farm's output, which will be accurately measured by a third party at the end of the growing season.

Although the matter has not been discussed, if Gary is caught supplying fewer than 1 00 units of a he will face immediate dismissal. Dismissal will result in irreparable damage to his reputation, thereby impairing future employment opportunities, so Gary will avoid putting himself in danger of dismissal at any cost.

Required

( l ) Do you think that this contract will achieve its intention of motivating "more effort"

from Gary?

(2) Suppose that Gary and Helmut agree on a contract that pays $ 1 ,000 plus 10% of any output that is in excess of a target that is set equal to the average yield in surrounding farm properties. Would that condition change Gary's behavior?

(3) Ignore the variation in Requirement 2. What will happen if Gary is risk-neutral and effort-

averse? Can you think of a better contract than the existing one? (4) Ignore the variation in Requirement 2. How does the situation in the original contract change if X is of the form X = aθ?