Problem 5: Moral Hazard (Principal-Agent Problem)

Consider a firm that hires people to load and unload shipping trucks. The company cannot perfectly observe whether each individual worker works or shirks (i.e., not do their job), all the firm can observe has an insignificant effect on the overall outcome for the firm. The firm does however care about the effort level of their pool of workers so they do want to induce them to actually work. Due to the fact that the single worker has no measurable impact on the outcome for the firm, the company cannot make wage offers contingent upon the outcome. The only thing a firm can do is to offer a fixed wage and then fire any worker they observe to be shirking. Their observation is imperfect though and so the firm only observes a worker shirking with some probability. The firm also occasionally makes mistakes and even fires workers who were working. The structure of the game is that:

(1) the firm offers a wage contract,

(2) the worker choose to accept or reject (if they reject they receive some level of reservation utility bar u = 10 and the firm receives 0),

(3) If the worker chose to shirk he is fired with probability p=0.5 and has no effort cost while if the worker did not shirk there is no chance that he will be fired, but he pays an effort cost e=5.

(4) If a worker gets fired, he does not receive his wage but instead receive his reservation utility of bar u = 10. The utility for a worker in any state is simply the wage he receives less the cost of any effort.

Assume the firm’s revenues are such that they can profitably pay the wage required to induce high effort but they lose money if all their workers shirk.

a. Begin with a simpler case in which we will assume that the firm could actually contract on effort level. What wage contract would the firm offer to a worker if the firm wants to elicit high effort?

For the following parts, reassert all the original structure under the assumption that effort level is unobservable! 

b. What are the conditions that must be satisfied to elicit high effort?

1. What is the lowest wage that satisfies IR condition?

2. What is the lowest wage that satisfies both conditions?

3. Do the wages you found in b.1 and b.2 differ. If yes, why? If no, why? (Briefly explain it).

c. (*Small bonus question) Besides firing a person who shirks, what else can the firm when designing contracts in order to elicit high effort? Be very brief.