Principle Agent Problem [Dealing with hidden action]
Assume that the employer (principle) wants its employee (agent) to work hard [You can safely assume that this maximizes the principle's expected profits from his business]. There are two effort levels available, eL = 0 and eH = 2 . The effort level of the agent is not directly observable for the principle. Then the principle has to base his wage contract on the outcomes, year end profits for the firm. Two outcomes are possible, πH = 1000 and πL = 0. The outcome does not only depend on the effort level of the agent, but on the market conditions as well. But high effort level increases the chances of ending up with the good outcome. With high effort level probability of ending up with the good outcome πH is 0.9, and it is only 0.1 when the effort level is low.
Agent's utility function is given as U (w,e) = W ½ - 4e . Note that his utility depends negatively on the effort level he exerts; it is costly for him to exert effort _ it creates disutility. Agent's reservation utility is U0 = 1 by assumption, not getting the job he can stay at home and read all day and that worth 1 util for him. Put yourself in the place of the principle and design a wage contract for your agent. Again your aim is to exert high effort. Denote the wage payments agent receives when good outcome or when bad outcome is realized as wH and wL , respectively.
a. Indicate the condition that creates the incentive to exert high effort level for the agent [incentive compatibility constraint].
b. Indicate the condition that must hold for the agent to accept this contract [participation constraint or individual rationality constraint].
c. Determine the wage contract that would make the agent work and work hard [Go with the minimum possible wages, you want to maximize the profits].