A friend of yours has come seeking advice regarding the construction of an incentive contract for her employees. Your friend is interested in trying to maximize her expected income from the business: VooDoo Records. The profits of VooDoo Records depend on the fickle tastes of the public and the effort of its flagship band, The Tumbling Grandfathers. The probability that the latest release of the Grandfathers will be well received and profits high depends on the effort of the band. If the band exerts a high level of effort (eh ), the probability of acceptance is φ1.
If the band shirks and exerts a low level of effort (el ), the probability of acceptance is reduced to φ2. The reservation utility of the band has been normalized to 0. The utility function of the band is U(y, e) = 2y1/2 - e. Suppose that eh = 2, el = 1, φ1 = .75, and φ2 = .25. If the band is once again adored by the public, gross profits for VooDoo Records will be 10. If the band is rejected, gross profits will fall to 5. Gross profits are the profits VooDoo Records will earn before payments to the Tumbling Grandfathers.
(a) What is the full-information contract? Provide an intuitive explanation for your results.
(b) Suppose that your friend cannot observe the effort level of the band. Explain why the full- information contract is not incentive compatible. Why is this called moral hazard?
(c) Find the optimal incentive-compatible contract. Provide an intuitive explanation for your results.
(d) What is the expected income of your friend under full and asymmetric information? Why is she worse off under asymmetric information?