7. A risk-neutral principal hires an agent to work on a project at wage to. The agent's utility function is U(w,e₁)=√w-g(e) where g(e) is the disutility associated with the effort level e exerted on the project. The agent can choose one of two possible effort levels, e, or ez, with associated disutility levels g(e) = 4, and g(e₂) = 2.5. If the agent chooses effort level ₁, the project yields 100 with probability 1/2, and 0 with probability 1/2. If he chooses e2, the project yields 100 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. (a) If effort is observable, which effort level should the principal implement? Derive the best wage contract that implements this effort. Does this involve sharing risk with the agent? Explain your answer. (b) If effort is not observable, which effort level should the principal imple- ment? What is the best wage contract that implements this effort?

7. A risk-neutral principal hires an agent to work on a project at wage to. The agent's utility function is U(w,e₁)=√w-g(e) where g(e) is the disutility associated with the effort level e exerted on the project. The agent can choose one of two possible effort levels, e, or ez, with associated disutility levels g(e) = 4, and g(e₂) = 2.5. If the agent chooses effort level ₁, the project yields 100 with probability 1/2, and 0 with probability 1/2. If he chooses e2, the project yields 100 with probability 1/4 and 0 with probability 3/4. The reservation utility of the agent is 0. (a) If effort is observable, which effort level should the principal implement? Derive the best wage contract that implements this effort. Does this involve sharing risk with the agent? Explain your answer. (b) If effort is not observable, which effort level should the principal imple- ment? What is the best wage contract that implements this effort?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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question1-3
3. A risk-neutral principal hires an agent to work on a project at wage w. The agent's utility function is: v(w)-g(e), where v(w)= Jw and g(e)=e/2 The agent can choose one of two possible effort levels, e¡ = 4 or e, = 6 . If the agent chooses effort level e, = 4 the project yields 100 with probability 1/4 and 0 with probability 3/4. If he chooses e, = 6 the project yields 100 with probability ½ and 0 with probability ½. The reservation utility of the agent is 0. (a) Suppose the effort level chosen by the agent is observable by the principal. Find the contract chosen by the principal. Show graphically in terms of contingent utilities v(w,00) and v(w.)