Consider a relationship between a principal and an agent in which the agent's effort influences the...

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Consider a relationship between a principal and an agent in which the agent's effort influences the result but is not observable. The principal is risk-neutral, and the agent is risk-averse, having a utility function U (w, e) = Vw-e, where w represents the wage and e represents the effort. The agent can choose between low effort e= 0, or high effort e 3. His reservation utility is 21. The production technology is such that only three results x are possible, where x represents the value of the result to the principal xe {0, 1,000, 2,500}. The probabilities conditional on effort are: Prob (x 0le=0) =0.4; Prob (x= 1,000le=0) =0.4; Prob (x= 2,500le=0)30.2; Prob (x 0le=3)%3= 0.2; Prob (x= 1,000l e= 3) = 0.4; Prob (x= 2,500 l e= 3) = 0.4. (a) What are the optimal symmetric information contracts? What effort will the principal demand from the agent? (b) What is the optimal contract under which the agent will exert an effort of e=0 if the only verifiable variable in the relationship is the result x? (c) Given a moral hazard problem, what is the constrained maximization problem that determines the optimal contract if the principal wants the agent to exert an effort of e 3? (Kuhn-Tucker may be useful.) (d) Which contract will the principal offer the agent under a moral hazard problem? (e) Discuss the optimal contract if the agent were risk-neutral. Consider a relationship between a principal and an agent in which the agent's effort influences the result but is not observable. The principal is risk-neutral, and the agent is risk-averse, having a utility function U (w, e) = Vw-e, where w represents the wage and e represents the effort. The agent can choose between low effort e= 0, or high effort e 3. His reservation utility is 21. The production technology is such that only three results x are possible, where x represents the value of the result to the principal xe {0, 1,000, 2,500}. The probabilities conditional on effort are: Prob (x 0le=0) =0.4; Prob (x= 1,000le=0) =0.4; Prob (x= 2,500le=0)30.2; Prob (x 0le=3)%3= 0.2; Prob (x= 1,000l e= 3) = 0.4; Prob (x= 2,500 l e= 3) = 0.4. (a) What are the optimal symmetric information contracts? What effort will the principal demand from the agent? (b) What is the optimal contract under which the agent will exert an effort of e=0 if the only verifiable variable in the relationship is the result x? (c) Given a moral hazard problem, what is the constrained maximization problem that determines the optimal contract if the principal wants the agent to exert an effort of e 3? (Kuhn-Tucker may be useful.) (d) Which contract will the principal offer the agent under a moral hazard problem? (e) Discuss the optimal contract if the agent were risk-neutral.