Question: Problem #4 Assume that the principal is risk-neutral and cares only for the expected value of his…

01 May Question: Problem #4 Assume that the principal is risk-neutral and cares only for the expected value of his…

Posted at 18:24h in 2Past Paper by Exams

Problem #4 Assume that the principal is risk-neutral and cares only for the expected value of his company’s revenue, while the agent is both risk- and ‘work-averse. The agent’s utility function depending on income and effort devoted to work is given bt the following function: U(w,e) e, where w is the non-negative wage and e is effort. For simplicity assume that only two levels of effort are possible: e 0 (low) and e 1 (high). The agent has the possibility to undertake work elsewhere and his utility derived from working there will amount to 1. The revenue of the company depends both of effort devoted to work by the agent and on random events, which neither the principal nor the agent can control. To be precise, the revenues are given by the following lottery depending on the agent’s effort: Leo (10, 2/3; 30, 1/3) Le 1-(10, 1/3; 30, 2/3) a) What contract will the principal sign with the agent if he can observe the latter’s effort? How will the risk burden be divided between them in this case? b) If the principal cannot observe the agent’s effort, how can he incentivize the former to choose the effort level desired by the principal? How will the risk burden be divided between them in this case? What utility levels will the agent and the principal achieve?

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