Question

1. I wish to hire an agent to sell a piece of property for me. The amount the property will sell for is random, and can be either $1,000,000 or $1,100,000. If the agent works hard the amount the property sells for will be $1,100,000 with probability 0.7 and $1,000,000 with probability 0.3. If the agent does not work hard, the property will sell for $1,100,000 with probability 0.4 and S1,000,000 with probability 0.6 I am risk neutral, and wish to maximize profits: the revenue from the sale less what I pay the agent. The agent is risk averse. Her utility depends on the money she receives and whether or not she works hard. If she does not work hard and earns payment M her utility is U(M) M1. If she works hard and earns M her utility is U(M) M-40. If she does not take the job she can obtain a certain utility of 150 elsewhere (a) Suppose that I can observe whether the agent works hard, and I can base a contract on that information. Will I choose for her to work hard? What will the agent's expected utility be? (b) Now suppose that I cannot observe whether the agent works hard. However, I can make her payment depend upon the sale price of the property. IfI decide for her to not work hard, what will be my expected profit? What will be her expected utility? (c) Suppose I wish to induce the agent to work hard. To do so, I will choose a payment MH that she will receive if the sales price is high, and an amount ML that she will receive if the sales price is low. Write out the constraints that MH and ML must satisfy. Provide intuition for each constraint. Explain whether you expect each constraint to hold with equality (d) Suppose that I choose to pay MH = 52,901 and M-9344.4. Will this satisfy the constraints specified in (c)? Do I prefer this contract to the one identified in (b)? Explain.

Answer 1

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