ECONOMICS OF INFORMATION AND INSURANCE

ECO 499 H Problem Set 1 Deadline: Monday, February 13, AT THE BEGINNING OF CLASS

[I will collect all works and then discuss the solutions in class, so you may wish to make a copy of your work before submitting it]

1. Answer the following questions AS BRIEFLY AS POSSIBLE:

(a) Name the condition(s) that guarantee(s) that the wage of the agent increases with the principal�s gross payo¤. (b) What do Grossman and Hart (1983) propose as an alternative of the �rst-

order approach when dealing with moral hazard with a continuum of feasible actions? (c) Which measure of executive compensation should we use when estimating

the company�s expected cost of hiring the executive? (d) How would a shift in demand from �rm-speci�c to general managerial

skills a¤ect CEO pay? Explain. (e) Give two possible explanations for the lack of RPE in the compensation

contracts of older/senior CEOs (f) Why may a CEO agree to work for a salary of $1? (g) Do you expect CEO�s pay-performance sensitivity to increase or decrease

with the volatility of the �rm�s stock returns. Explain. (h) What are the implications of the theory of career concerns for the pay-

performance sensitivity of junior versus senior CEOs?

2. A principal (she) hires an agent (he) to run a project which has a payo¤ xS if successful and 0 if unsuccessful, where xS > 0 If the agent receives a wage w and exerts e¤ort a, his utility is ln(w) � a. The agent can either shirk in which case a = 0 or work hard in which case a = 1. If the agent works hard and the state of the economy is good, then the project is successful with probability 0:6. If the agent shirks and the state of the economy is bad, then the project is successful with probability 0:1. If the agent works hard, but the state of the economy is bad, then the project is successful with probability 0:4. This is also the case if the state of the economy is good, but the agent shirks. The principal is risk-neutral and cares about the payo¤ of the project net of agent�s compensation. The agent�s reservation utility is 0 and does not depend on the state of the economy.

(a) Assume that the principal can observe both the state of the economy and the e¤ort of the agent. Also assume xS = 20.

(i) Suppose that the state of the economy is GOOD. Find the level of e¤ort that the principal would recommend to the agent, the wage received by the agent if the project fails, and the wage received by the agent if the project succeeds.

(ii) Would your answers change if the state of the economy is BAD? If no, why? If yes, how?

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(b) Now, assume that the principal can observe the state of the economy, but not the e¤ort exerted by the agent. Also assume that xS is such that the principal �nds it optimal to recommend HIGH EFFORT no matter the state of the economy.

(i) Suppose that the state of the economy is GOOD. Find the wage received by the agent if the project fails and the wage received by the agent if the project succeeds. Which of these wages is higher?

(ii) Suppose that the state of the economy is BAD. Find the wage re- ceived by the agent if the project fails and the wage received by the agent if the project succeeds. Which of these wages is higher?

(iii) Find whether the wage received by the agent if the project SUC- CEEDS is higher when the state of the economy is good or when it is bad. So, does it satisfy relative performance evaluation (RPE)?

(iv) Find whether the wage received by the agent if the project FAILS is higher when the state of the economy is good or when it is bad. So, does it satisfy RPE?

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