ECO 499 S1 Problem Set 1[I will collect all works and then discuss the solutions in class, soyou may wish to make a copy of your work before submitting it]1. Answer the following questions AS BRIEFLY AS POSSIBLE:(a) Do you expect that the share of stock and option grants in CEOtotal pay should be increasing or decreasing with the volatility of the ?rm?sstock returns. Explain.(b) Which measure of executive compensation should we use(i) when estimating the strength of managerial incentives(ii) when estimating the company?s cost of hiring the executive.(c) When may a principal want to sell a project to the agent?(d) Which is greater: the mean or the median of CEO pay?(e) Is the historical increase in CEO pay driven by cash pay or equity-based pay?(f) What are the implications of the theory of career concerns for thepay-performance sensitivity of junior versus senior CEOs?(g) Why may RPE fail for 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 wagew and exerts e¤ort a, his utility is ln(w) ?? a. The agent can either shirk inwhich case a = 0 or work hard in which case a = 1. If the agent works hard andthe state of the economy is good, then the project is successful with probability0:9. If the agent shirks and the state of the economy is bad, then the projectis successful with probability 0:1. If the agent works hard, but the state ofthe economy is bad, then the project is successful with probability 0:8. Thisis also the case if the state of the economy is good, but the agent shirks. Theprincipal is risk-neutral and cares about the payo¤ of the project net of agent?scompensation. The agent?s reservation utility is 0 and does not depend on thestate of the economy.(a) Assume that the principal can observe both the state of the economyand the e¤ort of the agent. Also assume xS = 20.(i) Suppose that the state of the economy is GOOD. Find the level ofe¤ort that the principal would recommend to the agent, the wage received bythe agent if the project fails, and the wage received by the agent if the projectsucceeds.1(ii) Would your answers change if the state of the economy is BAD? Ifno, why? If yes, how?(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 theprincipal ?nds it optimal to recommend HIGH EFFORT no matter the state ofthe economy.(i) Suppose that the state of the economy is GOOD. Find the wagereceived by the agent if the project fails and the wage received by the agent ifthe 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 theproject 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 FAILSis higher when the state of the economy is good or when it is bad. So, does itsatisfy RPE?2