1. Consider the following numerical example of a principal-agent problem. There are two states of nature, s = 1, 2, with outcomes (revenues) of x1 and x2, respectively. The agent has two possible effort levels to choose from. In particular, Possible outcomes of "the enterprise": x1 = 100, x2 = 900 Possible effort levels: e = en (low effort), e = en (high effort) Probabilities of outcomes: pi(er) = 0.9 , pz(el) = 0.1 and pi(eH) = 0.7, pz(en) = 0.3 where pi(e) i the probability of outcome x; given effort level e, for i = 1, 2. Principal's utility function: B(y) =y, where y is net income received from the enterprise. Agent's utility function: U(w,e) = w - - v(e), where w is payment received, e is effort expended, and v(e) is disutility of effort. Let UR = 9 be the agent's reservation utility and let v(er) = 1 and v(en) = 1 + 0 where 0 >0. (1) For general values e and, for 0 = 1 in particular, find the optimal feasible contract from the principal's point of view under symmetric information (i.e., when effort can be observed and is verifiable in a contract). Explain why there is some range of values of 0 for which the optimal contract under symmetric information involves the principal specifying the low level of effort in the contract. Find this range of values. (ii) Find the optimal contract for general value 0 when there is asymmetric information (i.e., the principal cannot observe or verify the level of effort) and the principal wishes to extract a high level of effort from the agent. Describe the way you find the solution using a relevant graph (i.e., similar to the graph used in the example that appears at the end -pp. 12 to 15 - of the lecture notes for Topic 7: The Problem of Moral Hazard). (iii) Explain why (and how) the range of values of 0 for which the optimal contract involves the principal specifying the low level of effort differs under asymmetric information compared to symmetric information. Explain carefully using intuition. Also, explain the mathematical steps you would need to take to demonstrate this result