Consider the following three-effort two-return scenario. The returns are G = 50,000 and B = 25,000. Effort i is denoted by e', with i = 1,2,3. The probability of G given effort e is given by 0.75 (i = 1), 0.5 (i = 2), and 0.25 (i = 3). Payoff functions for principal and agent are given by, respectively, (x, w) = x - w and u(w, e)=w-c(e) where x indicates the return, w indicates the reward to the agent and c(e) indicates the cost of effort e, which is given by c(e) = 40, c(e) = 20, and c(e) 5. The reservation utility for the agent is u = 120. (a) Write down the optimal contracts under symmetric information (first best, no moral hazard) for each level of effort and the associated profits for the principal. What effort level does the principal prefer? (b) Write down the optimal contracts under asymmetric information (second best, moral hazard) for each level of effort and the associated profits for the principal. What is the optimal effort level and the contract that the principal offers? Where does the moral hazard problem have its influence?