4. (30 points total) a. (5) Suppose a firm employs two workers, each with a cost of effort function C(E) = E2/6. The firm pays each worker a + b.E. The worker's utility = a + bE C(E). The firm's production function is y=E, and the output price is fixed at 1. = = What is optimal contract for each worker? (That is, solve for the values of a and b that yield the profit-maximizing level of effort for the firm.) b. (5) Now suppose instead that individual output is unobservable, but only the sum is observable, so the firm pays + b[(E1+E2)/2], where E is the effort and output of worker 1, etc. If you solve for the optimal contract, do you expect b to be larger or smaller than in part a? Explain. c. (5) Solve for the optimal contract in part b. d. (5) Now suppose the firm hires N workers. What does b have to be under the optimal contract? And what about a? Show this and explain. Is this contract likely to be feasible? 4. (30 points total) a. (5) Suppose a firm employs two workers, each with a cost of effort function C(E) = E2/6. The firm pays each worker a + b.E. The worker's utility = a + bE C(E). The firm's production function is y=E, and the output price is fixed at 1. = = What is optimal contract for each worker? (That is, solve for the values of a and b that yield the profit-maximizing level of effort for the firm.) b. (5) Now suppose instead that individual output is unobservable, but only the sum is observable, so the firm pays + b[(E1+E2)/2], where E is the effort and output of worker 1, etc. If you solve for the optimal contract, do you expect b to be larger or smaller than in part a? Explain. c. (5) Solve for the optimal contract in part b. d. (5) Now suppose the firm hires N workers. What does b have to be under the optimal contract? And what about a? Show this and explain. Is this contract likely to be feasible