The owner of a farm hires a worker to harvest crops that sell for a price p> 0. The crop yield is a random variable y 20 distributed according to c.d.f F(-e), where e {0, 1} is the worker's effort. The worker has a utility function: u(w, e) = w - ce where w is the wage paid, c> 0 is the marginal cost of effort, and 0 < 3 < 1. The reservation utility for the worker is u. [Hint: Recall that for a random variable z with probability density function f(-) we have E[u(r)] = [ f(r)u(x)dx.] a) Suppose that the principal can observe effort and wishes to induce high effort. Find the optimal contract. b) Find a condition under which the principal finds it optimal to induce high effort. c) Suppose now that effort is unobservable, but that the principal wishes to induce high effort. Characterize the optimal contract when 3= 1. How does this compare to the case of observable effort?