Microeconomics problem

17. Consider the following principal agent problem with moral hazard (effort is not contractible). The firm's prots are given by: 77 = 6+ 2, where e is the manager's effort and z is a random variable with 13(2) 2 0, Va'r(z) = 02. Assume that the contract is given by the linear payment scheme: w = a + bx, where a, is a xed salary and b is the share of prots. The agents's cost of supplying effort is c = .582, so his net income is y = w (3. Let his utility, or, be given by the linear mean variance utility function, u = E(y) .5R Varfy), where R > 0 is a parameter (capturing risk aversion). Find the solution to this principal agent problem (the optimal values of (1,1) and e)