A risk-neutral manager has utility function u(x,y) = 20ln (x + 1) +y. Units have been chosen so that T = 3. (The individual is endowed with 3 units of leisure x and 0 units of income y. The manager's best alternative opportunity is to consume 3 units of leisure and not work. If the manager supplies e units of effort then the firm's profit R will be 10e +, where is a random variable with expected value zero. (R is profit before deducting the manager's pay.)
Suppose that the owner offers the manager the linear compensation contract y = 0R + F, where 0 and F are constants, with 0≤0 ≤ 1. Determine the manager's effort supply function. Show that e increases when 0 increases.
Solve for the contract that maximizes the owner's expected profit.
What is the owner's expected profit, the manager's expected utility, and the effort supplied by the manager under the contract that maximizes the owner's expected profit?
Is the outcome that maximizes the owner's expected profit efficient? Explain.