There is someone who we will refer to as B.B. who has just invented a wonderful new device for monitoring the effort level of employees. This device will take precise measurements of the effort of employees and the Department of Justice has certified that its measurements are admissible and valid in court proceedings. B.B. now has a problem: how does he price his wonderful new invention? Let us assume that he is trying to sell it to one particular Principal named Skinner (will refer to him as S). S has risk neutral preferences and wishes to contract with an Agent, A, to have A sell some books for him. A is risk neutral, has a utility function of u(w, e) = w − e and can choose either eh > el, or not work at all and has reservation utility of u. There are 3 possible outcomes for A’s e§orts. He can either sell many books, a few books or no books (xg, xm, xb). If eh is chosen then these states occur with probabilities (0.75, 0.15, 0.10). If el is chosen they occur with probabilities (0.30,0.30,0.40).
Let’s let xg = 500, xm = 100, xb = 0, eh = 35, el = 0 and u = 225.
a. Assume for the moment that S could monitor A’s effort choice perfectly. What contract would S o§er to A in equilibrium? Be sure to indicate what action he wants to induce and the profit that S would receive in this case.
b. Now assume that S can not observe the effort choice of A but can observe the outcome in terms of level of sales. What contract will he offer in equilibrium?
c. Now B.B. knows everything he needs to know in order to set his price for his new invention. How much can he charge S for the use of his wonderful new device? Explain clearly why you are right.