CHAPTER 17 • Markets with Asymmetric Information 653 can more easily earn large bonuses even if they not operate efficiently For example, if a manager estimates capacity to be 18,000 rather than 20,000, and the plant actually produces only 16,000, her bonus increases from $8000 to $9000 Thus this scheme fails to elicit accurate information about capacity and does not ensure that plants will be run as efficiently as possible Now let’s modify this scheme We will still ask managers how much their plants can feasibly produce and tie their bonuses to this estimate However, we will use a slightly more complicated formula than the one in (17.3) to calculate the bonus: If Q Qf, B = 3Qf + 2(Q - Qf) If Q … Qf, B = 3Qf - 5(Qf - Q) (17.4) The parameters (.3, 2, and 5) have been chosen so that each manager has the incentive to reveal the true feasible production level and to make Q, the actual output of the plant, as large as possible To see that this scheme does the job, look at Figure 17.4 Assume that the true production limit is Q* = 20,000 units per year The bonus that the manager will receive if she states feasible capacity to be the true production limit is given by the line labeled Qf = 20,000 This line is continued for outputs beyond 20,000 to illustrate the bonus scheme but dashed to signify the infeasibility of such production Note that the manager’s bonus is maximized when the firm produces at its limits of 20,000 units; the bonus is then $6000 Suppose, however, that the manager reports a feasible capacity of only 10,000 Then the bonus is given by the line labeled Qf = 10,000 The maximum bonus is now $5000, which is obtained by producing an output of 20,000 But note that this is less than the bonus that the manager would receive if she correctly stated the feasible capacity to be 20,000 The same line of argument applies when the manager exaggerates available capacity If the manager states feasible capacity to be 30,000 units per year, the Bonus (dollars per year) Q f = 30,000 10,000 Q f = 20,000 Q f = 10,000 8000 INCENTIVE DESIGN IN AN INTEGRATED FIRM A bonus scheme can be designed that gives a manager the incentive to estimate accurately the size of the plant If the manager reports a feasible capacity of 20,000 units per year, equal to the actual capacity, then the bonus will be maximized (at $6000) 6000 4000 2000 F IGURE 17.4 10,000 20,000 30,000 40,000 Output (units per year)