(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 678

CHAPTER 17 • Markets with Asymmetric Information 653

can more easily earn large bonuses even if they do 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 7 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

0

F IGURE 17.4

10,000

20,000

30,000
40,000
Output (units per year)