Roger B. Myerson Prize Lecture

332

Buyer

’

s value

$20

$100

$80

1, $50

0, *

$0

0, *

0, *

 P(trade), E(price if trade)

Seller

’

s value

Figure 10. An allocatively efficient trading plan with initial ownership reversed.

4. A RISKY PRODUCTION PROJECT  

WITH MORAL HAZARD IN MANAGEMENT 

Our second example involves production, and here we can introduce prob-

lems of moral hazard, because valuable inputs that are required for produc-

tion may be misused or diverted by the manager of the production process. 

For simplicity, let us consider a one-time production project that requires an 

initial capital input worth K=100, and then returns revenue worth R=240 if 

the project is a success, or returns no revenue (0) if the project is not a suc-

cess. The project’s probability of success depends on the manager’s hidden 

action. If the manager diligently applies good effort to managing the project, 

then probability of success is p

G

 = 1/2. On the other hand, if the manager be-

haves badly and abuses his managerial authority in the project then the prob-

ability of success is p

B

 = 1/4, but the manager can get hidden private benefits 

worth B=30 from such abuse of power.

4

 With these parameters, the expected 

returns from the project are greater than the cost of its capital inputs if the 

manager chooses to be good, as p

G

R > K. But if the manager chose to behave 

badly, then the capital input cost would be greater than the expected returns 

plus private benefits, as K > p

B

R + B. So by the expected value criterion, the 

project can be worth undertaking only if the manager chooses good diligent 

effort.

Let A denote the total value of all personal assets that the manager can of-

fer to invest in the project. We may call A the manager’s collateral (although 

it may also include the value of his time in managing the project). The worst 

that our social plan can do to the manager, if the project fails, is to take away 

his collateral, in which case the manager’s net payoff would be –A. We as-

sume that A

take this project on his own, and so capital for this project must be provided 

by others in society.

Let us consider this problem from the perspective of society at large, that 

is, of the people other than the manager who must provide the required 

capital input. Can society at large derive any positive expected benefit from 

investment in the project? The manager’s pay cannot depend on his hidden 

effort, which is not directly observable, but his pay can depend on whether 

the project is a success or not. The basic variable in the incentive scheme 

here is the net payoff w that society will pay to the manager if the project 

succeeds. (Here a net payoff of 0 would mean that the manager just keeps 

4 

This is a version of the basic moral-hazard example in section 3.2 of Tirole (2006).

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333

his collateral.) If society undertakes the investment in this project, then the 

social plan should recommend to the manager that he should exert good ef-

fort, but to give him an incentive to obey this recommendation, the wage w 

from success must satisfy the moral-hazard constraint:

p

G

w 

–

 (1–p

G

)A > B + p

B

w – (1–p

B

)A.

Also, the manager could refuse to participate in the project at all, if he does 

not get a positive expected net payoff from his participation, and so w must 

also satisfy the participation constraint:

p

G

w – (1–p

G

)A > 0.

(It can be verified that paying the manager more than –A in case of failure 

cannot improve his incentives for participating with good behavior.) The 

manager’s limited assets imply that w must also satisfy the following limited-

liability constraint (or resource constraint):

w > –A.

Subject to these constraints, let us maximize the expected net profit for soci-

ety at large. When the manager obeys the recommendation to be good, this 

expected social profit is

V = p

G

(R–w) + (1–p

G

)A – K.

Let us consider the case where the manager is not very rich, so that in par-

ticular

 A < Bp

G

/(p

G

–p

B

), 

that is, A < 60 for our numerical example. Then the optimal incentive mecha-

nism satisfies the moral-hazard constraint as an equality, and has

w = B/(p

G

–p

B

) – A = 120–A.

So the manager must be allowed to get a moral-hazard rent that has expected 

value 

p

G

w–(1–p

G

)A = Bp

G

/(p

G

–p

B

)–A = 60–A.

Thus, the expected net profit for society at large cannot be more than 

p

G

R–K–(60–A) = A–40. 

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334

This amount is negative when A<40. So in this example, we cannot get any 

positive expected profit for society unless the manager himself can contrib-

ute assets A worth at least 40. That is, to deter abuse of power without an ex-

pected loss to the rest of society, the manager must have stakes in this project 

worth at least 40% of the cost of the capital input here. If no one has such a 

large personal wealth to offer as collateral to this investment, as might be the 

case in an egalitarian socialist society, then society at large cannot profitably 

undertake this investment.

Thus, moral-hazard incentive constraints can also provide an analytical 

framework where the initial allocation of property rights may affect the pos-

sibility of productive investments. Indeed, this simple example may provide 

an analytical perspective on problems of socialism, as Hayek was seeking. 

Modern industrial production requires integrated managerial control over 

large scale assets, and whoever exercises that control will have great moral-

hazard temptations, which are represented by the parameter B in this model. 

When managers have great temptations B, the moral-hazard incentive con-

straint cannot be satisfied unless managers have large stakes in success of 

their projects. If, unlike capitalist entrepreneurs, socialist managers do not 

have substantial personal assets that they can invest in their projects, then 

the necessary stakes can only be achieved by allowing socialist managers to 

take a large share of the benefits from successful projects. So considerations 

of moral hazard cast doubt on the egalitarian socialist ideal that profits from 

industrial means of production should all belong to the general public. 

There is one way to extend our model that might help to ward off this 

specter of a privileged socialist managerial elite which closely resembles the 

capitalist elite. Suppose that the socialist system allowed the possibility of 

physically punishing managers in case of failure. In this extended model, the 

incentive mechanism could have two variables: w the manager’s payment for 

success; and z the manager’s cost of punishment for failure. Unproductive 

punishment of a manager would be different from seizing a manager’s per-

sonal assets, however, as punishment would not yield any benefit to the rest 

of society. (Any such unproductive punishment would be allocatively inef-

ficient, of course, but we understand that punishment may sometimes be 

a necessary deterrent in incentive-efficient social rules.) Then the optimal 

incentive problem for society at large would choose w and z to

maximize V = p

G

(R–w) + (1–p

G

)A – K

subject to w > –A, z > 0,

p

G

w – (1–p

G

)(A+z) > B + p

B

w – (1–p

B

)(A+z), [moral hazard]

p

G

w – (1–p

G

)(A+z) > 0. 

[participation]

For our numerical example when A<60, the optimal solution threatens 

punishment z = 60–A for failure and pays w = 60 for success, which wipes out 

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