Moral hazard and
contracts
Introduction

Review
 Adverse
Selection
 Signals
 Seperating
«

equilibrium
Unobserved types »
Moral hazard
«
Unobserved actions »

The principal-agent problem

Incentives and contracts
Moral hazard (and risk)
Ex:
You just bought theft insurance for your
home. Do you install an alarm system?
The
tendency to be less careful when risks
are eliminated is an example of moral hazard.
Because
insurance changes the costs of
misfortune, and because people's choices
depend on costs and benefits, insurance
should change people's behavior. They should
make less effort to avoid misfortune, and this
change in behavior is called moral hazard.
Moral hazard (and management)
When
a manager has a secure position from which
he or she cannot be readily removed.
When
a manager is protected by someone higher in
the corporate structure.
When
funding and/or managerial status for a project
is independent of the project's success.
When
the failure of the project is of minimal overall
consequence to the firm, regardless of the local
impact on the managed division.
When
there is no clear means of determining who is
accountable for a given project.
Moral hazard (and finance)
Bailout
by the government creates a risk for
moral hazard.
Credit
CEO’s
...
card users...
objectives vs. Shareholders
The principal-agent problem
If your employer pays you a fixed monthly salary, are
you motivated to work hard?
Agent: person who acts (employee)
Principal: party affected by the actions (employer)
The problem comes from the fact that the principal
cannot observe the effort level of the agent, only his
performance.
Example
You are managing an employee in a watch factory.
He can provide a level of effort which is low (e = 0) or
high (e = 1). Both of you are risk-neutral.
Uncertainty about demand. Firm’s revenue:
Unfavorable context
(50%)
Favorable context
(50%)
Low effort (e = 0)
R = 10 000 $ R = 20 000 $
High effort (e = 1)
R = 20 000 $ R = 40 000 $
Working hard costs him the equivalent of 10,000$.
If effort is observable
If w(e=0) is your employee’s base salary, how
must you choose w(e=1) to motivate him to
work hard?
Is it profitable for you?
If effort is observable
If w(e=0) is your employee’s base salary, how
must you choose w(e=1) to motivate him to
work hard?
w1 at least 10,000$
Is it profitable for you?
ER(e=0)=0.5*10K$+0.5*20K$= 15K$
ER(e=1)=0.5*20K$+0.5*40K$-10K$ = 20K$
If only revenue is observable
If you pay your employee a fixed salary (w(R) ≡
constant), which level of effort will he choose?
If only revenue is observable
If you pay your employee a fixed salary (w(R) ≡
constant), which level of effort will he choose?
On a constant salary, because effort is costly,
his dominant strategy is to exert no effort
because it only reduces his net benefit.
(Moral hazard!)
Performance premium
If you offer the following payment scheme:
 w(R)
= $1,000 if R = $10,000 or $20,000
 w(R)
= $24,000 if R = $40,000
Which effort level will your employee choose?
What will your (expected) profit be?
Performance premium
Expected utility (net benefit):

w(R) = 1 000 $ if R = 10 000 $ or 20 000 $

w(R) = 24 000 $ if R = 40 000 $
Low effort
(e = 0)
High effort
(e = 1)
Unfavorable cntxt.(50%)
Favorable cntxt. (50%)
EU(R) = 1000 $
EU(R) = 1000 $
EU(R) = 1K$-10K$ = -9K$
EU(R) = 24K$ -10K$ = 14K$
Because the agent is risk-neutral, he picks the effort level
that maximizes his expected net-beneft.
EU(e=1)=(14000-9000)/2=2500$
>
EU(e=0)=1000$
Performance premium
Expected Profits: R-W(R)
Low effort
(e = 0)
High effort
(e = 1)
Unfavorable
cntxt.(50%)
Favorable cntxt.
(50%)
10K$-1K$=9K$
20K$-1K$=19K$
20K$-1K$=19K$
40K$24K$=16K$
π(e=0) = 50%*9K$ + 50%*19K$=14K$
π(e=1) = 50%*19K$ + 50%*16K$=17.5K$
We can expect profits of 17,500$ because the
agent should exert a high effort.
Revenue sharing
If you use the following payment schedule

w(R) = R – $18,000 if R > $18,000

w(R) = $1,000 otherwise
What will your employee’s expected net benefit
be if he exerts low effort?
What will his net benefit be if he exerts high
effort?
What will he choose? What will your
expected(?) profit be?
Revenue sharing
If you use the following payment schedule:

w(R) = R – 18 000 $ if R > 18 000 $

w(R) = 1 000 $ otherwise
Low effort
(e = 0)
High effort
(e = 1)
Unfavorable cntxt.(50%)
Favorable cntxt. (50%)
EU(R) = 1000 $
EU(R) = 2000 $
EU(R) = 2K$-10K$ = -8K$
EU(R) = 22K$-10K$ =12K$
Here too, high effort is the worker’s dominant strategy.
EU(e=1)=2K$ > EU(e=0)=1.5K$
Revenue sharing
Expected profits: R-W(R)
Low effort
(e = 0)
High effort
(e = 1)
Unfavorable
cntxt.(50%)
Favorable cntxt.
(50%)
10K$-1K$=9K$
20K$-2K$=18K$
20K$-2K$=18K$
40K$22K$=18K$
π(e=0) = 50%*9K$ + 50%*18K$=13.5K$
π(e=1) = 50%*18K$ + 50%*18K$=18K$
We can expect profits of 18,000$ if the agent
exerts a high effort.
Conclusions

Our environment has an impact on our
behavior  incentives matter!

Next: final exam 
Exercise 10

As Chairman of the Board of ASP Industries you estimate
that your firm’s annual profit is given by the table below.
Profit () is conditional upon market demand and the effort
of your new CEO. The probabilities of each demand
condition occurring are also shown in the table.
Market Demand
Low
Demand
Medium
Demand
High
Demand
Market Probabilities
.30
.40
Low Effort
=$5 million
=$10 million
=$15
million
=$15 million
=$17
million
High Effort
=$10
million
.30
Exercise 10

You must design a compensation package for the CEO that
will maximize the firm’s expected profit. While the firm is risk
neutral, the CEO is risk averse. The CEO’s utility function is:
Utility = W½ when making low effort
Utility = W½ -100, when making high effort,

where W is the CEO’s income. (The -100 is the “utility cost”
to the CEO of making a high effort.) You know the CEO’s
utility function, and both you and the CEO know all of the
information in the preceding table.

You do not know the level of the CEO’s effort at time of
compensation or the exact state of demand. You do see the
firm’s profit, however.
Exercise 10

Of the three alternative compensation
packages below, which do you as Chairman
of ASP Industries prefer and why?
1.
PACKAGE 1: Pay the CEO a flat salary of
$575,000 per year.
2.
PACKAGE 2: Pay the CEO a fixed 6
percent of yearly firm profits.
3.
PACKAGE 3: Pay the CEO a flat salary of
$500,000 per year and then 50 percent of
any firm profits above $15 million.
Exercise 11

A firm’s short-run revenue is given by:
R = 10e – e²

where e is the level of effort by a typical
worker (all workers are assumed to be
identical).

A worker chooses his level of effort to
maximize his wage net of effort (the per-unit
cost of effort is assumed to be 1).
U=w-e
Exercise 11

Determine the level of effort and the level
of profit (revenue less wage paid) for each
of the following wage arrangements.

Explain why these differing principal-agent
relationships generate different outcomes.
1.
w = 2 for e  1; otherwise w = 0.
2.
w = R/2
3.
w = R - 12.5