Remedies to Moral Hazard
Based on "Further topics in moral hazard" by Eric Rasmusen
http://www.rasmusen.org
June 2012
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
1 / 20
Ways to Alleviate Agency Problems
1
Reputation: Managers are promoted on the basis of past e¤ort or
truthfulness.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
2 / 20
Ways to Alleviate Agency Problems
1
Reputation: Managers are promoted on the basis of past e¤ort or
truthfulness.
2
Risk-sharing contracts: The executive receives not only a salary, but
call options on the …rm’s stock. If he reduces the stock value, his
option fall in value.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
2 / 20
Ways to Alleviate Agency Problems
1
Reputation: Managers are promoted on the basis of past e¤ort or
truthfulness.
2
Risk-sharing contracts: The executive receives not only a salary, but
call options on the …rm’s stock. If he reduces the stock value, his
option fall in value.
3
Boiling in oil:
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
2 / 20
Ways to Alleviate Agency Problems
1
Reputation: Managers are promoted on the basis of past e¤ort or
truthfulness.
2
Risk-sharing contracts: The executive receives not only a salary, but
call options on the …rm’s stock. If he reduces the stock value, his
option fall in value.
3
Boiling in oil:
4
Selling the store: the managers buy the …rm in a leveraged buyout.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
2 / 20
Ways to Alleviate Agency Problems
1
Reputation: Managers are promoted on the basis of past e¤ort or
truthfulness.
2
Risk-sharing contracts: The executive receives not only a salary, but
call options on the …rm’s stock. If he reduces the stock value, his
option fall in value.
3
Boiling in oil:
4
Selling the store: the managers buy the …rm in a leveraged buyout.
5
E¢ ciency wages.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
2 / 20
Ways to Alleviate Agency Problems
1
Reputation: Managers are promoted on the basis of past e¤ort or
truthfulness.
2
Risk-sharing contracts: The executive receives not only a salary, but
call options on the …rm’s stock. If he reduces the stock value, his
option fall in value.
3
Boiling in oil:
4
Selling the store: the managers buy the …rm in a leveraged buyout.
5
E¢ ciency wages.
6
Tournaments.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
2 / 20
Ways to Alleviate Agency Problems
1
Reputation: Managers are promoted on the basis of past e¤ort or
truthfulness.
2
Risk-sharing contracts: The executive receives not only a salary, but
call options on the …rm’s stock. If he reduces the stock value, his
option fall in value.
3
Boiling in oil:
4
Selling the store: the managers buy the …rm in a leveraged buyout.
5
E¢ ciency wages.
6
Tournaments.
7
Monitoring: The directors hire a consultant to evaluate the
executive’s performance.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
2 / 20
Ways to Alleviate Agency Problems
1
Reputation: Managers are promoted on the basis of past e¤ort or
truthfulness.
2
Risk-sharing contracts: The executive receives not only a salary, but
call options on the …rm’s stock. If he reduces the stock value, his
option fall in value.
3
Boiling in oil:
4
Selling the store: the managers buy the …rm in a leveraged buyout.
5
E¢ ciency wages.
6
Tournaments.
7
Monitoring: The directors hire a consultant to evaluate the
executive’s performance.
8
Repetition: Managaers are paid less than their marginal products for
most of their career, but are rewarded later with higher salaries or
generous pensions if the career record has been good.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
2 / 20
Insurance
The agent is considering buying theft insurance for a car with a value
of 12.
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to Moral Hazard
June 2012
3 / 20
Insurance
The agent is considering buying theft insurance for a car with a value
of 12.
Before he buys insurance his dollar wealth is 0 if there is a theft and
12 otherwise.
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Remedies
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to Moral Hazard
June 2012
3 / 20
Insurance
The agent is considering buying theft insurance for a car with a value
of 12.
Before he buys insurance his dollar wealth is 0 if there is a theft and
12 otherwise.
If he is careful Theft occurs with probability 0.5.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
3 / 20
Insurance
The agent is considering buying theft insurance for a car with a value
of 12.
Before he buys insurance his dollar wealth is 0 if there is a theft and
12 otherwise.
If he is careful Theft occurs with probability 0.5.
If he is careless the probability rises to 0.75.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
3 / 20
Insurance
The agent is considering buying theft insurance for a car with a value
of 12.
Before he buys insurance his dollar wealth is 0 if there is a theft and
12 otherwise.
If he is careful Theft occurs with probability 0.5.
If he is careless the probability rises to 0.75.
He is risk averse, and other things equal, he has a midl preference to
be careless, a preference worth some small amount ε.
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Remedies
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to Moral Hazard
June 2012
3 / 20
Insurance
The agent is considering buying theft insurance for a car with a value
of 12.
Before he buys insurance his dollar wealth is 0 if there is a theft and
12 otherwise.
If he is careful Theft occurs with probability 0.5.
If he is careless the probability rises to 0.75.
He is risk averse, and other things equal, he has a midl preference to
be careless, a preference worth some small amount ε.
The insurance company is risk-neutral.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
3 / 20
Insurance
The agent is considering buying theft insurance for a car with a value
of 12.
Before he buys insurance his dollar wealth is 0 if there is a theft and
12 otherwise.
If he is careful Theft occurs with probability 0.5.
If he is careless the probability rises to 0.75.
He is risk averse, and other things equal, he has a midl preference to
be careless, a preference worth some small amount ε.
The insurance company is risk-neutral.
Competition among insurance companies.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
3 / 20
Observable Care
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to Moral Hazard
June 2012
4 / 20
Observable Care
If the agent chooses Careful,
π a = 0.5U (12
πp
x ) + 0.5U (0 + y
= 0.5x + 0.5(x
x)
y)
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June 2012
5 / 20
Observable Care
If the agent chooses Careful,
π a = 0.5U (12
πp
x ) + 0.5U (0 + y
= 0.5x + 0.5(x
x)
y)
If the agent chooses Careless
π a = 0.25U (12
πp
x ) + 0.75U (0 + y
= 0.25x + 0.75(x
x) + ε
y)
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June 2012
5 / 20
Unobservable Care
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
6 / 20
Unobservable Care
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to Moral Hazard
June 2012
7 / 20
Unobservable Care
Partial-insurance (Example: premium of 6 and payout of 8). We can
think of it in two ways:
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to Moral Hazard
June 2012
8 / 20
Unobservable Care
Partial-insurance (Example: premium of 6 and payout of 8). We can
think of it in two ways:
Full insurance except for a deductible of four (the company pays for
all losses in excess of four)
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Remedies
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to Moral Hazard
June 2012
8 / 20
Unobservable Care
Partial-insurance (Example: premium of 6 and payout of 8). We can
think of it in two ways:
Full insurance except for a deductible of four (the company pays for
all losses in excess of four)
Insurance with a coinsurance rate of one-third. (The insurance
company pays two-thirds of all losses)
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June 2012
8 / 20
E¢ ciency Wages
Is the aim of an incentive contract to punish the agent if he chooses the
wrong action? Not exactly. Rather, it is to create a di¤erence between
the agent’s expected payo¤ from right and wrong actions, something
which can be done either with the stick of punishment or the carrot of
reward. It is important to keep this in mind, because sometimes
punishments are simply not available
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to Moral Hazard
June 2012
9 / 20
E¢ ciency Wages
The Lucky Executive Game
Players: A corporation and an executive
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to Moral Hazard
June 2012
10 / 20
E¢ ciency Wages
The Lucky Executive Game
Players: A corporation and an executive
The corporation o¤ers the executive a contract which pays w (q )
depending on pro…t, q.
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to Moral Hazard
June 2012
0
10 / 20
E¢ ciency Wages
The Lucky Executive Game
Players: A corporation and an executive
The corporation o¤ers the executive a contract which pays w (q )
depending on pro…t, q.
0
The executive accepts the contract, or rejects it and receives his
reservation utillity of U = 5.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
10 / 20
E¢ ciency Wages
The Lucky Executive Game
Players: A corporation and an executive
The corporation o¤ers the executive a contract which pays w (q )
depending on pro…t, q.
0
The executive accepts the contract, or rejects it and receives his
reservation utillity of U = 5.
The executive exerts e¤ort e of either 0 or 10.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
10 / 20
E¢ ciency Wages
The Lucky Executive Game
Players: A corporation and an executive
The corporation o¤ers the executive a contract which pays w (q )
depending on pro…t, q.
0
The executive accepts the contract, or rejects it and receives his
reservation utillity of U = 5.
The executive exerts e¤ort e of either 0 or 10.
Both players are risk neutral
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
10 / 20
E¢ ciency Wages
The Lucky Executive Game
Players: A corporation and an executive
The corporation o¤ers the executive a contract which pays w (q )
depending on pro…t, q.
0
The executive accepts the contract, or rejects it and receives his
reservation utillity of U = 5.
The executive exerts e¤ort e of either 0 or 10.
Both players are risk neutral
Corporation’s payo¤: q
w.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
10 / 20
E¢ ciency Wages
The Lucky Executive Game
Players: A corporation and an executive
The corporation o¤ers the executive a contract which pays w (q )
depending on pro…t, q.
0
The executive accepts the contract, or rejects it and receives his
reservation utillity of U = 5.
The executive exerts e¤ort e of either 0 or 10.
Both players are risk neutral
Corporation’s payo¤: q
Executive’s payo¤: w
w.
e.
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
10 / 20
E¢ ciency Wages
The Lucky Executive Game
Players: A corporation and an executive
The corporation o¤ers the executive a contract which pays w (q )
depending on pro…t, q.
0
The executive accepts the contract, or rejects it and receives his
reservation utillity of U = 5.
The executive exerts e¤ort e of either 0 or 10.
Both players are risk neutral
Corporation’s payo¤: q
Executive’s payo¤: w
w.
e.
Nature chooses pro…t according to Table 1.
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June 2012
10 / 20
E¢ ciency Wages
The Lucky Executive Game
.
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to Moral Hazard
June 2012
11 / 20
E¢ ciency Wages
The Lucky Executive Game
The participation constraint is
0.1[w (0)
10] + 0.9[w (400)
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10]
5
June 2012
12 / 20
E¢ ciency Wages
The Lucky Executive Game
The participation constraint is
0.1[w (0)
10] + 0.9[w (400)
10]
5
so his expected wage must equal 15
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
12 / 20
E¢ ciency Wages
The Lucky Executive Game
The participation constraint is
0.1[w (0)
10] + 0.9[w (400)
10]
5
so his expected wage must equal 15
The incentive compatibility constraint is
0.5w (0) + 0.5w (400)
0.1w (0) + 0.9w (400)
Based on "Further topics in moral hazard" by Eric Rasmusen
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10
June 2012
12 / 20
E¢ ciency Wages
The Lucky Executive Game
The participation constraint is
0.1[w (0)
10] + 0.9[w (400)
10]
5
so his expected wage must equal 15
The incentive compatibility constraint is
0.5w (0) + 0.5w (400)
0.1w (0) + 0.9w (400)
10
which can be written as w (400) w (0) 25, so the gap between
the executive’s wage for high output and low output must equal at
least 25.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
12 / 20
E¢ ciency Wages
The Lucky Executive Game
The participation constraint is
0.1[w (0)
10] + 0.9[w (400)
10]
5
so his expected wage must equal 15
The incentive compatibility constraint is
0.5w (0) + 0.5w (400)
0.1w (0) + 0.9w (400)
10
which can be written as w (400) w (0) 25, so the gap between
the executive’s wage for high output and low output must equal at
least 25.
A contract that satis…es both constraints (and binding) is
w (0) = 7.5 and w (400) = 17.5.
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
12 / 20
E¢ ciency Wages
The Lucky Executive Game
The participation constraint is
0.1[w (0)
10] + 0.9[w (400)
10]
5
so his expected wage must equal 15
The incentive compatibility constraint is
0.5w (0) + 0.5w (400)
0.1w (0) + 0.9w (400)
10
which can be written as w (400) w (0) 25, so the gap between
the executive’s wage for high output and low output must equal at
least 25.
A contract that satis…es both constraints (and binding) is
w (0) = 7.5 and w (400) = 17.5.
But his contract is not feasible if we require w (q ) 0.
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
12 / 20
E¢ ciency Wages
The Lucky Executive Game
The participation constraint is
0.1[w (0)
10] + 0.9[w (400)
10]
5
so his expected wage must equal 15
The incentive compatibility constraint is
0.5w (0) + 0.5w (400)
0.1w (0) + 0.9w (400)
10
which can be written as w (400) w (0) 25, so the gap between
the executive’s wage for high output and low output must equal at
least 25.
A contract that satis…es both constraints (and binding) is
w (0) = 7.5 and w (400) = 17.5.
But his contract is not feasible if we require w (q ) 0.
This is an example of the common and realistic bankruptcy
constraint. (the principal cannot punish the agent by taking away
more than waht the agent owns in the …rst place)
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June 2012
12 / 20
E¢ ciency Wages
The Lucky Executive Game
So what can be done?
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June 2012
13 / 20
E¢ ciency Wages
The Lucky Executive Game
So what can be done?
What can be done is to use the carrot instead of the stick and
abandon satisfying the participation constraint as an equality.
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
13 / 20
E¢ ciency Wages
The Lucky Executive Game
So what can be done?
What can be done is to use the carrot instead of the stick and
abandon satisfying the participation constraint as an equality.
All that is needed for constraint (2) is a gap of 25 between the high
wage and the low wage.
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
13 / 20
E¢ ciency Wages
The Lucky Executive Game
So what can be done?
What can be done is to use the carrot instead of the stick and
abandon satisfying the participation constraint as an equality.
All that is needed for constraint (2) is a gap of 25 between the high
wage and the low wage.
Setting the low wage as low as is feasible, the corporation can use the
contract
w (0) = 0, w (400) = 25
and induce high e¤ort.
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
13 / 20
E¢ ciency Wages
The Lucky Executive Game
So what can be done?
What can be done is to use the carrot instead of the stick and
abandon satisfying the participation constraint as an equality.
All that is needed for constraint (2) is a gap of 25 between the high
wage and the low wage.
Setting the low wage as low as is feasible, the corporation can use the
contract
w (0) = 0, w (400) = 25
and induce high e¤ort.
Executive’s expected utility: 0.1(0) + 0.9(25)
than his reservation utility.
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to Moral Hazard
10 = 12.5 > 5. More
June 2012
13 / 20
E¢ ciency Wages
The Lucky Executive Game
So what can be done?
What can be done is to use the carrot instead of the stick and
abandon satisfying the participation constraint as an equality.
All that is needed for constraint (2) is a gap of 25 between the high
wage and the low wage.
Setting the low wage as low as is feasible, the corporation can use the
contract
w (0) = 0, w (400) = 25
and induce high e¤ort.
Executive’s expected utility: 0.1(0) + 0.9(25) 10 = 12.5 > 5. More
than his reservation utility.
The corporation’s payo¤ is 337.5 (= 0.1(0 0) + 0.9(400 25)).
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
13 / 20
E¢ ciency Wages
The Lucky Executive Game
So what can be done?
What can be done is to use the carrot instead of the stick and
abandon satisfying the participation constraint as an equality.
All that is needed for constraint (2) is a gap of 25 between the high
wage and the low wage.
Setting the low wage as low as is feasible, the corporation can use the
contract
w (0) = 0, w (400) = 25
and induce high e¤ort.
Executive’s expected utility: 0.1(0) + 0.9(25) 10 = 12.5 > 5. More
than his reservation utility.
The corporation’s payo¤ is 337.5 (= 0.1(0 0) + 0.9(400 25)).
Such payo¤ is higher than the one associated to the low e¤ort and:
195 = 0.5(0 5) + 0.5(400 5).
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to Moral Hazard
June 2012
13 / 20
E¢ ciency Wages
The Lucky Executive Game
So what can be done?
What can be done is to use the carrot instead of the stick and
abandon satisfying the participation constraint as an equality.
All that is needed for constraint (2) is a gap of 25 between the high
wage and the low wage.
Setting the low wage as low as is feasible, the corporation can use the
contract
w (0) = 0, w (400) = 25
and induce high e¤ort.
Executive’s expected utility: 0.1(0) + 0.9(25) 10 = 12.5 > 5. More
than his reservation utility.
The corporation’s payo¤ is 337.5 (= 0.1(0 0) + 0.9(400 25)).
Such payo¤ is higher than the one associated to the low e¤ort and:
195 = 0.5(0 5) + 0.5(400 5).
Since high enough punishments are infeasible, the corporation has to
use higher rewards.
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June 2012
13 / 20
E¢ ciency Wages
Executives, of course, will be lining up to work for this corporation,
since they can get an expected utility of 12.5 there and only 5
elsewhere
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to Moral Hazard
June 2012
14 / 20
E¢ ciency Wages
Executives, of course, will be lining up to work for this corporation,
since they can get an expected utility of 12.5 there and only 5
elsewhere
Potential successors would be willing to pass up alternative jobs in
order to be in position to get this unusually attractive job.
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to Moral Hazard
June 2012
14 / 20
E¢ ciency Wages
Executives, of course, will be lining up to work for this corporation,
since they can get an expected utility of 12.5 there and only 5
elsewhere
Potential successors would be willing to pass up alternative jobs in
order to be in position to get this unusually attractive job.
Thus, the model generates unemployment.
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
14 / 20
E¢ ciency Wages
Executives, of course, will be lining up to work for this corporation,
since they can get an expected utility of 12.5 there and only 5
elsewhere
Potential successors would be willing to pass up alternative jobs in
order to be in position to get this unusually attractive job.
Thus, the model generates unemployment.
The employer pays a wage higher than that needed to attract workers,
and workers are willing to be unemployed in order to get a chance at
the e¢ ciency-wage job.
Based on "Further topics in moral hazard" by Eric Rasmusen
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to Moral Hazard
June 2012
14 / 20
E¢ ciency Wages
Executives, of course, will be lining up to work for this corporation,
since they can get an expected utility of 12.5 there and only 5
elsewhere
Potential successors would be willing to pass up alternative jobs in
order to be in position to get this unusually attractive job.
Thus, the model generates unemployment.
The employer pays a wage higher than that needed to attract workers,
and workers are willing to be unemployed in order to get a chance at
the e¢ ciency-wage job.
To induce a worker not to shirk, the …rm can o¤er to pay a premium
over the marketclearing wage, which he loses if he is caught shirking
and …red.
Based on "Further topics in moral hazard" by Eric Rasmusen
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June 2012
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E¢ ciency Wages
If one …rm …nds it pro…table to raise the wage, however, so do all
…rms. One might think that after the wages equalized, the incentive
not to shirk would disappear. But when a …rm raises its wage, its
demand for labor falls, and when all …rms raise their wages, the
market demand for labor falls, creating unemployment. Even if all
…rms pay the same wage, a worker has an incentive not to shirk,
because if he were …red he would stay unemployed, and even if there
is a random chance of leaving the unemployment pool, the
unemployment rate rises su¢ ciently high that workers choose not to
risk being caught shirking.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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June 2012
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Tournaments
Games in which relative performance is important are called
tournaments.
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June 2012
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Tournaments
Games in which relative performance is important are called
tournaments.
Tournaments are especially useful when the principal wants to elicit
information from the agents
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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June 2012
16 / 20
Tournaments
Games in which relative performance is important are called
tournaments.
Tournaments are especially useful when the principal wants to elicit
information from the agents
A principal-designed tournament is sometimes called a yardstick
competition because the agents provide the measure for their wages
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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June 2012
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Tournaments
Let …rm Apex have two possible production techniques, Fast and
Careful.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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June 2012
17 / 20
Tournaments
Let …rm Apex have two possible production techniques, Fast and
Careful.
Independently for each technique, Nature chooses production cost c
= 1 with probability φ and c = 2 with probability (1 φ).
Based on "Further topics in moral hazard" by Eric Rasmusen
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June 2012
17 / 20
Tournaments
Let …rm Apex have two possible production techniques, Fast and
Careful.
Independently for each technique, Nature chooses production cost c
= 1 with probability φ and c = 2 with probability (1 φ).
The manager can either choose a technique at random or investigate
the costs of both techniques at a utility cost to himself of α.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
17 / 20
Tournaments
Let …rm Apex have two possible production techniques, Fast and
Careful.
Independently for each technique, Nature chooses production cost c
= 1 with probability φ and c = 2 with probability (1 φ).
The manager can either choose a technique at random or investigate
the costs of both techniques at a utility cost to himself of α.
The shareholders can observe the resulting production cost, but not
whether the manager investigates.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
17 / 20
Tournaments
Let …rm Apex have two possible production techniques, Fast and
Careful.
Independently for each technique, Nature chooses production cost c
= 1 with probability φ and c = 2 with probability (1 φ).
The manager can either choose a technique at random or investigate
the costs of both techniques at a utility cost to himself of α.
The shareholders can observe the resulting production cost, but not
whether the manager investigates.
The wage contract: w1 if c = 1 and w2 if c = 2.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
17 / 20
Tournaments
Let …rm Apex have two possible production techniques, Fast and
Careful.
Independently for each technique, Nature chooses production cost c
= 1 with probability φ and c = 2 with probability (1 φ).
The manager can either choose a technique at random or investigate
the costs of both techniques at a utility cost to himself of α.
The shareholders can observe the resulting production cost, but not
whether the manager investigates.
The wage contract: w1 if c = 1 and w2 if c = 2.
Manager’s utility: log(w ) if he does not investigate and log(w )
he does.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
α if
17 / 20
Tournaments
Let …rm Apex have two possible production techniques, Fast and
Careful.
Independently for each technique, Nature chooses production cost c
= 1 with probability φ and c = 2 with probability (1 φ).
The manager can either choose a technique at random or investigate
the costs of both techniques at a utility cost to himself of α.
The shareholders can observe the resulting production cost, but not
whether the manager investigates.
The wage contract: w1 if c = 1 and w2 if c = 2.
Manager’s utility: log(w ) if he does not investigate and log(w )
he does.
α if
Reservation utility: log(w ).
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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June 2012
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Tournaments
If the shareholders want the manager to investigate, the contract
must satisfy the self-selection constraint
φ log(w1 ) + (1
φ) log(w2 )
[1
(1
φ)2 ] log(w1 ) + (1
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φ)2 log(w2 )
June 2012
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Tournaments
If the shareholders want the manager to investigate, the contract
must satisfy the self-selection constraint
φ log(w1 ) + (1
φ) log(w2 )
[1
(1
φ)2 ] log(w1 ) + (1
φ)2 log(w2 )
Turning inequality (4) into an equality and simplifying we get
w1
(5)
φ(1 φ) log( ) = α
w2
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June 2012
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Tournaments
If the shareholders want the manager to investigate, the contract
must satisfy the self-selection constraint
φ log(w1 ) + (1
φ) log(w2 )
[1
(1
φ)2 ] log(w1 ) + (1
φ)2 log(w2 )
Turning inequality (4) into an equality and simplifying we get
w1
(5)
φ(1 φ) log( ) = α
w2
The (binding) participation constarint is
log(w ) = [1
(1
φ)2 ] log(w1 ) + (1
φ)2 log(w2 )
Based on "Further topics in moral hazard" by Eric Rasmusen
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(6)
α
June 2012
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Tournaments
If the shareholders want the manager to investigate, the contract
must satisfy the self-selection constraint
φ log(w1 ) + (1
φ) log(w2 )
[1
φ)2 ] log(w1 ) + (1
(1
φ)2 log(w2 )
Turning inequality (4) into an equality and simplifying we get
w1
(5)
φ(1 φ) log( ) = α
w2
The (binding) participation constarint is
log(w ) = [1
(1
φ)2 ] log(w1 ) + (1
φ)2 log(w2 )
(6)
α
Solving equations (5) and (6)
w1 = w e α/φ
w2 = w e
α/(1 φ)
Based on "Further topics in moral hazard" by Eric Rasmusen
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June 2012
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Tournaments
If the shareholders want the manager to investigate, the contract
must satisfy the self-selection constraint
φ log(w1 ) + (1
φ) log(w2 )
[1
φ)2 ] log(w1 ) + (1
(1
φ)2 log(w2 )
Turning inequality (4) into an equality and simplifying we get
w1
(5)
φ(1 φ) log( ) = α
w2
The (binding) participation constarint is
log(w ) = [1
φ)2 ] log(w1 ) + (1
(1
φ)2 log(w2 )
(6)
α
Solving equations (5) and (6)
w1 = w e α/φ
w2 = w e
α/(1 φ)
The expected cost to the …rm is
[1
(1
φ)2 ]w e α/φ + (1
φ )2 w e
Based on "Further topics in moral hazard" by Eric Rasmusen
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α/(1 φ)
June 2012
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Tournaments
If the parameters are φ = 0.1, α = 1, and w = 1, the values are
w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
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June 2012
19 / 20
Tournaments
If the parameters are φ = 0.1, α = 1, and w = 1, the values are
w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
Quite possibly the shareholders decide it is not worth making the
manager investigate.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
19 / 20
Tournaments
If the parameters are φ = 0.1, α = 1, and w = 1, the values are
w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
Quite possibly the shareholders decide it is not worth making the
manager investigate.
But suppose that Apex has a competitor, Brydox, in the same
situation
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
19 / 20
Tournaments
If the parameters are φ = 0.1, α = 1, and w = 1, the values are
w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
Quite possibly the shareholders decide it is not worth making the
manager investigate.
But suppose that Apex has a competitor, Brydox, in the same
situation
The shareholders of Apex can threaten to boil their manager in oil if
Brydox adopts a low-cost technology and Apex does not.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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to Moral Hazard
June 2012
19 / 20
Tournaments
If the parameters are φ = 0.1, α = 1, and w = 1, the values are
w1 = 22, 026 and w2 = 0.33, and the expected cost 4185.
Quite possibly the shareholders decide it is not worth making the
manager investigate.
But suppose that Apex has a competitor, Brydox, in the same
situation
The shareholders of Apex can threaten to boil their manager in oil if
Brydox adopts a low-cost technology and Apex does not.
If Brydox does the same, the two managers are in a prisoner’s
dilemma, both wishing not to investigate, but each investigating from
fear of the other
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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June 2012
19 / 20
Tournaments
Apex’s forcing contract speci…es w1 = w2 to fully insure the
manager, and boiling-in-oil if Brydox has lower costs than Apex
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
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June 2012
20 / 20
Tournaments
Apex’s forcing contract speci…es w1 = w2 to fully insure the
manager, and boiling-in-oil if Brydox has lower costs than Apex
The contract need satisfy only the participation constraint that
log(w α) = log(w ), so w = 2.72 and Apex’s cost of extracting the
manager’s information is only 2.72, not 4.185.
Based on "Further topics in moral hazard" by Eric Rasmusen
Remedies
(http://www.rasmusen.org)
to Moral Hazard
June 2012
20 / 20
Tournaments
Apex’s forcing contract speci…es w1 = w2 to fully insure the
manager, and boiling-in-oil if Brydox has lower costs than Apex
The contract need satisfy only the participation constraint that
log(w α) = log(w ), so w = 2.72 and Apex’s cost of extracting the
manager’s information is only 2.72, not 4.185.
Competition raises e¢ ciency, not through the threat of …rms going
bankrupt but through the threat of managers being …red.
Based on "Further topics in moral hazard" by Eric Rasmusen
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June 2012
20 / 20