Moral Hazard
Economics 302 - Microeconomic Theory II: Strategic Behavior
Instructor: Songzi Du
compiled by Shih En Lu
(Chapter 25 in Watson (2013))
Simon Fraser University
March 10, 2016
ECON 302 (SFU)
Lecture 9
March 10, 2016
1 / 17
Objectives
1
Understand what moral hazard is.
2
Know how to find the first-best outcome.
3
Know how to set up the second-best problem, and how to solve it in
simple cases.
4
Understand the economic intuition behind the above procedures.
5
Understand how moral hazard results in inefficiency
ECON 302 (SFU)
Lecture 9
March 10, 2016
2 / 17
Moral Hazard
Increased risk (“hazard”) of bad (“immoral”) behaviour due to
unobserved and/or unverifiable actions.
Hidden action: what happens when one side of the market doesn’t
observe what the other side does.
Hidden action can lead to moral hazard: informed side might engage
in “bad” behaviour.
Moral hazard in agency — slack off because your boss doesn’t
observe your effort.
If actions were observed and verifiable, the problem would go away:
can condition pay on effort.
ECON 302 (SFU)
Lecture 9
March 10, 2016
3 / 17
Moral Hazard in Agency
Parties sign a contract/agreement, but their interests diverge and
some actions are not contractible (because those actions are not
observable, or not verifiable).
The agent will engage in opportunistic behaviour if what he/she does
doesn’t impact pay.
Need to provide incentives by contracting on an observable and
verifiable outcome that correlates with the hidden actions.
This is part of why we have various forms of performance pay:
commissions, piece rates, bonuses, stock options, penalties for bad
performance, etc.
ECON 302 (SFU)
Lecture 9
March 10, 2016
4 / 17
Example
Two parties: an agent/employee (A) and a principal/employer (P)
P hires A to work on a project, which can be a success (s = 1) or a
failure (s = 0)
A can exert effort (e = 1) or slack off (e = 0)
√
A has utility u(w ) − e = w − e, where w is her wage, normalized so
that her outside option gives utility 0.
P is risk-neutral, and therefore has utility sV − w , where V is the
value of a successful project. P’s outside option is cancel the project
and get 0.
When A exerts effort, the project succeeds with probability p > 0;
otherwise, it fails.
ECON 302 (SFU)
Lecture 9
March 10, 2016
5 / 17
Socially Optimal Outcome (I)
What outcome is best socially if we didn’t have an information
problem?
If A and P take their outside options, they both get 0.
√
If A works for P and slacks off, they get w and −w respectively.
Obviously, we need w = 0 for both parties to be willing, so we’re back
to 0 and 0.
ECON 302 (SFU)
Lecture 9
March 10, 2016
6 / 17
Socially Optimal Outcome (II)
If A works for P and exerts effort, they get
respectively.
√
w − 1 and pV − w
When pV > 1, we can set w ∈ (1, pV ) and make both P and A
better off.
In other words, if the project is sufficiently valuable and likely
to succeed, any Pareto efficient outcome must involve A
working for P and exerting effort.
What if pV < 1?
ECON 302 (SFU)
Lecture 9
March 10, 2016
7 / 17
Optimal Risk-Sharing
We assumed that conditional on effort, P pays A a fixed wage. Why
is that socially optimal?
Effective benefit of compensation scheme to A is its certainty
equivalent CE .
If the wage weren’t fixed, then CE < E [w ] because A is risk-averse.
But P is risk-neutral, so the effective cost of the compensation
scheme is E [w ].
Therefore, can create Pareto improvement by moving to a fixed wage
between CE and E [w ].
In a nutshell: when a risk-neutral and a risk-averse agent share
risk, the risk-neutral agent must bear all risk in any Pareto
efficient outcome (absent other considerations).
ECON 302 (SFU)
Lecture 9
March 10, 2016
8 / 17
Principal’s First-Best Outcome
Let’s keep our assumption that we don’t have an information
problem, so P can observe A’s effort. What would P like to do (the
first-best outcome for P)?
By optimal risk-sharing, P should only condition wage on effort.
P needs to pay A enough to make A as well off as her outside
option. (Paying less means that A will not work for P; paying more is
just throwing away money.)
√
If P doesn’t require effort, we need w ≥ 0, so w = 0.
√
If P requires effort, she needs to make sure w − 1 ≥ 0, so she will
choose w = 1 when effort is exerted, and w = 0 when it isn’t.
P will require effort when that gives her a higher profit:
pV − 1 > 0 ⇐⇒ pV > 1.
ECON 302 (SFU)
Lecture 9
March 10, 2016
9 / 17
Relation between P’s First-Best and Social Optimum
The conditions for P’s first-best to require effort and for the social
optimum to require effort are the same.
This is not a coincidence!
P wants to maximize total surplus because she can get all of it
by paying A just enough to make her as well off as the outside
option.
For the rest of this week, we will use “first-best,” “social optimum”
and “socially efficient outcome” interchangeably.
ECON 302 (SFU)
Lecture 9
March 10, 2016
10 / 17
Moral Hazard in Example
Now, let’s look at the problem: P doesn’t actually observe A’s effort
level, so can’t condition wage on it.
But if wage doesn’t depend on e, A should just slack off!
As a result, there is no way to get the first-best outcome when
pV > 1.
There is another way to induce effort: conditioning wage on the
outcome.
This won’t give us the first-best outcome because the agent will bear
some risk. But it is sometimes better than not inducing effort at all.
ECON 302 (SFU)
Lecture 9
March 10, 2016
11 / 17
Second-Best Problem
Let w0 be the wage in case of failure, and w1 be the wage in case of
success.
To induce effort, P needs to make effort as attractive as slacking off
(incentive compatibility - IC)
pu(w1 ) + (1 − p)u(w0 ) − 1 ≥ u(w0 )
P also still needs to offer no worse than the outside option
(individual rationality - IR)
pu(w1 ) + (1 − p)u(w0 ) − 1 ≥ 0
P’s payoff is p(V − w1 ) − (1 − p)w0 . P needs to maximize this subject
to the above two constraints. This is P’s second-best outcome.
ECON 302 (SFU)
Lecture 9
March 10, 2016
12 / 17
Binding Constraints
Suppose you’re doing a constrained optimization problem, and you
have constraints that are inequalities, like IC and IR.
We say that a constraint binds if it holds with equality at an
optimum.
Example: max x s.t. x ≤ 2 and x ≥ 0.
x ≤ 2 is binding since the maximum occurs at x = 2.
x ≥ 0 is not binding and can be ignored.
ECON 302 (SFU)
Lecture 9
March 10, 2016
13 / 17
Second-Best Outcome (I)
Suppose IR doesn’t bind in our problem, so that the optimum
(w0∗ , w1∗ ) satisfies pu(w1∗ ) + (1 − p)u(w0∗ ) − 1 > 0.
Then P could reduce w0∗ slightly, and both IR and IC would still hold.
But reducing w0∗ increases P’s profit, which contradicts (w0∗ , w1∗ )
being an optimum.
So IR must actually bind: pu(w1∗ ) + (1 − p)u(w0∗ ) − 1 = 0 at the the
optimum (w0∗ , w1∗ ).
Therefore, IC becomes: 0 ≥ u(w0∗ ). Thus, w0∗ = 0 at the the
optimum (w0∗ , w1∗ ).
ECON 302 (SFU)
Lecture 9
March 10, 2016
14 / 17
Second-Best Outcome (II)
∗
∗
∗
At the the optimum (w
1 ), we have u(w0 ) =
p0 , w
1
∗
∗
∗
therefore pu(w1 ) = p w1 = 1 =⇒ w1 = p2 .
p ∗
w0 = 0 and
P’s second-best payoff is then p(V − w1∗ ) − (1 − p)w0∗ = p(V −
This is better than allowing A to slack off and getting 0 when V
1
).
p2
> p12 .
Compare the above condition to the condition for the first-best to
involve effort pV > 1 ⇐⇒ V > p1 .
So when p1 < V < p12 , the second-best is cancelling the project even
though the first-best involves undertaking the project.
ECON 302 (SFU)
Lecture 9
March 10, 2016
15 / 17
Second-Best Outcome (III)
We can also compare P’s second-best (when V >
first-best payoff.
Second-best payoff: p(V −
1
)
p2
= pV −
1
)
p2
payoff to P’s
1
p
First-best payoff: pV − 1
Which one is bigger? What’s the intuition?
ECON 302 (SFU)
Lecture 9
March 10, 2016
16 / 17
Comments
In the second-best when V > p12 , P knows that A will exert high
effort. But P still varies the wage because she has to provide
incentives for effort.
P makes a lower profit in the second best because varying the
wage lowers A’s certainty equivalent. So P has to compensate
by paying more on average. Sometimes this lower profit causes the
project to be cancelled, even though the project will be undertaken in
the first best.
Second best is not Pareto efficient.
If the cost of monitoring effort is lower than the profit loss in the
second-best, then P will instead monitor.
Repeated interactions can also reduce the severity of moral hazard.
ECON 302 (SFU)
Lecture 9
March 10, 2016
17 / 17