lecture 9 - moral hazard

Moral HazardEconomics 302 - Microeconomic Theory II: Strategic Behavior

Instructor: Songzi Du

compiled by Shih En LuSimon Fraser University

March 16, 2015

ECON 302 (SFU) Lecture 9 March 16, 2015 1 / 18

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 insimple cases.

4 Understand the economic intuition behind the above procedures.


Asymmetric Information

When one side of the market knows more than the other.

This week: hidden actions (e.g. employment, insurance).

Next week: hidden characteristics (e.g. product, insurance, ability,willingness to pay).

Often means that the socially optimal outcome cannot beachieved.

Just like market power, this is a form of market inefficiency.


Moral Hazard

Increased risk (hazard) of bad (immoral) behaviour due tounobserved and/or unverifiable actions.

Today: moral hazard in agency slack off because your boss doesntobserve your effort.

If actions were observed and verifiable, the problem would go away:can condition pay on effort.


Moral Hazard in Agency

Parties sign a contract/agreement, but their interests diverge andsome actions are not contractible (because those actions are notobservable, or not verifiable).

The agent will engage in opportunistic behaviour if what he/she doesdoesnt impact pay.

Need to provide incentives by contracting on an observable andverifiable 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 badperformance, etc.


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 afailure (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 sothat her outside option gives utility 0.

P is risk-neutral, and therefore has utility sV w , where V is thevalue of a successful project. Ps outside option is cancel the projectand get 0.

When A exerts effort, the project succeeds with probability p > 0;otherwise, it fails.


Socially Optimal Outcome (I)

What outcome is best socially if we didnt have an informationproblem?

If A and P take their outside options, they both get 0.

If A works for P and slacks off, they getw and w respectively.

Obviously, we need w = 0 for both parties to be willing, so were backto 0 and 0.


Socially Optimal Outcome (II)

If A works for P and exerts effort, they getw 1 and pV w

respectively.

When pV > 1, we can set w (1, pV ) and make both P and Abetter off.

In other words, if the project is sufficiently valuable and likelyto succeed, any Pareto efficient outcome must involve Aworking for P and exerting effort.

What if pV < 1?


Optimal Risk-Sharing

We assumed that conditional on effort, P pays A a fixed wage. Whyis that socially optimal?

Effective benefit of compensation scheme to A is its certaintyequivalent CE .

If the wage werent fixed, then CE < E [w ] because A is risk-averse.

But P is risk-neutral, so the effective cost of the compensationscheme is E [w ].

Therefore, can create Pareto improvement by moving to a fixed wagebetween CE and E [w ].

In a nutshell: when a risk-neutral and a risk-averse agent sharerisk, the risk-neutral agent must bear all risk in any Paretoefficient outcome (absent other considerations).


Principals First-Best Outcome

Lets keep our assumption that we dont have an informationproblem, so P can observe As effort. What would P like to do (thefirst-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 outsideoption. (Paying less means that A will not work for P; paying more isjust throwing away money.)

If P doesnt require effort, we needw 0, so w = 0.

If P requires effort, she needs to make surew 1 0, so she will

choose w = 1 when effort is exerted, and w = 0 when it isnt.

P will require effort when that gives her a higher profit:pV 1 > 0 pV > 1.


Relation between Ps First-Best and Social Optimum

The conditions for Ps first-best to require effort and for the socialoptimum to require effort are the same.

This is not a coincidence!

P wants to maximize total surplus because she can get all of itby paying A just enough to make her as well off as the outsideoption.

For the rest of this week, we will use first-best, social optimumand socially efficient outcome interchangeably.


Moral Hazard in Example

Now, lets look at the problem: P doesnt actually observe As effortlevel, so cant condition wage on it.

But if wage doesnt depend on e, A should just slack off!

As a result, there is no way to get the first-best outcome whenpV > 1.

There is another way to induce effort: conditioning wage on theoutcome.

This wont give us the first-best outcome because the agent will bearsome risk. But it is sometimes better than not inducing effort at all.


Second-Best Problem

Let w0 be the wage in case of failure, and w1 be the wage in case ofsuccess.

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

Ps payoff is p(V w1) (1 p)w0. P needs to maximize this subjectto the above two constraints. This is Ps second-best outcome.


Binding Constraints

Suppose youre doing a constrained optimization problem, and youhave constraints that are inequalities, like IC and IR.

We say that a constraint binds if it holds with equality at anoptimum.

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.


Second-Best Outcome (I)

Suppose IR doesnt bind in our problem, so that the optimum(w0 ,w

1 ) satisfies pu(w

1 ) + (1 p)u(w0 ) 1 > 0.

Then P could reduce w0 slightly, and both IR and IC would still hold.But reducing w0 increases Ps profit, which contradicts (w

0 ,w

1 )

being an optimum.

So IR must actually bind: pu(w1 ) + (1 p)u(w0 ) 1 = 0 at the theoptimum (w0 ,w

1 ).

Therefore, IC becomes: 0 u(w0 ). Thus, w0 = 0 at the theoptimum (w0 ,w

1 ).


Second-Best Outcome (II)

At the the optimum (w0 ,w1 ), we have u(w

0 ) =

w0 = 0 and

therefore pu(w1 ) = pw1 = 1 = w1 = 1p2 .

Ps second-best payoff is then p(V w1 ) (1 p)w0 = p(V 1p2 ).This is better than allowing A to slack off and getting 0 when V > 1

p2.

Compare the above condition to the condition for the first-best toinvolve effort pV > 1 V > 1p .So when 1p < V 1p2

) payoff to Psfirst-best payoff.

Second-best payoff: p(V 1p2

) = pV 1pFirst-best payoff: pV 1Which one is bigger? Whats the intuition?


Comments

In the second-best when V > 1p2

, P knows that A will exert higheffort. But P still varies the wage because she has to provideincentives for effort.

P makes a lower profit in the second best because varying thewage lowers As certainty equivalent. So P has to compensateby paying more on average. Sometimes this lower profit causes theproject to be cancelled, even though the project will be undertaken inthe first best.

Second best is not Pareto efficient.

If the cost of monitoring effort is lower than the profit loss in thesecond-best, then P will instead monitor.

Repeated interactions can also reduce the severity of moral hazard.


lecture 9 - moral hazard

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