agent completethe fire. exposure their person, duetoa

The contracts of at least 33 major league

baseball players

^{have Incentive clauses}

providing a bonus ifthat player

is named

^{the Most Valuable} _Player in a Division Series.Unfortunately, no such award isgiven for a^{Division Series.*}

ifsk n employee cruises the Internet for

jokes instead of

working when the boss is llrffk not watching. ^{A driver of a rental car takes it off the} highway and ruins the sus-

lM tiapension. The dentist caps your tooth, not

because

you need it, but because he

wants a

new high-definition, flat-screen

^TV.

Each of these examples illustrates an inefficient

use of resources duetoa

^{mora/ hazard,}

whereby an informed person takes advantage

of a less-informed person,

^{often through}

an unobserved action (Chapter 18). In

this chapter,

^{we examine how to} design contracts that eliminate

inefficiencies due to

^{moral hazard} problems without shifting risk to

people who hate bearing risk\342\200\224or contracts that at least reach a

good compromisebetween

these

^two goals.

For example, insurance companies face

a trade-offbetweenreducing

^{moral hazards}

and increasing the risk of insurance

buyers. Because

^{an insurance} company pools risks,

it acts as though it is risk neutral

(Chapter 16).The

^{firm offers insurance contracts to}

risk-averse homeowners so

that they can reduce their exposure

^{to risk. If homeowners}

can buy full insurance so

that they

^{will suffer no loss if a fire occurs, some}

of them

^fail

to take reasonable precautions. They might store

flammable liquids

^{and old newspapers}

in their houses, increasing the

chance ofa catastrophic fire.

A contract that avoids this moral hazard problem

specifies that the insurance

company will not pay in the event of a fire^{if the} _company ^can show that the policyholders

stored flammable materials

^{in their home. If this} approach is impractical, however,

the insurance

company might offer a contract that provides incomplete

insurance, covering

only a fraction of the damage from a

fire. The less completethe

^{coverage, the greater}

the incentive for policyholders

to avoid dangerous activities

^{but the} greater the risk that the

risk-averse homeowners

^{must bear.}

To illustrate methods of controlling moral

hazards and the trade-off

^{between moral}

hazards and risk, we focus in this

chapter on contractsbetweena

principal\342\200\224such as an

employer\342\200\224and an agent\342\200\224suchas an employee. The principal

contracts

^{with the} agent

to take some action

that benefitsthe principal.

^{Until now, we have assumed that firms}

can

produce efficiently.

^{However, if a principal cannot} practically monitor an

agent all the time,the agent

^{may steal, not work hard, or} engage inother

opportunistic behavior that lowers

productivity.2

Opportunistic behavior by an informed agent harms

a less-informed principal.

Sometimes the losses are so great that both

parties would be better

^{off if both had full}

information and if opportunistic behavior were impossible.

1TomFitzGerald,\"Top of the Sixth,\" San Francisco Chronicle,January

31, 1997-.C6.

2Sometimes the principal's problem is not so muchone of monitoringas

oneof

legally verifying

that opportunistic behavior occurred. Forexample,an

insurance

company (principal) might be able to determine ^{that the homeowner} _{(agent) engaged} in arson but might havetrouble_proving ^it.

662 CHAPTER 19 Contracts and Moral

Hazards

pin.this

\342\200\242chapter,-we^^i -\"examine sjxmatn^S^

.-'topics\" ^;:;,:^'>;^'-/

19.1

When you contract with people whose actions you

cannot observe or evaluate,

^they

may take advantage of you. If

you pay someone

by the hour to prepare your tax return,

you do not

^{know whether that} _person ^worked all the

hours billed. Ifyouretaina

^lawyer

to represent you in a suit arising

from an accident,you do not

^{know whether the}

settlement that the lawyer recommends is in

your best interest orthe

lawyer's.

Of course, many people behave honorably even

if they have opportunities to exploit

others.

Many people also honestly believe that they are

putting in a

^full day's work even when they are not

working as hard as

they might. Aiko, who manages Pat's Printing

Shop, is paid

^{an hourly wage. She works} every hour

she is supposed to,

^{even though}

Pat rarely checks on her.

Nonetheless,

^Aiko may not be spending her time

as effectively as possible.She politely(but

impersonally) asks everyone who enters the shop, \"May

I

help

^{you?\" If she were to receive the} appropriate

financial

incentives\342\200\224say, a share of

the shop's profit\342\200\224she would memorize the names of her

customers, greet

^them

enthusiastically by name when they enter the store,

and check

^with _nearby ^{businesses to} find

out whether they

would be interested in

^{new services.}

A MODEL

We can describe many

principal-agent interactions usingthe following model. This

model stresses that the output or profit from

this relationshipand the risk borne

by

the two parties depend on the actions

of the agent and the stateof nature.

In a typical principal-agent relationship, the principal, Paul,

owns some property,

such asa

^{firm, or has a} property right such as

the right to sue for damages

^{from an}

injury. Paul hires or contracts with

an agent,

^{Amy, to take some action a that increases}

the value of his

property or that produces profit, tt, from using

his property.

The principalandthe

^{agent need each other. If Paul hires} Amy

to run his ice-cream shop,

^{Amy needs Paul's shop and Paul needs Amy's}

^{efforts to sell ice} cream.

^The profit

1. Principal-Agent Problem: The way that an uninformed

principal contracts

^{with an}

Informed agent determines whether moral hazards

occur

^{and how risks are shared.}

2. Production Efficiency:

The agent's

^{output depends on the} type of contract used and

the

ability of the principal to monitor the agent's

actions.

3.

^{Trade-Off Between} Efficiency in Production and ⁱⁿ Risk Bearing: A principal and an

agent ^{may agree to a contract that does not} eliminate

moral hazards

oroptimaily

share risk but strikes a balance between

these

^two objectives.

4. Payments Linked to Production or

Profit: Employees

^{work harder if they are rewarded}

for greater ^{individual or group} productivity.

5. Monitoring: Employees work

harder

^{If an} _employer monitors their behavior and makes It

worthwhileforthemto keep

^{from being fired.}

6. Contract Choice: Byobserving whichtype of contract an agent picks when offered

a

choice,

^{a principal may obtain enough} information toreduce

moral hazards.

from the ice cream sold,

tt, depends on the numberof hours, a,

^that Amy works. The profit may also

depend on the outcome of 8,

^{which represents the state} of nature:

tt =

Tr(a, 8).

For example, profit

^{may depend on whether the ice-cream machine breaks,}

^{8 = 1,} or

does

^{not break, 8 = 0. Or it} _may

_depend ^on

^{whether it is a hot} _day, ⁸⁼

^the temperature.

In extreme cases,the

^{profit function} depends only on the agent's actions

or only on the state of nature.

^{At one} extreme, profit depends only on

the agent's action, tt = ir(a),

if

^{there is} only one state of nature1, no

uncertainty due to randomevents.Inour

example,the profit function has this form if

demand does not

vary with weather and if the

ice-cream machine

is reliable.

At the other extreme, profit depends only on

the state ofnature, tt = tt(8),

^{such as in}

an insurance market in which

profit or

^value _{depends only} ^on the state of nature

and not on the actionsofan agent.

^{For instance, a couple buys insurance against rain}

^on

the

_day ^{of their} wedding. The value they place

on their outdoorwedding

^{ceremony is}

tt(8), which depends only on the

weather, 8, because no actions

^{are involved.}

TYPES OF CONTRACTS

A verbol controct isn't worth the poper it's ^{written on.} \342\200\224Samuel Goldwyn

When a formal market exists, the

principal may deal impersonally

^{with an anonymous}

agent by buying a good

or service of

^known quality at the market price. There is

no

opportunityfor opportunism. In this

chapter, we focus on situations in which either

a formal

^{market does not exist} or a principal and

an agentagree on a customized

contract that is designed to reduce opportunism.

A contract

between a principaland

^{an agent determines how the outcome of their}

partnership (such asthe profitoroutput) is

split between them. Three common types of contracts

are fixed-fee, hire, and contingent

^contracts.

In a fixed-fee contract, the payment

to the agent, F, is

independent of the agent's actions, a, the state

of nature, 8, or the outcome, tt.

^The principal keeps the residual profit, ir(fl, 8) \342\200\224

F. Alternatively, the principal may get a

fixed amount and the agent

may receive the residual profit. For example, the

agent may

^{pay a fixed rent for the right}

to

use the principal's property.3

In a hire contract, the payment to the

agent depends on the agent's actions

^as they are observed by the principal.

Two commontypes of hire contracts

pay employees an hourly rate\342\200\224a wage per hour\342\200\224or a piece rate\342\200\224a payment per unit of output

produced. If w is the wage per hour

(or the price per piece

^{of output) and Amy works a}

hours

(or producesa units of output),

^{then Paul pays Amy wa and keeps the}

^residual

profit ir(fl, 8)

\342\200\224 wa.

In a contingent contract, the payoff

to each person dependson the state

^of nature,

which may not be known

to the partiesat the time

they write the contract. For

example, Penn agrees to pay Alexis a

higher amount to

^{fix his roof if it is} _raining than

if it

is not.

3Jefferson Hope says in the Sherlock Holmesmystery A Study in Scarlet, ^\"1 applied at a cab-owner's

office,and soon

got

employment. 1was to bring acertainsuma weekto^the owner, and whatever was over that 1might keep for myself.\"

CHAPTER 19 Contracts and

Moral Hazards

Onetype of contingent

^{contract is a splitting or sharing contract, where}

^{the payoff}

to each person isa

^{fraction of} the total profit (which is observable).

Alain sells Pamela's house

^{for her for} ir(a, 8) and receives a

commission of

^{7% on the sales} _price. ^He

receives

0.07Tr(a, 8), and she keeps

^{0.93Tr(a, 8),}

EFFICIENCY

The type of contract selected

depends on

^{what the} parties can observe. A principal is

more likely to useahire contract if

^the principal can easily monitor the agent's actions.

A contingent contract may be chosen if

the state of nature

^{can be observed after the}

work is completed. ^{A fixed-fee contract does not depend on} observing

anything, so it

can always be used.

Ideally, the principal and

agent agree to

^{an efficient contract: an} _agreement with provisions that

ensure that no

_party ^{can be made better} off without harming

the other

party. Using an efficient contract results in

efficiencyin productionand

efficiency in risk

sharing.

Efficiency in production requires

that the principal's and the agent's

^combined

value (profits, payoffs), tt, is maximized. We say

that production is efficient if

Amy

manages Paul's firm so that the

sum of their profits cannot

^{be increased. In our}

examples, the moral hazard hurts the principal more

than it helpsthe agent, so total

profit

falls. Thus achieving efficiency in production requires

preventing the moralhazard.

Efficiency in risk bearing requires that risk

sharing is optimal in thatthe person

who least minds facing risk\342\200\224the risk-neutral or less-risk-averse person\342\200\224bearsmore

of the risk.

In Chapter 16

^{we saw that} risk-averse people are willing to _pay ^a risk

premium to avoid risk, whereas risk-neutral people do

not care if

_they ^{face fair} risk or not.

Suppose that

Arlene is risk

^{averse and is} willing to pay arisk

premium of $100 to

^avoid

a particular risk. Peter is risk neutral

and would bear the risk withouta premium.

Arlene and Peter can strike a deal

whereby Peter agrees to bear all

^{of Arlene's risk in}

exchange for a payment

between $0 and $100. For simplicity

^we concentrate on

situations in which one party isrisk

averse and the other isrisk neutral.

(Generally, if both

parties are risk averse, with

one more risk

^{averse than the} other, both can be

made

better off ifthe less-risk-averse

person bears more but not all of the

risk.)

If

_everyone ^has full information\342\200\224there is no uncertainty and

no asymmetric

information\342\200\224efficiency can be achieved. The principal contracts with

the agent to

performa

^{task for some specified reward and observes whether}

^the agent completes

the

^task properly before paying, so no moral hazard

problem arises.

Throughoutthe restofthis

chapter, we examine what happens when the parties

do

not

^{have full} information. Production inefficiency is more likely

when eitherthe agent

has more information

^{than the} principal or both parties are uncertain

about the state of nature.

When the agent has more information than the

principal and

^{there is no} risk

because there isonly

one state ofnature, contracts

^{are used to achieve} _efficiency ⁱⁿ

production by conveying adequate information to the principal

to eliminate moral

^hazard

problems. Alternatively, incentives in the contract may

discourage the informed

person from engaging in opportunistic behavior. The contracts

do not

^{have to address}

efficiency in risk bearing because

there is no risk.

Given that they face both asymmetric information

and risk, the parties

^{try to}

contract to achieve efficiency in production and efficiency

in risk bearing.Often,

^however,

both objectives cannot be achieved, so the

parties must trade off

^{between them.}

The type

of contract that

^an agent and principal use affects production efficiency.

In the following example, production

^{efficiency is achieved by} maximizing total oxjoint

profit: the sum of the principal's

^{and the agent's individual} profits. To isolate the

production issues from risk bearing, we initially assume

that there is only one state

^of

nature, so the parties face no risk

due to random events:

^Total profit, Tr(a), is solely a

function of

the agent's action, a.

EFFICIENT CONTRACT

To be efficient and to maximize

joint profit,the contract

^{that a} principal offers to an agent must

havetwo properties.First,the contract

^must provide a large enough payoff that the

agent is

willing to participate in the contract. We know

that the principal's

^{payoff is}

adequate to ensure the principal's participation because the

principal offersthe contract.

Second,the contract

^{must be incentive} compatible in that it provides inducements

such that the

agent wants to perform the assigned task rather

than engage in

opportunistic behavior. That is, it is in the

agent's best interest to

^{take an action that}

maximizes joint profit. If the contract is not

incentive

compatible\342\200\224so the agent tries to

maximize personal

profit ratherthan joint

profit\342\200\224efficiency can be achieved only if the principal

monitors the

agent and forces the agent to act

so as to

^maximize joint profit.

We use an example to

illustrate

why some types of contracts lead to

efficiency and others do not.

^{Paula, the} principal, owns a store called Buy-A-Duck

(located near

^a

canal) that sells wood carvings of ducks.

Arthur, the agent,managesthe store.Paula

and

^Arthur's joint profit is

ir(a) = R(a)

- ma, (19. l)

where JR(a) is the sales revenue from selling

a carvings,

^{and ma is the cost of the} carvings.

Arthur has a constant

marginal cost m to obtain and selleach

duck, includingthe amount

he

_pays ^a local carver and the opportunity value

(best alternativeuse) ofhis time.

Because

^{Arthur bears the full} _marginal ^{cost of} _selling

one more

carving, he wants to sell the joint-profit-maxhnizing output

only if he also getsthe

^{full marginal benefit}

from selling one more

duck. To determinethe joint-profit-maximizing solution,

^we

can ask what Arthur would do if

he ownedthe shopandreceivedallthe profit,

^giving

him an incentive to maximize total

profit.

How

many ducks must Arthur sell to maximize the

parties'joint profit, Equation

19.1?

^{To obtain the} first-order condition to maximize profit,

we set the

^{derivative of}

Equation 19.1 equal to zero:

-\342\200\224\342\226\240=

~T^ - m

= 0. (19.2)

da

^da

According to Equation 19.2, joint profit is

maximized

by choosing the number of

ducks to

sell, a, such

^that marginal revenue, dR{a)/da, equals marginal cost,

m.

Suppose,for example,

^{that m = 12, the inverse demand}

curve they face isp =

24 \342\200\224

^a, and hence the revenue function is

R(a) = 24a

\342\200\224

-^a2- The marginal revenue function is

MR(a)

=

_dJR(fl)/da ⁼ ₂₄ \342\200\224

a. Substituting the marginal revenue function and

the

marginal cost into

Equation 19.2, we find thatM]R = 24\342\200\224a= 12=m = MC, or a

= 12.

Panel

^{a of} _Figure ^19,1 illustrates this result: The

marginal revenue

^curve, MR, intersects

666 CHAPTER 19 Contracts and

Moral Hazards

Figure 19.1 Maximizing Joint Profit

when the AgentGets

the

^{Residual Profit,}

(a) If the agent, ^Arthur, gets all the joint profit, tt, he

maximizes

^his profit by selling

12carvings ate, wherethe

marginal

revenue curve intersects his marginal cost

curve: Mfi=

MC= 12.If

^he pays the

principal, Paula, a fixed rent of $48,he

maximizes his profit by selling 12 carvings.

(A fixed rent does not affect either his

marginal revenue or his marginal cost.)

(b)^Joint profit at 12 carvings is$72,point B.

If^Arthur _pays ^{a rent} of $48to Paula,

Arthur's profit istt

- $48.

By selling

12 carvings and maximizing joint profit,

Arthur also maximizes his profit.

(a)Agent's Problem

(b)^Profits

12 24

a, Duck carvings per day

Tt, Joint profit

a. Duck carvings per day

the

marginal cost

^{curve, MC= m =} $12, at the

equilibrium point e.Panelb shows

^that

total profit, tt, reaches a maximum of

$72 at point E.

Which types of contracts lead to production efficiency? To

answer this question,

^we

first examine which contracts yield that outcome

when both parties

^{have full}

information and then consider which contracts bring

the desired result

^{when the} _principal

is relatively uninformed. It is

important to rememberthat

^{we are} considering a special case: Contracts that

work here

_may ^{not work in some} other settings,

whereas contracts that do not

^{work here} may be effective elsewhere.

FULL INFORMATION

Suppose that both Paula and

^{Arthur have full} information. Each knows the actions

Arthur

takes\342\200\224the number of carvings sold\342\200\224and the effect of those actions on profit.

Because she has full information,

^{Paula can dictate} exactly what Arthur is

to do.

Are there incentive-compatible contracts that

do not require such monitoring

^and

supervision? To answer this question, we consider

four kinds of contracts:

^{a fixed-fee}

rental contract, a hire contract, and

two types of contingent contracts.

Fixed-Fee Rental Contract. If Arthur contracts to

rent the store

^{from Paula for a fixed}

fee, F,joint

profit is maximized.

^{Arthur earns a residual} profit equal to the

joint profit minus the

^{fixed rent he} pays Paula, tr(fl) \342\200\224

F. Because the amount that Paula makes is

fixed,

^{Arthur gets the entire} marginal profit from selling

one more duck.

^{As a}

consequence, the amount, a, that maximizes Arthur's profit,

ir(a) - F=

R{a)

- ma -

F, (19.3)

also

^maximizes joint profit, tr(fl). To show this result,

we note

^{that his} first-order

condition based on Equation 19.3,

d[ir(a)

- F)

= \342\200\224\342\200\224dR(\302\253) - m - \342\200\224dF = \342\200\224dR(n)

m = 0, (19.4)

do do

do do

is identicaltothe first-order

^{condition in} Equation 19.2.

This result is

illustrated in Figure 19.1,

^{where Arthur} pays Paula F= $48 rent.

This fixed

payment does not affect his marginal cost. As a

result, he

^{maximizes his} _profit

after paving the rent, tt \342\200\224

$48, by equating his marginal revenue

to his marginal cost:

MR~MC= 12

^at point ein panel a.

Because Arthur pays

the same

^{fixed rent no matter how} _many units he

sells, the agent's profit

^{curve in panel b lies $48 below}

^the joint-profit

^{curve at every quantity.}

As aresult, Arthur's

net-profit curve peaks

^{(at point E*) at the same} quantity, 12,

where the joint-profit

^{curve peaks (at \302\243).Thus the fixed-fee rental contract is}

^incentive

compatible. Arthur participates in this contract because

he earns $24

^after paying for the

rent and the carvings

(point

\302\243*).

Hire Contract. Now suppose that Paula contracts

to

pay Arthur for each carving he sells.

If

she

_pays ^him $12 per carving, Arthur just

breaks even on each sale. He is

indifferent

between participating and not. Even if he

chooses to participate,he doesnot sell

^the

joint-profit-maximizing number of carvings unless Paula supervises

him. If she does

supervise him, she instructs him to sell

12 carvings, and shegetsall the

joint profit of $72.

For Arthur to want

to participateand to sell

carvings without supervision, he must receive more

than $12 percarving. If

^Paula pays Arthur $14 per carving, for example,

he makesa profit of$2per

^{carving. He now has an incentive to sell}

as many carvings as hecan

^{(even if the} price is less than the

cost of the carving),

^{which does not}

maximize joint profit, so this contract is not

incentive compatible.

Even if the Paula can control how many

carvings he sells, joint

^{profit is not}

maximized. Paula keeps the revenue minus what she pays

Arthur, $14 timesthe number

ofcarvings,

R(a)

- 14a.

Thus her objective differs

from the jomt-profit-maximizing objective, tt

^{(a) =} JR(fl) \342\200\22412a.

Joint profit is maximized when marginal

revenue equals the marginal cost

^{of $12.}

Because Paula's marginal cost, $14,

is larger, she directs

^{Arthur to sell fewer than}

the optimal

number of carvings.

^{Paula maximizes iR} \342\200\224

14a =

(24fl \342\200\224

\\a2)

\342\200\224

\\Aa \342\200\224 lOfl \342\200\224

\\a2. Given her first-order condition, where the

derivative of Paula's profit

^with

respect to a equals zero, 10\342\200\224a = 0, she maximizes her

profit

^{by selling 10 carvings. Joint}

profit is only

$70 at 10carvings, compared to

^{$72 at the} optimal 12 carvings.

668 CHAPTER

19 ContractsandMoral

^Hazards

Revenue-Sharing Contract. If Paula and Arthur

use a contingentcontract

^whereby

they share the revenue, joint profit is

not maximized. Supposethat

^{Arthur receives}

three-quarters of the revenue, fjR, and Paula

gets the rest,

\\R. Panel a of Figure 19,2

shows the

marginal revenue that

^{Arthur obtains from} selling an extra carving, MR*

=

\\MR. He maximizes his profit at $24 by

selling 8 carvings,for

^{which MR* =}

MC at e*.Paula

gets the remaining profitof $40,

^{which is the difference between their}

total profit

from selling 8 ducks

per day, tt = $64, and Arthur's

profit.

Thus their joint

^{profit in panel b at a =}

^{8 is $64,}

^{which is $8 less than the maximum}

possible

profit of $72 (point E).

^{Arthur has an incentive to sell fewer than}

^{the optimal}

number of

^{ducks because he bears the full} _marginal ^cost

^{of each}

carving he sells, $12, but gets only three-quarters

of the

marginal revenue.

Even if Paula controls how many

carvings are sold, joint

^{profit is not maximized.}

Because the amount she

makes,

fiR, depends only on revenue and not on

the cost of obtainingthe

^{carvings, she wants the} revenue-maximizing quantity sold. Revenue

is

Figure 19,2

Why Revenue Sharing Reduces Agent's Efforts, (a)Joint

profit is maximized at 12 carvings,

where MR= MC

= 12

^at equilibrium point e. If Arthur getsthree-quarters of the

revenue

^{and Paula} gets the rest, Arthur maximizes hisprofit by selling 8 carvings, where his new marginalrevenuecurve,^MR* \342\200\224

\\MR, equals his marginal cost at point e*.

(b)Joint

^{profit reaches a maximum}

of $72 at E,wherethey sell 12

carvings per day. If they split the revenue,

Arthur sells 8 ducks per day and gets

$24^at E*, and Paula receives the residual, $40

(=$64-$24).

a,

^{Duck carvings} per day

(a) Agent's Problem

0 (b)^Profits

2 72

**\342\200\224 o a. 64

Agent

24

8 :

/ ^:-

/ ;r

If

12 24

\342\226\240

a,'Duck carvings per day

'\342\226\240E

\342\200\242

\\ji. Joint profit

\\

i

ffl-12*. \\

rv Agenfs profit \\

12 16 24

maximized wheremarginal

^{revenue is zero at a = 24} (panel

a),

^{Arthur would not}

participate if the contract granted him only three-quarters

of the

^{revenue but} _required

him to sell 24

carvings, becausehe would lose

money.

SOLVED PROBLEM 19-1

Use calculus to

show that,

^{if Arthur receives} three-quarters of the revenue, |fl,

and

^Paula

gets the rest, he does not sell

the

Joint-profit-maximizing quantity.

Answer

1. Write Arthur's profitfunction,

calculatehis first-order condition, and

^solve forhis profit-maximkhtg output; Arthur's profit is

f K(#j - 12a

⁼ f (24a -

\\a2)

- 12a. To

maximize his profit, he needs to choose a

such that his

marginal profit with

respect to a equals zero:\302\247dK(a)/da

- 12 =

|(24

- a) - 12

^{= 0. Thus the} _output

that maximizes his

profit is a = 8;

2.

Compare this solution to the joint-profit-maximizing output: We know

that the

joint profit is

^{maximized at} 72, where a = 12. With revenue

sharing, a = 8 and joint

^{profits are only 64.}

Comment: Arthur produces too

little output becausehe bears the

^full marginal cost, 12, but earns only

three-quarters of the

marginal benefit (marginal

revenue), ^(24

\342\200\224

a), from the joint-profit-maximizing problem, 24

a.

Profit-Sharing Contract.

^{Paula and Arthur} may instead use a

contingent contract

by

which they divide the economic profit, it.

If they can agree

^{that the true marginal and}

average cost is

$12 per

^{carving (which includes Arthur's} opportunity cost of time),

the contract is incentive compatible because

^{Arthur wants to sell the} _optimal number of

carvings. Only

^{by maximizing total profit can he maximize}

his share of profit.

^As

Figure 19.3 illustrates, Arthur receives one-third of

the joint profit and chooses

^to

Figure 19.3 Why Profit Sharing Is

Efficient. If the agent,^{Arthur, gets a}

third of the joint profit,he

maximizes

^his

profit, jiT, by maximizing joint profit,it. k, Joint^profit

a, Duck carvings per day

CHAPTER 19

Contracts and

^{Moral Hazards}

Tabu 19.1 Production Efficiency and

Moral Hazard Problems for

Buy-A-Duck

Contract

Fixed-fee rental contract Rent (to principal)

Hire contract,per

^{unit pay}

Pay equals marginal cost

Pay is

greater

^{than marginal cost}

Contingent contract Share revenue Share profit

Full

Information Production

Efficiency

Yes

Noa Noc

No Yes

Asymmetric

Production

Efficiency

Yes

Nob No

Nob Nob

Information Moral

Hazard

Problem No

Yes Yes

Yes Yes

The agent may not participate and has noincentive to sell the optimal numberofcarvings. Efficiency can be achieved only if the principal supervises.

^Unlessthe agentsteals^{all the} revenue (or profit) from an extrasale,inefficiency results.

The agent sellstoo _many or the principal directs the agent toselltoo^few carvings.

produce the level of output, a

= 12,that maximizes joint profit.

^{Arthur gets one-third}

of profit, jtt = j(R \342\200\224

C) =

3R \342\200\224

3C, where R is revenue and C

is cost. Hemaximizes

his

profit where jMR =

^MC. Although he

gets only one-third ofthe

marginal revenue, 5MR, he bears ouly one-third of

the marginal cost.Dividing both sides

^{of the} equation by \\, we find that this condition isthe

same as the one

^for maximizing total profit: MR = MC.

Arthur earns $24, sohe is

willing to participate.

The second column of Table

19.1 summarizes our analysis.

^{Whether efficiency in}

production is achieved depends on

the type of contract

^{that the} principal and the agent use. If

the principal

^{has full} information (knows the agent's actions), the

principal achieves production

^{efficiency without having to} supervise by using

one of

^{the incentive-}

compatible contracts: fixed-fee rental or profit-sharing.

ASYMMETRIC INFORMATION

Now suppose that the principal, Paula, has less

information than the agent,

^{Arthur. She}

cannot observe the number of carvings

he sells or therevenue. Due to

^this asymmetric

information, Arthur can steal from Paula

without her detecting

^{the theft.}

As Table 19.1 shows, with asymmetric

information, the

_only ^{contract that results in}

production efficiency and

no moral

^hazard problem is the one whereby the principal

gets a fixed rent.

^{All the other contracts result in} inefficiency, and

Arthur has

^an

opportunityto take advantage of Paula.

Fixed-Fee

Rental Contract.

^Arthur pays Paula the fixed rent that she

is due because

Paula would know if she were paid less.

Arthur receivesthe residual profit, joint

^profit

minus the fixed rent, so he

wants to sell

^the joint-profit-maximizing number of carvings.

Hire Contract. If

Paula offers to

_pay Arthur the actual marginal cost of

$12 per

^carving

and he is honest, he may

refuse to participatein

^{the contract because he makes no} profit.

Even

if he participates, he

^{has no incentive to sell} the optimal

number of carvings.