Economic of Information

7/31/2019 Economic of Information

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11

THE ECONOMICS OF INFORMATION

Copyright 2005 by South-Western, a division of Thomson Learning. All rights reserved.


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Properties of Information

Information is not easy to define it is difficult to measure the quantity of

information obtainable from differentactions

there are too many forms of usefulinformation to permit the standard price-

quantity characterization used in supplyand demand analysis


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33

Properties of Information

Studying information also becomesdifficult due to some technical properties

of information it is durable and retains value after its use it can be nonrival and nonexclusive

in this manner it can be considered a public

good


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44

The Value of Information

In many respects, lack of informationdoes represent a problem involving

uncertainty for a decision maker the individual may not know exactly what theconsequences of a particular action will be

Better information can reduce uncertainty

and lead to better decisions and higherutility


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Assume that information can bemeasured by the number of messages

(m) purchased gandb will be functions ofm


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The individuals goal will be to maximize

E(U) =gU(Wg) +bU(Wb)

subject toI=pgWg+pbWb +pmm

We need to set up the Lagrangian

L =gU(Wg) +bU(Wb) + (I-pgWg-pbWb-

pmm)


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First-order conditions for a constrainedmaximum are:

0)(' ==

ggg

g

pWUWL

0)(' ==

bbbb

pWUW

L

0==

mpWpWp mbbggI

L


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The Value of Information First-order conditions for a constrained

maximum are:

0

)()(

)(')('

=

+

+

+=

mb

b

g

gb

b

g

g

bbb

g

gg

pdm

dWp

dm

dWp

dm

dWU

dm

dWU

dm

dWWU

dm

dWWU

m

L


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The first two equations show that theindividual will maximize utility at a point

where the subjective ratio of expectedmarginal utilities is equal to the priceratio (pg/pb)

The last equation shows the utility-maximizing level of information to buy


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1111

Asymmetry of Information

The level of information that a person buyswill depend on the price per unit

Information costs may differ significantlyacross individuals

some may possess specific skills for acquiringinformation

some may have experience that is relevant some may have made different former

investments in information services


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1212

Information and Insurance

There are a number of informationasymmetries in the market for insurance

Buyers are often in a better position toknow the likelihood of uncertain events

may also be able to take actions thatimpact these probabilities


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1313

Moral Hazard

Moral hazard is the effect of insurancecoverage on individuals decisions to

take activities that may change thelikelihood or size of losses

parking an insured car in an unsafe area choosing not to install a sprinkler system in

an insured home


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1414

Moral Hazard

Suppose a risk-averse individual facesthe risk of a loss (l) that will lower

wealth the probability of a loss is this probability can be lowered by the

amount the person spends on preventive

measures (a)


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Moral Hazard

Wealth in the two states is given byW1 = W0 - a

W2 = W0 - a - l

The individual chooses a to maximize

E(U) = E= (1- ) U(W1) +U(W2)


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Moral Hazard The first-order condition for a maximum is

0)(')()(')1()( 2211 =

+

=

WU

a

WUWU

a

WU

a

E

aWUWUWUWU

=+ )]()([)(')1()(' 1212

the optimal point is where the expected

marginal utility cost from spending oneadditional dollar on prevention is equal to thereduction in the expected value of the utility lossthat may be encountered in bad times


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1717

Behavior with Insurance

and Perfect Monitoring Suppose that the individual may purchase

insurance (premium =p) that paysxif a

loss occurs Wealth in each state becomes

W1 = W0 - a -p

W2 = W0 - a -p - l+x

A fair premium would be equal to

p = x


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and Perfect Monitoring The person can maximize expected utility

by choosingxsuch that W1 = W2

The first-order condition is

0)(1)('

)(1)(')1(

22

11

=

+

+

+=

aWU

aWU

aWU

aWU

a

E

l

l


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and Perfect Monitoring Since W1 = W2, this condition becomes

a

= l1

at the utility maximizing choice, the marginalcost of an extra unit of prevention should equalthe marginal reduction in the expected lossprovided by the extra spending

with full insurance and actuarially fairpremiums, precautionary purchases still occurat the optimal level


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2020

Moral Hazard

So far, we have assumed that insuranceproviders know the probability of a lossand can charge the actuarially fairpremium

this is doubtful when individuals can undertakeprecautionary activities

the insurance provider would have toconstantly monitor each persons activities todetermine the correct probability of loss


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Moral Hazard

In the simplest case, the insurer might seta premium based on the averageprobability of loss experienced by somegroup of people

no variation in premiums allowed for specificprecautionary activities

each individual would have an incentive to reducehis level of precautionary activities


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2222

Adverse Selection

Individuals may have different probabilitiesof experiencing a loss

If individuals know the probabilities moreaccurately than insurers, insurancemarkets may not function properly

it will be difficult for insurers to set premiumsbased on accurate measures of expected loss


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2323

Adverse Selection

certainty line

W1

W2

W

*

W*-

l

Assume that two individualshave the same initial wealth(W*) and each face a

potential loss ofl

E


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Adverse Selection

certainty line

W1

W2

W

*

W* -

l

Suppose that one person has a probability of loss equal to H, whilethe other has a probability of loss equal to l

E

F

G

Both individuals wouldprefer to move to thecertainty line if premiumsare actuarially fair


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Adverse Selection

certainty line

W1

W2

W

*

W* -

l

The lines show the market opportunities for each person to trade W1forW2 by buying fair insurance

E

F

Gl

l

=

)1(slope

H

Hslope

=

)(1

The low-risk person willmaximize utility at point

F, while the high-riskperson will choose G


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Adverse Selection If insurers have imperfect information

about which individuals fall into low- andhigh-risk categories, this solution isunstable

point Fprovides more wealth in both states high-risk individuals will want to buy

insurance that is intended for low-riskindividuals insurers will lose money on each policy sold


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Adverse Selection

certainty line

W1

W2

W

*

W* -

l

E

F

G

One possible solution would be for the insurer to offerpremiums based on the average probability of loss

H

Since EHdoes notaccurately reflect the true

probabilities of each buyer,they may not fully insure

and may choose a pointsuch as M

M


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Point M is not an equilibrium because further tradingopportunities exist for low-risk individuals

UH

U

L

Adverse Selection

certainty line

W1

W2

W

*

W* -

l

E

F

G

H

M

An insurance policysuch as Nwould beunattractive to high-risk individuals, butattractive to low-risk

individuals andprofitable for insurers

N


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Adverse Selection

If a market has asymmetric information,the equilibria must be separated in

some way high-risk individuals must have an incentive

to purchase one type of insurance, whilelow-risk purchase another


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Adverse Selection

certainty line

W1

W2

W

*

W* -

l

E

F

G

Suppose that insurers offer policy G. High-risk individualswill opt for full insurance.

UH

Insurers cannot offer any

policy that lies above UHbecausethey cannot prevent high-riskindividuals from takingadvantage of it


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Adverse Selection

certainty line

W1

W2

W

*

W* -

l

E

F

GUH

The policies G and Jrepresent a separatingequilibrium

The best policy that low-risk individuals can obtain is onesuch as J

J


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Adverse Selection

Low-risk individuals could try to signalinsurers their true probabilities of loss

insurers must be able to determine if the

signals are believable insurers may be able to infer accurate

probabilities by observing their clientsmarket behavior

the separating equilibrium identifies anindividuals risk category


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Adverse Selection

Market signals can be drawn from anumber of sources

the economic behavior must accuratelyreflect risk categories

the costs to individuals of taking thesignaling action must be related to the

probability of loss


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The Principal-Agent

Relationship One important way in which asymmetric

information may affect the allocation of

resources is when one person hiresanother person to make decisions

patients hiring physicians

investors hiring financial advisors car owners hiring mechanics stockholders hiring managers


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The Principal-Agent

Relationship In each of these cases, a person with

less information (the principal) is hiring a

more informed person (the agent) tomake decisions that will directly affect theprincipals own well-being


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The Principal-Agent

Relationship Assume that we can show a graph of the

owners (or managers) preferences in

terms of profits and various benefits (suchas fancy offices or use of the corporate

jet)

The owners budget constraint will have aslope of -1 each $1 of benefits reduces profit by $1


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The Principal-Agent

Relationship

Benefits

Profits

Owners constraint

U1

b*

*

If the manager is also theowner of the firm, he willmaximize his utility at profits

of * and benefits ofb*


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The Principal-Agent

Relationship

Benefits

Profits

Owners constraint

U1

b*

*

The owner-manager maximizesprofit because any other owner-manager will also want b* inbenefits

b* represents a truecost of doing business


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The Principal-Agent

Relationship Suppose that the manager is not the

sole owner of the firm suppose there are two other owners who

play no role in operating the firm $1 in benefits only costs the manager

$0.33 in profits the other $0.67 is effectively paid by the

other owners in terms of reduced profits


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The Principal-Agent

Relationship The new budget constraint continues to

include the point b*, * the manager could still make the same

decision that a sole owner could) For benefits greater than b*, the slope

of the budget constraint is only -1/3


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The Principal-Agent

Relationship

Benefits

Profits

Owners constraint

U1

b*

*

U2

Given the managers budgetconstraint, he will maximizeutility at benefits ofb**

**

b*

*

Agents constraint

**

*

Profits for thefirm will be

***


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The Principal-Agent

Relationship The firms owners are harmed by having

to rely on an agency relationship with

the firms manager The smaller the fraction of the firm that

is owned by the manager, the greater

the distortions that will be induced bythis relationship


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Using the Corporate Jet

A firm owns a fleet of corporate jetsused mainly for business purposes

the firm has just fired a CEO for misusingthe corporate fleet The firm wants to structure a

management contract that provides

better incentives for cost control


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Suppose that all would-be applicantshave the same utility function

U(s,j) = 0.1s0.5 +j

where s is salary andjis jet use (0 or 1)

All applicants have job offers from other

firms promising them a utility level of at

most 2.0


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Because jet use is expensive, = 800(thousand) ifj=0 and = 162 if j=1

the directors will be willing to pay the newCEO up to 638 providing that they canguarantee that he will not use the corporatejet for personal use

a salary of more than 400 will just besufficient to get a potential candidate toaccept the job without jet usage


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If the directors find it difficult to monitorthe CEOs jet usage, this could mean

that the firm ends up with < 0 The owners may therefore want to

create a contract where thecompensation of the new CEO is tied toprofit


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The Owner-Manager

Relationship Suppose that the gross profits of the firm

depend on some specific action that a

hired manager might take (a)net profits = = (a) s[ ( a)]

Both gross and net profits are maximizedwhen / a = 0

the owners problem is to design a salarystructure that provides an incentive for themanager to choose a that maximizes


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The Owner-Manager

Relationship The owners face two issues

they must know the agents utility function

which depends on net income (IM)IM= s[ (a)] = c(a) = c0

where c(a) represents the cost to the manager ofundertaking a

they must design the compensation systemso that the agent is willing to take the job

this requires that IM 0


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The Owner-Manager

Relationship One option would be to pay no

compensation unless the manager

chooses a* and to pay an amount equal toc(a*) + c0 ifa* is chosen Another possible scheme is s(a) = (a) f,

where f= ( a) c(a*) c0 with this compensation package, the

managers income is maximized by settings(a)/a = /a = 0


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The Owner-Manager

Relationship The manager will choose a* and receive

an income that just covers costs

IM= s(a*) c(a*) c0 = (a*) f c(a*) c0 = 0

This compensation plan makes the agent

the residual claimant to the firms profits


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Asymmetric Information Models of the principal-agent relationship

have introduced asymmetric informationinto this problem in two ways

it is assumed that a managers action is notdirectly observed and cannot be perfectlyinferred from the firms profits

referred to as hidden action

the agent-managers objective function is notdirectly observed

referred to as hidden information


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Hidden Action The primary reason that the managers

action may be hidden is that profitsdepend on random factors that cannot be

observed by the firms owner Suppose that profits depend on both the

managers action and on a random

variable (u)(a) = ( a) + u

where represents expected profits


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Hidden Action Because owners observe only and not

, they can only use actual profits intheir compensation function

a risk averse manager will be concerned thatactual profits will turn out badly and maydecline the job

The owner might need to design acompensation scheme that allows forprofit-sharing


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Hidden Information When the principal does not know the

incentive structure of the agent, theincentive scheme must be designed

using some initial assumptions about theagents motivation

will be adapted as new information becomes

available


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Important Points to Note:

Information is valuable because itpermits individuals to increase theexpected utility of their decisions

individuals might be willing to paysomething to acquire additionalinformation


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Information has a number of specialproperties that suggest thatinefficiencies associated withimperfect and asymmetric informationmay be quite prevalent

differing costs of acquisition

some aspects of a public good


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The presence of asymmetricinformation may affect a variety ofmarket outcomes, many of which areillustrated in the context of insurancetheory

insurers may have less information

about potential risks than do insurancepurchasers


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If insurers are unable to monitor thebehavior of insured individualsaccurately, moral hazard may arise

being insured will affect the willingness tomake precautionary expenditures

such behavioral effects can arise in any

contractual situation in which monitoringcosts are high


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Informational asymmetries can alsolead to adverse selection in insurancemarkets

the resulting equilibria may often beinefficient because low-risk individuals willbe worse off than in the full informationcase

market signaling may be able to reducethese inefficiencies


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Asymmetric information may alsocause some (principal) economicactors to hire others (agents) to makedecisions for them

providing the correct incentives to theagent is a difficult problem

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