Economics 202: Intermediate Microeconomic Theory

1. Welcome back

Asymmetric Information• Transactions can involve a considerable amount of

uncertainty– can lead to inefficiency when one side has better information

• The side with better information is said to have private information or asymmetric information

The Value of Contracts• Contractual provisions can be added in order to circumvent

some of the inefficiencies associated with asymmetric information– rarely do they eliminate them

Principal-Agent Model• The party who proposes the contract is called the principal• The party who decides whether or not to accept the

contract and then performs under the terms of the contract is the agent– typically the party with asymmetric information

Leading Models• Two models of asymmetric information

– the agent’s actions affect the principal, but the principal does not observe the actions directly

• called a hidden-action model or a moral hazard model– the agent has private information before signing the contract (his

type)• called a hidden-type model or an adverse selection model

First, Second, and Third Best• In a full-information environment, the principal could

propose a contract that maximizes joint surplus– could capture all of the surplus for himself, leaving the agent just

enough to make him indifferent between agreeing to the contract or not

• This is called a first-best contract

First, Second, and Third Best• The contract that maximizes the principal’s surplus subject

to the constraint that he is less well informed than the agent is called a second-best contract

• Adding further constraints leads to the third best, fourth best, etc.

Hidden Actions• The principal would like the agent to take an action that

maximizes their joint surplus• But, the agent’s actions may be unobservable to the

principal– the agent will prefer to shirk

• Contracts can mitigate shirking by tying compensation to observable outcomes

Hidden Actions• Often, the principal is more concerned with outcomes than

actions anyway– may as well condition the contract on outcomes

• Agent cannot completely control the outcome! – tying the agent’s compensation to outcomes exposes the agent to

risk– if the agent is risk averse, he may require the payment of a risk

premium before he will accept the contract

Owner-Manager Relationship• Suppose a firm has one representative owner and one

manager– the owner offers a contract to the manager– the manager decides whether to accept the contract and what

action e 0 to take• an increase in e increases the firm’s gross profit but is

personally costly to the manager

Economic Model• The firm’s gross profit is

g = e + – where represents demand, cost, and other economic factors

outside of the agent’s control• assume ~ (0,2)

– c(e) is the manager’s personal disutility from effort• assume c’(e) > 0 and c’’(e) > 0

Owner-Manager Relationship• If s is the manager’s salary, the firm’s net profit is

n = g – s

• The risk-neutral owner wishes to maximize the expected value of profit

E(n) = E(e + – s) = e – E(s)

Owner-Manager Relationship• We will assume the manager is risk averse with a constant

risk aversion parameter of A > 0• The manager’s expected utility will be

€

E[U] = E(s) − A2

Var (s) − c(e)

First-Best• With full information, it is relatively easy to design an

optimal salary contract– the owner can pay the manager a salary if he exerts a first-best

level of effort and nothing otherwise– for the manager to accept the contract (participation constraint)

– E(u) = s* - 0 - c(e*) 0

– Zero is the value of the next-best job offer, for simplicity

First-Best• The owner will pay the lowest salary possible [s* = c(e*)]• The owner’s net profit will be

E(n) = e* - E(s*) = e* - c(e*)

– FOC ? 1 - c’(e*) = 0 or equivalently, 1 = c’(e*)

– at the optimum, the marginal benefit equals the marginal cost of effort

Second Best• If the owner cannot observe effort, the contract cannot be

conditioned on e– the owner may still induce effort if some of the manager’s salary

depends on gross profit– suppose the owner offers a salary such as

s(g) = a + bg

– a is the fixed salary and b is the power of the incentive scheme

Second Best• This relationship can be viewed as a three-stage game

– owner sets the salary (choosing a and b)– the manager decides whether or not to accept the contract– the manager decides how much effort to put forth (conditional on

accepting the contract)

• Use backward induction

Second Best• Because the owner cannot observe e directly and the

manager is risk-averse, the second-best effort will be less than the first-best effort– the risk premium adds to the owner’s cost of inducing effort

• Stage 3’s (how much effort to give) first-order condition?

€

E[U] = E(s) − A2

Var (s) − c(e)

€

E[U] = a + be − A2

b2σ 2 − c(e)

Second Best• Result: Manager’s effort responds to increased incentives

– Graph of c’(e) vs. e

• Stage 2: Participation constraint

€

′ c (e) = b

€

E[U] = a + be − A2

b2σ 2 − c(e) ≥ 0

a ≥ c(e) + A2

b2σ 2 − be

€

s(π g ) = a + bπ g

Second Best• Stage 1: Owner chooses a and b

– Owner maximizes her expected surplus, subject to the participation constraint and the incentive compatibility constraint

– Participation

– Incentive compatibility constraint• Manager chooses e to suit himself rather than the owner, who

can’t observe e

• Rewrite surplus as

€

a = c(e) + A2

b2σ 2 − be

€

s(π g ) = a + bπ g

€

owner surplus = e − a − be

€

owner surplus = e − c(e) − Aσ 2[ ′ c (e)]2

2

Second Best• What is optimal e**? Optimal second-best effort.

• Second-best effort < 1 and so less than first-best effort e*=1. Asymmetric information leads to lower equilibrium effort.

• Second-best contract trades off incentive vs. insurance: the owner’s desire to induce high effort (b near 1) against need to insure risk-averse manager against salary variation (b near 0).

First- versus Second-Best Effort

ee**

MB1

e*

MC in first bestc’(e)

The owner’s MC is higher in the second best, leading to lower effort by the manager

MC in second bestc’(e) + risk term

Moral Hazard in Insurance• If a person is fully insured, he will have a reduced

incentive to undertake precautions– may increase the likelihood of a loss occurring

• The effect of insurance coverage on an individual’s precautions, which may change the likelihood or size of losses, is known as moral hazard

Is Education a Good Social Investment?• Empirical studies seem to indicate education is a good individual investment• Is education primarily a signaling device in the labor market?

• What if the informed player moves first? Unlike the uninformed principal, we were just discussing, who made an offer to the agent who had private info.

Is Education a Good Social Investment?• Example: If you have BA, you can earn $1,600,000 (over lifetime in PV).If not, you get $800,000. Clow-prod = 225,000(E-12) Chigh-prod = 50,000(E-12)

Low-prod worker: (16-9) < (8-0) no college High-prod worker: go to collegeFor a BA to be effective signal, cost of acquiring signal must be strongly & inversely

related to worker’s job productivity (psychic costs/innate ability)• If education doesn’t improve one’s skills, but only helps firms identify those with

the highest innate ability, higher education may be socially unnecessary!

PV ($100K)16

12

Education (years)12 16 200

8

4

Clow-prod

Chigh-prod