Lecture 6 Asymmetric Information 1

Asymmetric information 1Lecture 6 – Tom Holden

Intermediate Microeconomics Semester 2

http://micro2.tholden.org/

ECO2051 – Intermediate Microeconomics

http://micro2.tholden.org/

Introduction

• Asymmetric information (AI) occurs in interactions between two or more parties, when one knows more than the other.• E.g. buyers and sellers, or “principals” and “agents”.

• One party knows more than the other.

• Two main types of AI:• Hidden characteristics:

• E.g. What type of good are you buying? What type of person are you?

• Leads to “adverse selection” problems.

• Hidden actions:• If I cannot commit not to “cheat” in some way, you will assume I am cheating.

• Leads to “moral hazard” problems.


Examples of AI

• The seller knows the quality of a good, the buyer does not.

• The employee knows their productivity the worker does not.

• The insured knows how likely they are to claim, the insurer does not.

• The potential buyer knows their willingness to pay, the seller does not.

• Etc.


Reading

• Varian, Chapter 37

• MKR, Chapter 17 (second half)

• Additional reading for adverse selection in insurance markets (if desired):

• Frank Cowell, “Microeconomics: Principles and Analysis”• Chapter 11, especially 11.2.6

• Hugh Gravelle & Ray Rees, “Microeconomics”• Chapter 19, especially sub-section F


Aims for this topic

• Today: • To understand adverse selection.

• In product markets.• In insurance markets.

• To see how signalling may solve adverse selection.• Example of education.

• In a fortnight: • Moral Hazard.

• Principal-agent models.

• Note: This topic will not be on next week’s test.


Adverse selection: “Lemons” (1/5)

• The classic “lemons” example, due to Akerlof.

• Two types of used car:• plums (good)

• lemons (bad)

• Buyers can’t tell the difference between plums and lemons, but sellers know what they’re selling.



• Owner of a lemon willing to sell for $1000. Buyer willing to pay $1200.

• Owner of a plum willing to sell for $2000. Buyer willing to pay $2400.

• If a buyer can’t tell the difference between a plum and a lemon, and they think it’s equally likely that it could be either, then their expected value of the car is $1800. • It’s not worth it for a plum owner to sell.• Putting car up for sale signals that it’s a lemon. • If there are no plums then the buyer won’t be willing to offer $1800.

• Only market for lemons will operate and price paid will be between $1000 and $1200.



• Suppose buyers value plums at 𝑟𝑃 and lemons at 𝑟𝐿, with 𝑟𝑃 > 𝑟𝐿.

• Suppose sellers value plums at 𝑣𝑃 and lemons at 𝑣𝐿, with 𝑣𝑃 > 𝑣𝐿and 𝑟𝑃 > 𝑣𝑃 & 𝑟𝐿 > 𝑣𝐿.

• Suppose a fraction 𝑞∗ of cars that sellers would like to sell are plums.

• And suppose a fraction 𝑞 of all cars actually being sold are plums.

• So for a buyer, the expected value of a car is: 𝑞𝑟𝑃 + 1 − 𝑞 𝑟𝐿.

• So the price of a car must be less than 𝑞𝑟𝑃 + 1 − 𝑞 𝑟𝐿.



• Three cases:

• 𝑟𝐿 ≥ 𝑣𝑃, so 𝑞𝑟𝑃 + 1 − 𝑞 𝑟𝐿 ≥ 𝑣𝑃 for any 𝑞:• Then 𝑞 = 𝑞∗ and a price between 𝑣𝑃 and 𝑞∗𝑟𝑃 + 1 − 𝑞∗ 𝑟𝐿 is chosen, and both lemons

and plums are sold.

• Price under perfect competition? Consumer surplus?

• 𝑟𝐿 < 𝑣𝑃 and 𝑞∗ satisfies 𝑞∗𝑟𝑃 + 1 − 𝑞∗ 𝑟𝐿 ≥ 𝑣𝑃:• Again a price between 𝑣𝑃 and 𝑞∗𝑟𝑃 + 1 − 𝑞∗ 𝑟𝐿 is chosen, and both lemons and plums

are sold.

• Lowest possible 𝑞∗? Other equilibria?

• 𝑟𝐿 < 𝑣𝑃 and 𝑞∗ satisfies 𝑞∗𝑟𝑃 + 1 − 𝑞∗ 𝑟𝐿 < 𝑣𝑃:• Then if both lemons and plums were sold, sellers of plums would make a loss.

• Thus only lemons are sold, 𝑞 = 0 and the price is between 𝑣𝐿 and 𝑟𝐿.



• Extra condition for both lemons and plums to be sold:

• Suppose currently both plums and lemons were sold at a price 𝑣𝑃.

• A seller of a lemon might be tempted to offer a price of 𝑝 < 𝑣𝑃.

• A consumer would accept this if 𝑟𝐿 − 𝑝 ≥ 𝑟𝑃 − 𝑣𝑃.• The lower 𝑝 is, the more tempting this looks.

• The seller would never go below 𝑣𝐿, thus to rule out any lemon sellers undercutting the market, we must have: 𝑟𝐿 − 𝑣𝐿 < 𝑟𝑃 − 𝑣𝑃, i.e. 𝑣𝑃 − 𝑣𝐿 <𝑟𝑃 − 𝑟𝐿.

• Otherwise only lemons will be sold.


Quality choice (1/2)

• Suppose plums can be created (by sellers) for 𝑐𝑃 and lemons can be created for 𝑐𝐿, where 𝑐𝑃 ≥ 𝑐𝐿.

• Again assume 𝑟𝑃 > 𝑐𝑃 and 𝑟𝐿 > 𝑐𝐿.

• If 𝑐𝑃 = 𝑐𝐿, then firms are indifferent between producing the two cars, as long as there is a market for each.

• Suppose 𝑞∗ plums are produced.• There is an equilibrium for any 𝑞∗ satisfying:

•𝑐𝑃−𝑟𝐿

𝑟𝑃−𝑟𝐿≤ 𝑞∗ ≤ 1

• Are there any other equilibria?


Quality choice (2/2)

• Now suppose 𝑐𝑃 > 𝑐𝐿.

• Would sellers ever produce a plum?


Solutions to adverse selection

• Government quality certification?

• Reputation• Can only operate where there are positive economic profits to be earned.

• Compulsory sale/purchase.• E.g. mandatory health insurance purchase.

• Signalling.• E.g. warranties.


Adverse selection in insurance markets (1/5)

• High risk (𝐻) and low risk (𝐿) agents.

• Each can be in two states, 𝐺 for good and 𝐵 for bad.

• 𝑝𝐻 and 𝑝𝐿 are the probabilities of the bad state for high risk and low risk types respectively (so 𝑝𝐻 > 𝑝𝐿).

• Income in the good state is 𝑦𝐺 for both types, and its 𝑦𝐵 in the bad state for both types.

• Insurance sellers cannot tell they types apart and offer a premium of 𝜋 to both.



• Assuming both types have the same preferences, from our uncertainty lecture we have:

•𝑢′ 𝑦𝐵−𝜋𝑥𝐻+𝑥𝐻

𝑢′ 𝑦𝐺−𝜋𝑥𝐻=

𝜋 1−𝑝𝐻

𝑝𝐻 1−𝜋where 𝑥𝐻 is the amount of insurance purchased by

high risk types.

• And: 𝑢′ 𝑦𝐵−𝜋𝑥𝐿+𝑥𝐿

𝑢′ 𝑦𝐺−𝜋𝑥𝐿=

𝜋 1−𝑝𝐿

𝑝𝐿 1−𝜋where 𝑥𝐿 is the amount of insurance purchased

by low risk types.

• Thus: 𝑝𝐻𝑢

′ 𝑦𝐵−𝜋𝑥𝐻+𝑥𝐻

1−𝑝𝐻 𝑢′ 𝑦𝐺−𝜋𝑥𝐻=

𝑝𝐿𝑢′ 𝑦𝐵−𝜋𝑥𝐿+𝑥𝐿

1−𝑝𝐿 𝑢′ 𝑦𝐺−𝜋𝑥𝐿=

𝜋

1−𝜋.



• 𝑝𝐻 > 𝑝𝐿, so 𝑝𝐻

1−𝑝𝐻>

𝑝𝐿

1−𝑝𝐿, so:

•𝑢′ 𝑦𝐵−𝜋𝑥𝐻+𝑥𝐻

𝑢′ 𝑦𝐺−𝜋𝑥𝐻<

𝑢′ 𝑦𝐵−𝜋𝑥𝐿+𝑥𝐿

𝑢′ 𝑦𝐺−𝜋𝑥𝐿

• This in turn implies that 𝑥𝐻 > 𝑥𝐿 (i.e. high risk types insure more), as the fact that marginal utility is decreasing in consumption means:

•ⅆ

ⅆ𝑥

𝑢′ 𝑦𝐵−𝜋𝑥+𝑥

𝑢′ 𝑦𝐺−𝜋𝑥=

ⅆ

ⅆ𝑥

𝑢′ 𝑦𝐵+ 1−𝜋 𝑥

𝑢′ 𝑦𝐺−𝜋𝑥< 0



• We started this analysis by saying that the insurance company could not tell the two types apart.• But we have just proven that high risk types demand more insurance.

• Adverse selection!

• So in fact the insurance company can tell the types apart from their insurance demands, so will want to offer a higher premium to the high risk types.• E.g. the insurance company might choose to make their premium an

increasing function of the amount insured.

• Has to ensure that the high risk types do not benefit from pretending to be low risk and taking a lower amount of cheaper insurance.



• Suppose making the premium a function of the amount demanded is not feasible.• Let the fraction of high risk in the population be 𝑞.

• Expected insurer profit is: 𝑞 𝜋 − 𝑝𝐻 𝑥𝐻 + 1 − 𝑞 𝜋 − 𝑝𝐿 𝑥𝐿• The actuarially fair premium is equal to the probability of the bad state in the

whole population, i.e. 𝑞𝑝𝐻 + 1 − 𝑞 𝑝𝐿.

• If insurers set 𝜋 to this level then profits are:𝑞 𝑞𝑝𝐻 + 1 − 𝑞 𝑝𝐿 − 𝑝𝐻 𝑥𝐻 + 1 − 𝑞 𝑞𝑝𝐻 + 1 − 𝑞 𝑝𝐿 − 𝑝𝐿 𝑥𝐿= 𝑞 1 − 𝑞 𝑝𝐿 − 𝑝𝐻 𝑥𝐻 + 1 − 𝑞 𝑞 𝑝𝐻 − 𝑝𝐿 𝑥𝐿= 𝑞 1 − 𝑞 𝑝𝐻 − 𝑝𝐿 𝑥𝐿 − 𝑥𝐻 < 0• So in the face of adverse selection, insurers will price above the actuarially

fair level, causing inefficiency.

• In fact the more they charge, the bigger the gap between 𝑥𝐻 and 𝑥𝐿, so the more they want to charge. May lead to 𝑥𝐿 = 0.


Compulsory purchase

• Suppose all agents were forced to buy 𝑥∗ units of insurance.• E.g. in the UK we are all forced to buy the same amount of health insurance

through taxes.• In the US many jobs come with health insurance bundled in.

• Then the expression for profits with the actuarially fair premium from the last slides would be: 𝑞 1 − 𝑞 𝑝𝐻 − 𝑝𝐿 𝑥∗ − 𝑥∗ = 0

• So with free entry of insurers, premiums would be set to the actuarially fair level.

• This may leave both high and low risk types better off, since they will both now face lower premiums (though the low risk type will not be as well off as if types were observable).


Signalling and screening

• Signalling occurs when the informed side of the market chooses to reveal something about their hidden characteristics.• In our lemons model, sellers of plums might like to offer warranties.• This would be too expensive for lemon sellers.

• In order to contain information, signals must be “incentive compatible”: agents must have no incentive to send the signal normally sent by a different type.

• The uninformed side of the market uses the signal to ‘screen’ for the type of characteristics they want.

• Another way of thinking of this is that the informed side of the market ‘self-selects.’


Signalling and price discrimination

• Two types of train travellers from Portsmouth to London.• Business travellers are willing to pay £60, pleasure travellers are willing to

pay £20.

• Business travellers prefer to be in London by 9.30.

• Pleasure travellers are willing to travel later therefore they will buy an off peak ticket if it’s cheaper.

• If the price is over £20, pleasure travellers would not travel.• This is a loss of welfare on both sides as marginal cost of an extra passenger

(especially later in the day) is very low.

• If price is set at £20 or below firm wouldn’t be extracting maximum profit from business travellers.


Price discrimination requires:

• That the firm has some monopoly power.

• That the firm can identify different types of consumer.

• That consumers cannot engage in arbitrage.

• In this example the consumers are willingly revealing their types to the firm.

• They signal their types by the type of ticket they buy (provided this is incentive compatible).• If business prices get too high the business traveller will start to behave like a

pleasure traveller.


Signalling and education

• A firm wishes to hire workers.

• If productivity is observable then each worker is paid a wage equal to their marginal product.

• Imagine productivity is not observable and there are two types of workers, high ability and low ability.

• In this case the firm can only pay workers according to their expected productivity.

• High productivity workers would clearly prefer to differentiate themselves if possible.

• If education is cheaper for them, then by obtaining education they can mark themselves as high ability.• Plausible that high ability types find the work easier.• High ability types may have higher opportunity costs though.


Diagrammatic analysis of education as a signal

No university degree University degree

Taking education has a disutility.Therefore individuals are happier with no university degree and moremoney

earnings

Years of education

Indifference curves are different for workers of different abilities

No university degree University degree

Low ability person finds education harder, so they’re willing to trade more money for less ed. IC is therefore steeper.earnings

Years of education

low abilityhigh ability

Education signalling (1/4)

• Let 𝑎𝐻 be the productivity of the able type and 𝑎𝐿 be the productivity of the less able one. (𝑎𝐻 > 𝑎𝐿).

• Suppose there are 𝑞 able types in total, so in the absence of signalling the wage is given by 𝑞𝑎𝐻 + 1 − 𝑞 𝑎𝐿.

• Suppose the able type can acquire education at a cost of 𝑐𝐻 and the less able type can acquire it at a cost 𝑐𝐿, with 𝑐𝐻 < 𝑐𝐿.



• Suppose no one acquires any education.

• Does anyone have any incentive to deviate to acquiring some?• Imagine for the moment that a firm promised a wage of 𝑎𝐻 to anyone acquiring

at least 𝑒⋄ units of education.• Acquiring this education would make sense for a low type if𝑞𝑎𝐻 + 1 − 𝑞 𝑎𝐿 ≤ 𝑎𝐻 − 𝑐𝐿𝑒

⋄, i.e. if 𝑐𝐿𝑒⋄ ≤ 1 − 𝑞 𝑎𝐻 − 𝑎𝐿 .

• Thus for the firm’s offer to be sensible, it must be the case that

𝑒⋄ >1

𝑐𝐿1 − 𝑞 𝑎𝐻 − 𝑎𝐿 .

• Anyone acquiring more than 1

𝑐𝐿1 − 𝑞 𝑎𝐻 − 𝑎𝐿 units of education in this

situation would be unambiguously a high type, so in a competitive market they would be paid 𝑎𝐻.

• But as 𝑐𝐻 < 𝑐𝐿 high type people would strictly prefer this.

• Thus, no one acquiring any education is not an equilibrium. There is no “pooling” equilibria.



• Suppose instead that high types acquire 𝑒∗ units of education, and low types acquire none.

• Then high types will be paid 𝑎𝐻 and low types will be paid 𝑎𝐿.

• For a high type not to want to pretend to be a low type it must be the case that: 𝑎𝐻 − 𝑐𝐻𝑒

∗ > 𝑎𝐿, i.e. 𝑒∗ <𝑎𝐻−𝑎𝐿

𝑐𝐻.

• For a low type not to want to pretend to be a high type it must be the case that: 𝑎𝐿 > 𝑎𝐻 − 𝑐𝐿𝑒

∗. i.e. 𝑒∗ >𝑎𝐻−𝑎𝐿

𝑐𝐿.

• Since 𝑐𝐻 < 𝑐𝐿 these inequalities may be satisfied simultaneously, so there is a “separating” equilibria in which different types acquire different education levels.



• The separating equilibria is inefficient since education is pure waste in this model.• The same output would be produced had no one acquired any education.

• Income is trivially lower for low types.

• For high types, income is 𝑎𝐻 − 𝑐𝐻𝑒∗ < 𝑎𝐻 −

𝑐𝐻

𝑐𝐿𝑎𝐻 − 𝑎𝐿 = 1 −

𝑐𝐻

𝑐𝐿𝑎𝐻 +

𝑐𝐻

𝑐𝐿𝑎𝐿, so if 1 −

𝑐𝐻

𝑐𝐿< 𝑞, income is lower for high types too.

• If instead we had assumed that 𝑐𝐻 > 𝑐𝐿 (high types find education more costly, perhaps due to better outside options), then we would have found the pooling equilibria existed, but the separating did not.• So e.g. a high graduate tax may actually reduce inefficiency.


Education and adverse selection (1/3)

• In the last model education signalling was unambiguously bad when high types find education easier than low types.

• But in the presence of adverse selection it may be welfare improving.

• Suppose that all agents value not being employed at 𝑣 times their productivity (where 0 < 𝑣 ≤ 1).

• This may be the value of watching TV, or the value of the goods you could produce yourself without being employed.



• In the absence of signalling, with everyone working at firms, the wage would be 𝑞𝑎𝐻 + 1 − 𝑞 𝑎𝐿 as before.

• But suppose 𝑣 > 𝑞 + 1 − 𝑞𝑎𝐿

𝑎𝐻.

• Then high types prefer staying at home to earning a wage of 𝑞𝑎𝐻 +1 − 𝑞 𝑎𝐿 in a firm.

• Thus without signalling, only low types work in firms, for a wage of 𝑎𝐿.



• The deadweight loss (DWL) due to adverse selection is 1 − 𝑣 𝑎𝐻.

• When 𝑣 ≈ 𝑞 + 1 − 𝑞𝑎𝐿

𝑎𝐻, the DWL is roughly 1 − 𝑞 𝑎𝐻 − 𝑎𝐿 .

• The DWL due to signalling is 𝑒∗𝑐𝐻.

• With 𝑒∗ ≈𝑎𝐻−𝑎𝐿

𝑐𝐿this DWL is roughly

𝑐𝐻

𝑐𝐿𝑎𝐻 − 𝑎𝐿 .

• So when 𝑐𝐻

𝑐𝐿< 1 − 𝑞, signalling may be welfare improving under

adverse selection.


The meaning of inefficiency in an AI context

• It’s not a lack of information that causes problems in the circumstances we have identified; it’s the presence of asymmetric information.

• If neither party knew which cars were lemons, then the market could operate.

• This is the appropriate comparison, not one with full information.

• Signalling improves efficiency because it makes the best use of the information available.

• Outcomes which do not do this are inefficient.


Evaluating the signalling hypothesis

• The human capital model states that education actually improves productivity.

• Both models predict that:• Those with higher education will earn more.• Those with more education are more productive.• Education will be obtained early in life.

• Is the expensiveness of the education system an argument against the signalling view? Could the market provide a cheaper signal?

• Robin Hanson: “People in business signal to each other all the time. In fact, most of the on-the-job business learning that employees do after college, such as how to dress well, how to give presentations, how to write memos, how to talk with clients, etc. might be skills that are mainly useful to signal innate features to bosses, co-workers, clients, etc. So employers might pay more for students with prestigious degrees because such degrees show an ability to learn how to later send good business signals.” http://is.gd/zxjdw2• Education as “Learning to signal” makes it even harder to distinguish the signalling

and the human capital views.

• Distinguishing between the two theories is crucial for policy though.


http://is.gd/zxjdw2

Tests of signalling / human capital

• Signalling model assumes employers do not have full information, education likely to be less important when they have the opportunity to learn about productivity.• Importance of education may go down over time.

• Signalling model likely to be associated with ‘sheepskin’ effects, which put a value on accreditation.• Evidence in Varian suggests those years of education which lead to a

certificate have a bigger impact on your wage.

• Manoli (2008) http://is.gd/ohVCvb suggests signalling accounts for up to 40% of the educational wage premium.• Learning to signal better may account for the rest…


http://is.gd/ohVCvb

In the next topic

• We’ll discuss moral hazard, with a focus on insurance markets.

• We’ll also use this framework to compare healthcare systems between the UK and the US.

• And we’ll introduce the principal-agent problem, another way of thinking about and solving moral hazard problems.


Lecture 6 Asymmetric Information 1

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