lecture #8 · • hence, “too many” lemons crowd out the peaches from the market. •...

Lecture #8

Asymmetric information 1: adverse selection, signaling

Asymmetric informationAssumption so far: perfect informationNow: imperfect informationAsymmetric information: the situation when one of theparties to the transaction has more information thanthe other.Examples: the seller knows more about the good than the buyer, employees know more about their skills and talents than the

employers, the managers have more information about the production

costs, the firm’s competitive position in the market, andinvestment potential, than the owners

insurers lack significant information about the insured, whichis accessible to the latter.

Asymmetric information leads to erroneous market allocation!

• equilibrium may be not Pareto-optimal• equilibrium may not exist

• In what ways can asymmetric information affect the functioning of a market?

• Four applications will be considered:– adverse selection, – signaling,– moral hazard (increased exposure to risk

when insured),– incentivising.

Asymmetric Information in Markets

Adverse selection

On the seller’s part: crowding a better product outof the market by a worse one; hidden informationleads to insufficient supply of the high-qualityproduct.

On the buyer’s part: crowding better clients out byworse ones; increasing costs for the producerexclude better clients from the market.

Adverse Selection

• Consider a used car market.• Two types of cars: (low-quality) “lemons” and

(high-quality) “peaches”.

• Each lemon seller will accept $1,000.• Each lemon buyer is willing to pay at most $1,200.• Each peach seller will accept $2,000.• Each peach buyer is willing to pay at most $2,400.

Adverse Selection

• If every buyer can tell a peach from a lemon, then lemons sell for between $1,000 and $1,200, and peaches sell for between $2,000 and $2,400. → Gains-to-trade when buyers are well informed.

• But suppose no buyer can tell a peach from a lemon before buying.

• What is the most a buyer is willing to pay for any car?

Adverse Selection

• Let q be the fraction of peaches.• 1 – q is the fraction of lemons.• Expected value (EV) to a buyer of any car

is at most

• EV is the maximum price a buyer would be willing to pay for a car.

EV q q= − +$1200( ) $2400 .1

Adverse Selection

• Suppose $EV > $2000.• Every seller can negotiate a price between

$2000 and $EV (no matter if the car is a lemon or a peach).

• All sellers gain from being in the market.

Adverse Selection

• Suppose $EV < $2000.• A peach seller cannot negotiate a price

above $2000 and will exit the market.• So all buyers know that remaining

sellers own lemons only.• Then, buyers will be willing to pay at

most $1200 and only lemons are sold.

Adverse Selection

• Hence, “too many” lemons crowd out the peaches from the market.

• Gains-to-trade are reduced since no peaches are traded.

• The presence of the lemons inflicts an external cost on buyers and peach owners.

Adverse Selection• How many lemons can be in the market

without crowding out the peaches?• Buyers will pay $2000 for a car only if

q – the fraction of peaches• So if over one-third of all cars are

lemons, then only lemons are traded.

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2000$2400$)1(1200$

≥⇒

≥+−=

q

qqEV

Adverse Selection

• A pooling equilibrium – A market equilibrium in which both types of cars are traded and cannot be distinguished by the buyers.

• A separating equilibrium – A market equilibrium in which only one of the two types of cars is traded, or both are traded but can be distinguished by the buyers.

Adverse Selection• Low-quality products crowd high-quality

products out of the market.• The market fails to supply mutually

beneficial transactions.• Too many low-quality cars are sold in the

market and not enough high-quality ones.• Adverse selection may lead to a situation

when only low-quality cars are sold in the market.

Adverse Selection• In reality, differences in the cars’ quality may

not be that large.• Sellers may also lack complete information.• The car quality verification is possible to be

conducted by a buyer but is costly.• Even with a low price, the supply of high-quality

cars will not fall to zero.• However, compared with the complete

information case, many high-quality cars will not be sold.

Adverse Selection

• What if there is more than two types of cars in the market?

• Suppose that– car quality (= sellers’ value) is uniformly

distributed between $1000 and $2000,– any car that a seller values at $x is

valued by a buyer at $(x+300).• Which cars will be traded?

Adverse Selection

Sellers’ values1000 2000

Adverse Selection


The expected value of anycar to a buyer is

$1500 + $300 = $1800.

Sellers who value their cars at more than $1800 exit the market.

Adverse Selection


The distribution of valuesof cars remaining on offer

Adverse Selection


The expected value of anyremaining car to a buyer is

$1400 + $300 = $1700.

Now sellers who value their cars between $1700 and $1800 exit the market.

Adverse Selection

• Where does this unraveling of the market end?

• Let vH be the highest seller’s value of any car remaining in the market.

• The seller’s expected value of a car is12

1000 12

× + × vH.

Adverse Selection

• So a buyer will pay at most

• This must be the price which the seller of the highest value car remaining in the market will accept; that is,

12

1000 12

300× + × +vH .

12

1000 12

300× + × + =v vH H.≥

Adverse Selection

12

1000 12

300× + × + =v vH H

⇒ =vH $1600.

Adverse selection drives out all carsvalued by sellers at more than $1600.

Crowding out high-quality cars by low-quality ones.

≤

Adverse Selection with Quality Choice

• So far, we have had constant numbers of cars of each quality.

• Now consider a case when every seller can choose the quality (or value) of her product.

• Two umbrella types: high-quality and low-quality.

• Which type will be manufactured and sold?

• Buyers value a high-quality umbrella at $14 and a low-quality umbrella at $8.

• Before buying, no buyer can tell quality.• Marginal production cost of a high-quality

umbrella is $11.• Marginal production cost of a low-quality

umbrella is $10.


• Suppose every seller makes only high-quality umbrellas.

• Every buyer pays $14 and sellers’ profit per umbrella is $14 - $11 = $3.

• But then a seller can make low-quality umbrellas for which buyers still pay $14, so increasing profit to $14 - $10 = $4.

• There is no market equilibrium in which only high-quality umbrellas are traded.

• Is there a market equilibrium in which only low-quality umbrellas are traded?


• All sellers make only low-quality umbrellas.

• Buyers pay at most $8 for an umbrella, while marginal production cost is $10.

• There is no market equilibrium in which only low-quality umbrellas are traded.


• Now we know there is no market equilibrium in which only one type of umbrella is manufactured.

• Is there an equilibrium in which both types of umbrella are manufactured?


• A fraction q of sellers make high-quality umbrellas; 0 < q < 1.

• Buyers’ expected value of an umbrella isEV = 14q + 8(1 – q) = 8 + 6q.

• High-quality manufacturers must recover the manufacturing cost, so

EV = 8 + 6q ≥ 11 ⇒q ≥ 1/2.


• So at least half of the sellers must make high-quality umbrellas for there to be a pooling market equilibrium.

• But then a high-quality seller can switch to making low-quality and increase profit by $1 on each umbrella sold.

• Since all sellers reason this way, the fraction of high-quality sellers will shrink towards zero.

• Then, buyers will pay only $8.• So there is no equilibrium in which both umbrella

types are traded.


• The market has no equilibriumwith just one umbrella type traded,with both umbrella types traded.

• The only equilibrium is with zero production of the umbrellas.

• Adverse selection has destroyed the entire market!


Adverse SelectionOn a seller’s part: • crowding a better product out of the market

by a worse one,• hidden information leads to insufficient

supply of a high-quality product.

On a buyer’s part: • crowding better clients out by worse ones,• increasing costs for the producer exclude

better clients from the market.

Adverse selection – other examples• the baseball player market: players moving to a

new MLB team are injured more often

• mergers and acquisitions: the fact that we succeeded in acquiring a company is a bad signas regards its value. Asymmetric informationeliminates part of the benefits that could be gained from synergy.

Days on medical leaveFirst

contractNew

contractchange

in %All 4.73 12.55 165.4In the old team 4.76 9.68 103.4In the new team 4.67 17.23 268.9

Adverse selection – other examples• life and health insurance

– more willing to buy life and health insurance will be:• those whose health condition is bad,• those with unhealthy lifestyle• family members of those who suffer various health problems• ...

– verifying such suspicions is costly for the insurer• motor vehicle insurance

– buyers of insurance differ in:• intensity of use of their car, driving skills• manner of driving, care for the car• their car’s technical condition• ...

– many of these characteristics are not observable for the insurer but are known to the insured

Adverse selection – other examples

• loans– a significant component of the costs of credit is the

risk of default or delay in paying back the loan– such risk depends on individual characteristics– unreliable, dishonest persons, having difficulties in

sustaining employment etc. may be more willing to take loans

– again, premiums rise, more reliable clients drop out

How to counteract adverse selectionof clients/buyers?

• restrict voluntariness– mandatory insurance (role of the state, e.g. social

security)– selling group insurance to firms

• mitigate asymmetry of information– segregation into various risk groups (e.g. depending

on driver’s age, accident history, color of the car, etc.)– bonus-malus arrangements, credit history etc.

Avoiding adverse selection(the seller)

– reputation• rankings, information from others etc.

– standards• e.g. McDonald’s, Holiday Inn (“No Surprises”) etc.

– warranties• accepting complaints

– signalling quality• certificates, diplomas etc.

Signalling

• Question: How do potential employees convince employers about the quality of their services?– weak signalling: dress (used as easily by the

low-quality employees as by the high-quality ones)

– strong signalling: diploma (less effort required to obtain it by higher-quality employees, thank by the lower-quality ones)

Signalling

• assumption: 2 groups of employees:– group 1: low productivity

• APL = MPL = 1– group 2: high productivity

• APL = MPL = 2– groups 1 and 2 are of equal sizes

• APL for the joint group of employees = 1.5

Signalling

• purely competitive labor and product market– P = 10 000 Euro– employees hired based on 10-year contracts– group 1: TR = 100 000 Euro

• (1 x 10 000 x 10)– Group 2: TR = 200 000 Euro

• (2 x 10 000 x 10)

Signalling

• complete information– w = MRP– group 1: w = 10 000 Euro/year– group 2: w = 20 000 Euro/year

• asymmetric information – w = AP– group 1 & 2: w = 15 000 Euro/year– pooling equilibrium

Signalling

• Signalling – education level– y = number of years of university education– C = costs of education

• Fees, cost of books, effort, opportunity costs etc.– group 1 C1(y) = 40000y Euro – group 2 C2(y) = 20000y Euro

Signalling• costs of education are higher for the low-quality

employees– more effort, more expenses (e.g. private lessons,

fees for repeating the year)• decisions regarding remuneration (wage):

– y=y* signals that the employee belongs to group G2and obtains remuneration (wage) = 20 000 Euro

– y below y* signals that the employee belongs to group G1 and obtains remuneration (wage) = 10 000 Euro

• y* is an arbitrary level, however must be identifiable by employers

Signalling

• how many years of education will both groups of employees choose?

• goal: obtaining such education level which assures that benefits from it will be higher than costs of obtaining it

• For group 1 it does not pay to study for y* years, i.e. – 100 000 < 40 000y*, y* > 2.5

• group 2 does study:– 100 000 > 20 000y*, y* < 5

Signalling

• there is no reason to study less than y* years because remuneration (wage) will then be the same as in the case of no education

• Similarly, there are no incentives to obtain education higher than y* because this will not cause an increase in the remuneration (wage)

Signalling• the equilibrium will be found within the interval of

y* between 2.5 and 5• if y* = 4

– members of group 1, minimazing their costs, will not study

– for members of group 2 education will be remunerative up to 4 years of university studies y* = 4

• the employer will read the signals given by potential employees and employ them at adequate remuneration levels(separating equilibrium)

47

Signalling

Value of education

100K

Years of study

Years of study

0 1 2 3 4 5 6 0 1 2 3 4 5 6

200K

100K

200KC1(y) = 40 000y

B(y) B(y)

y* y*

C2(y) = 20 000y

optimal choice of ygroup 2

Group 2Group 1

optimal choice of ygroup 1

Value of education

Other examples of signalling

• piles of books are a signal of quality

• because printing something of low quality in such large quantity could result in bankrupcy

• similarly: expenses on advertisement, marketing campaigns etc.

Signalling – summary

• education pays off even if everything that we/you learn during our/your studies is useless for our/your work

• the university diploma is a signal of talent and willingness to work hard

• vide: demand for physicists• in order to work, the signal must:

– be relatively costly for the ‟low quality” group– be understandable for both sides of the market

lecture #8 · • hence, “too many” lemons crowd out the peaches from the market. •...

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