1. Asymmetric Information
Chapter 37
Asymmetric Information

2. Information in Competitive Markets
In order for a market to be purely competitive all agents must be fully informed about traded commodities and other aspects of the market – about quality, prices, availability.
What about markets for medical care, or services like those of a plumber or carpenter, or insurance, or used cars?

3. Asymmetric Information in Markets
A market where buyers or sellers are imperfectly informed is a market with imperfect information.
A market with imperfect information where one side is better informed than the other is a market with asymmetric information.
A doctor knows more about illnesses and medical treatment than does the buyer.
An insurance buyer knows more about his life-style and the risks connected with it than does the seller.
Someone who sells ”Swiss watches” on the internet knows where they are made better than the buyer.

4. In what ways can asymmetric information affect the functioning of a market?
Asymmetric information is a big topic – we will look at four aspects:
adverse selection
signaling
moral hazard
incentives contracting.

5. 1. Adverse Selection Consider a used car market.
Two types of cars; “lemons” and “plums”.
Each lemon seller will accept $1,000; a buyer will pay at most $1,200.
Each plum seller will accept $2,000; a buyer will pay at most $2,400.
If every buyer can tell a plum from a lemon, then lemons sell for between $1,000 and $1,200, and plums sell for between $2,000 and $2,400.

6. Suppose no buyer can tell a plum from a lemon before buying:
What is the most a buyer will pay for any car?
Let q be the fraction of plums.
1 - q is the fraction of lemons.
Expected value to a buyer of any car is at most

7. If E[V] > $2000.
Every seller can negotiate a price between $2000 and E[V] (no matter if the car is a lemon or a plum).
All sellers gain from being in the market.
if E[V] < $2000.
A plum seller cannot get a price above $2000 and will exit the market so all buyers know that remaining sellers own lemons only.
Buyers will pay at most $1200 and only lemons are sold.

8. Hence “too many” lemons “crowd out” the plums from the market.
Gains-to-trade are reduced since no plums are traded.
The presence of the lemons inflicts an external cost on buyers and potential plum owners.
What is ”too many”?
Plum sellers will sell only if the price  $2000.
Plum buyers will buy only if the price ≤ E[V].
Deals are possible only if
E[V] = 1200(1-q)+2400q  2000
q = 2/3

9. What if there is more than two types of cars?
Suppose that
car quality 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?

10. 1000
1500
2000
Seller values

11. So sellers who value their cars at more than $1800 exit the market.
The expected value of any
car to a buyer is
$ $300 = $1800.
1000
1500
2000
Seller values
So sellers who value their cars at
more than $1800 exit the market.

12. The cars that remain on the market
1000
1400
1800
Seller values

13. So now sellers who value their cars
The expected value of any
remaining car to a buyer is
$ $300 = $1700.
1000
1400
1800
Seller values
So now sellers who value their cars
between $1700 and $1800 exit the market.

14. Where does this end? Will NO cars be sold at all?
Let vH be the highest seller value of any car remaining in the market.
The expected seller value of a car is
½*1000+½*vH
So a buyer will pay at most
½*1000+½*vH+300 = ½vH
No more cars will leave the market if and only if
800 + ½vH = vH
vH = 1600

15. Adverse Selection with Quality Choice
There are two kinds of umbrellas; high-quality and low-quality.
The seller can choose which kind to produce.
But the buyer won’t know the quality until after they have bought and used the umbrella.
Which will be manufactured and sold?
MC for producer
Buyers
value at
High quality 11 14
Low quality 10 8

16. If 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.

17. 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.

18. 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 is
E[V] = 14q + 8(1 - q) = 8 + 6q.
High-quality manufacturers must recover the manufacturing cost
E[V] = 8 + 6q ³ 11 Þ q ³ 1/2.

19. 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 they will all start making low-quality umbrellas -- but then buyers will pay only $8.
So there is no equilibrium in which both umbrella types are traded either.

20. Signaling
Adverse selection happens because buyers can’t tell the quality of the goods.
What if information can be improved by high-quality sellers signaling credibly that they are high-quality?
E.g. warranties, professional credentials, references from previous clients, certification, membership of professional or branch organisations etc.
In many cases it is most efficient if the signaling is done by an independent, public body. (For example, licence to practise medicine, food standards, safety of electrical equipment).

21. Assume that a labour market has two types of workers; high-ability and low-ability.
A high-ability worker’s marginal product is aH.
A low-ability worker’s marginal product is aL.
aL < aH.
Employers would be willing to employ high-ability workers in more highly paid jobs than low ability workers – if they can tell which is which.
Could they use education as a criterion?

22. Monthly wages by education and gender Sweden 2006 (1000s SEK)
Source: Statistics Sweden 22

23. Why do wages increase with education?
The usual answer from economists is ”human capital”:
Supply of labour:
Getting an education is an investment – the seller of labour power won’t do it without compensation.
Demand for labour:
Education gives skills that make the worker more productive – the employer is willing to pay more.

24. Demand for education:
Each person maximises the present value of life-time utility.
If, for simplicity, we equate this with maximising the present value of life-time income:
PV of [addition to wages due to education minus (direct costs of education + opportunity cost of education)]

25. Age-income profiles with secondary and tertiary education for a given individual25

26. “Signalling”, education and productivity
DOES education increase productivity?
Some economists advance signalling as an alternative theory. They say:
“Education doesn’t change productivity but more productive individuals acquire education to show potential employers that they are very productive.” 26

27. There are two types of workers
Assume:
There are two types of workers
A-workers add /year to production
B-workers
The employer has to pay an A-worker
The employer does not want to pay a B-worker
Both A- and B-workers will claim that they are A-workers when they are interviewed.
What should the employer do to “get the right worker in the right job”? (Avoid mismatches.)
Education can “signal” that a person is a high-productivity worker if the cost of acquiring education is lower for a high-productivity worker than for a low-productivity worker. 27

28. Assume that there is a correlation between productivity in studies and productivity at work.
As an example, assume that the PV of life-time difference in productivity at work between A- and B-workers is 1.5 million SEK.
Assume that the marginal (opportunity) cost of acquiring one HP (point) at university is for B-workers and for A-workers. 28

29. If the employer requires 180 HP to hire somebody in a “type A-job”:
A-workers: 180*7=1260<1500
B-workers: 180*8=1440<1500
If the employer requires 210 HP:
A-workers: 210*7=1470<1500
B-workers: 210*8=1680>1500

30. Is this the right cut-off point?
Requiring 150 HP for a high-wage job does not separate A- workers from B-workers but requiring 210 HP does. With this threshold there will be no mismatches.
Is this the right cut-off point?
The cut-off must not be more than 1.5 m/7000214,
otherwise A-workers will not acquire the required schooling.
The threshold must not be less than 1.5 m/8000188,
otherwise B-workers will acquire the signal for high-productivity jobs too. 30

31. Generally:
Type 1 workers have a PV of life productivity of PV1 and a cost of acquiring one year of education of C1
Type 2 workers have a PV of life prodictivity of PV2 and a cost of acquiring one year of education of C2
To get only type 1 workers to apply for ”Type 1”-jobs the employer should require a length of schooling of y years where 31

32. Human capital or signalling – which is it? And does it really matter?
Is it “She’s got a degree from Karlstad University, she must have learnt a lot of useful stuff – hire her” or is it “She managed to get a degree from Karlstad University, she must be really clever – hire her”.
Answer: We can’t know which is it, but probably a bit of both.
And for the individual it doesn’t make much difference. According to both theories, the wage will increase with education.
For the allocative function of wages it doesn’t make much difference.
BUT for assessing the effect of public investment in education it matters very much! 32

33. 3. Moral Hazard
If you have full car insurance are you more likely to leave your car unlocked?
Moral hazard is a reaction to incentives to increase the risk of a loss
and is a consequence of asymmetric information.

34. If an insurer knows the exact risk from insuring an individual, then a contract specific to that person can be written.
If all people look alike to the insurer, then one contract will be offered to all insurees; high-risk and low-risk types are then pooled, causing low-risks to subsidize high-risks.

35. Examples of efforts to avoid moral hazard by using signals are:
higher life and medical insurance premiums for smokers or heavy drinkers of alcohol
lower car insurance premiums for contracts with higher deductibles or for drivers with histories of safe driving.

36. 4. Incentives Contracting
A worker is hired by a principal to do a task.
Only the worker knows the effort she exerts (asymmetric information).
The effort exerted affects the principal’s payoff.
The principal’s problem: design an incentives contract that induces the worker to exert the amount of effort that maximizes the principal’s payoff.

37. e is the agent’s effort.
Principal’s reward is y = f(e)
An incentive contract is a function s(y) which specifies the worker’s payment when the principal’s reward is y. The principal’s profit is thus
Let û be the worker’s utility of not working.
To get the worker’s participation, the contract must offer the worker a utility of at least û
The worker’s utility cost of an effort level e is c(e).

38. So the principal’s problem is choose e so as to
(participation
constraint)
subject to
To maximize his profit the principal
designs the contract to provide the
worker with her reservation utility level.

39. subject to Since s(f(e)) is constrained to be equal to
û + c(e), we can substitute and solve
The principal’s profit is maximized when
f’(e) – c’(e) = 0

40. The contract that maximizes the
principal’s profit is one that makes the
worker choose the effort level e* that
equalizes the worker’s marginal effort
cost to the principal’s marginal payoff
from worker effort.
That is to say:

41. Examples of incentives contracts a. Rental Contracting
The principal keeps a lump-sum R for himself and the worker gets all profit above R; i.e.
Why does this contract maximize the principal’s profit?

42. s(f(e)) – c(e) = f(e) – R – c(e)
Given that the contract is:
s(f(e) = f(e) – R
the worker’s payoff is
s(f(e)) – c(e) = f(e) – R – c(e)
and to maximize this the worker should choose the effort level for which
f’(e) – c’(e) = 0
f’(e) = c’(e)
and this implies e = e*

43. How large should be the principal’s rental fee R?
The principal should extract as much rent as possible without causing the worker not to participate, so R should satisfy
s(f(e*)) – c(e*) – R = û
i.e.
R = s(f(e*)) – c(e*) – û
In theory, this means rent is better than traditional sharecropping BUT
With rent the worker bears the whole risk and with risk aversion this is not efficient for the worker.

44. Examples of Incentives Contracts b. Wages contracts
In a wages contract the payment to the worker is
s(e) = we + K
w is the wage per unit of effort. K is a lump-sum payment.
To maximise profits, the employer should set w = f’(e*) and K such that it makes the worker just indifferent between participating and not participating. (K equal to the worker’s reservation wage.)

45. Examples of Incentives Contracts c. Take-it-or-leave-it
The worker is given only two options:
Choose e = e* and be paid a lump-sum L, or choose e ¹ e* and be paid zero.
The worker’s utility from choosing e ¹ e* is - c(e), so the worker will choose e = e*.
L is chosen to make the worker indifferent between participating and not participating.

46. Incentives Contracts in General
The common feature of all efficient incentive contracts is that they make the worker the full residual claimant on profits.
In other words, the last part of profit earned must go entirely to the worker.
But that means that the worker bears the whole risk if something outside his/her control happens.
Incentive contracts also require that the principal has a lot of information.

47. Problem with incentive contracts:
For example:
The principal must know how output depends on the worker’s effort.
A take-it-or-leave-it scheme involves a great risk for workers – if circumstances other than effort occur the worker gets no payment at all.
When we take imperfect into account, incentive contracts appear as much less attractive arrangements.
With real world imperfect information a scheme that is less perfect on paper may actually be better.

48. Finally, from chapters 31-37: Need for government in the economy - or in some cases civil society organisations
Competitive markets ensure choice and efficiency – but that conclusion depends crucially on a number of assumptions that are never fully realised
There are a number of reasons why it is inefficient or inappropriate or even impossible to have “markets without state”.

49. Markets need institutions
At the minimum, no market can function with legislation and legal institutions that ensure that contracts are fulfilled.
Even this minumum requires state expenditure and expenditure requires taxes.
So despite what we know about dead-weight losses connected with taxation, a market economy could not function without them.

50. Market failures
State or intervention in the form of regulations and/or taxes and/or subsidies are necessary:
Ensure adequate provision of public goods.
Correct for externalities.
Control monopolies.
Counteract asymetric information.
In some cases civil society organisations independent of producers could also fulfil these roles.

51. Markets need information
Is it true that ”the consumer is king” in the market?
Rational econmic decisions presuppose full information.
Consumers (and firms dealing with other firms) needs to know what they buy. Therefore there are:
Licences required to practise certain professions
Public institutions to guide consumers (Konsumentverket, the Consumer Ombudsman)
Public institutions issuing certification for certain goods.
Legal requirements on producers to give product information
Arrangements to ”localise” information (Grameen bank).
Voluntary organisations certifying goods
Producer organised (branch associations)
Or independent of producers (organic goods, Fair Trade)

52. “Failure of markets”
Even if a market outcome is efficient, the resulting distribution of resources may be ethically unacceptable. Markets alone cannot ensure the well-being of children, of people with disabilities, of the poor, of unborn generations.
Not everything should be commodities. Should people have the right to buy or sell body organs? To sell themselves as slaves? To buy or sell sex?