Chapter 38 Asymmetric Information Key Concept: adverse selection and moral hazard .

1. Chapter 38 Asymmetric Information • Key Concept: adverse selectionandmoral hazard. • Incentives, incentives, incentives!

2. Chapter 38 Asymmetric Information • So far we assume buyers and sellers are both perfectly informed about the quality of goods being sold in the market. • In reality, it is often the case that one of the transacting party has less information than the other.

3. One example is the labor market. It may be difficult for a firm to determine how productive its employees are. • When a consumer buys a used car, it may be hard to determine whether it is a good car or a lemon. By contrast, the seller may has a pretty good idea. • This asymmetric information may cause significant problems with the efficient functioning of a market.

4. Consider a market with 100 people who want to sell their used cars and 100 people who want to buy a used car. • Everyone knows that 50 cars are lemons and 50 are plums. • The current owner knows the quality of his car, but the potential purchasers do not.

5. The owner of a lemon is happy to part with his car for 1000 and that of a plum for 2000. • The buyers are willing to pay 1200 for a lemon and 2400 for a plum. • If information is symmetric, then the lemon will sell at some price between 1000 and 1200 while the plum between 2000 and 2400.

6. What if the information is not symmetric? • Since there are 50 lemons and 50 plums, buyers are willing to pay up to 0.5x1200+ 0.5x2400=1800.

7. Yet at 1800, only the owners of lemons are willing to sell their cars. • However, in equilibrium, buyers cannot have wrong expectation, so they expect to see only lemons in the market. • When this happens, buyers are willing to pay only 1200.

8. Thus only lemons get sold while none of the plums do. • This differs from the case when information is symmetric. • None of the plums ever get sold. Even though the willingness to pay is higher than the willingness to sell. No transactions will take place.

9. This is an example of adverse selection. There are some other examples like insurance, car insurance, health insurance, so market equilibrium is typically not efficient.

10. If insurance companies base their rates on the average incidence of health problems, people who want to purchase it the most are the ones who are likely to need it the most. • Thus, the rates must reflect this disparity. • Marriage market?

11. Adverse selectionarises when an informed individual’s trading decisions depend on his privately held information in a manner that adversely affects uninformed market participants (hidden information).

12. In the used-care market, an individual is more likely to decide to sell his car when he knows it is a lemon. • When adverse selection is present, uninformed traders will be wary of any informed trader who wishes to trade with them, and their willingness to pay will be low.

13. This fact may even exacerbate the adverse selection problem. • If the price that can be received by selling a used car is very low, only sellers with really bad cars will offer them to sell.

14. There are ways evolved to alleviate this inefficiency. • For instance, compulsory purchase plan, employee insurance as fringe benefits.

15. The high-risk people are better off because they can purchase insurance at rates that are lower than the actual risk they face and the low risk people can purchase insurance that is more favorable to them than the insurance offered if only high–risk people purchased it.

16. Talk a bit about reputation and standardization.

17. Some practices also emerge. • For instance, the owner of a plum can offer a warranty, a promise to pay the purchaser some agreed upon amount if the car turned out to break down. • Or he can allow the purchaser to take his car to a technician to examine his car. Now these are called signaling.

18. Let us look at a prototype example. • Suppose we have two types of workers, able and unable. • Able workers have MPL of a2 while unable a1 and a2>a1.

19. The fraction of able workers is b. The faction of unable workers is 1-b. • If firms can distinguish two types of workers, then they will offer wage a2 to able and to a1 unable.

20. However, if they cannot, they can only offer ba2+(1-b)a1. • Now if under this wage, both types will work, then there is no problem of efficiency loss even information is asymmetric.

21. Suppose now workers can acquire education to signal his type. • Now workers acquire education first and then firms decide how much to pay after observing the choice of education by workers. • Assume the education does not affect the productivity at all to simplify.

22. Let e2 be the education acquired by able and e1 by unable. • Let c2e2 be the cost for able and c1e1 for unable. • Suppose further that c2<c1.

23. Let e* satisfy (a2-a1)/c1 < e*< (a2-a1)/c2. • Then we have an equilibrium where able workers get education e* and unable 0. • Firms pay a2 when they see e*and pay a1 when they see 0.

24. Let e* satisfy (a2-a1)/c1 < e*< (a2-a1)/c2. • Does anyone have an incentive to deviate? • Would unable mimic able? If he did, then the gain is a2-a1 while the cost is c1 e*. • The first inequality guarantees that this is not profitable.

25. Let e* satisfy (a2-a1)/c1 < e*< (a2-a1)/c2. • What about able workers? Would he deviate to acquire education of 0? • If he did, the loss is a2-a1 while the gain (saved cost) is c2e*. The second inequality guarantees that loss is bigger than gain and so it is not profitable to do so.

26. Hence it is indeed an equilibrium. • In this equilibrium, able and unable workers separate. • This is called a separating equilibrium where two types choose different signals to separate.

27. However, in this setup it is a pure waste to signal. • Able workers find it in their interest to pay for acquiring the signal, even though it does not change his productivity.

28. This is because we start from a situation where the market is efficient. • When the competitive equilibrium is not efficient, though signaling has cost, it might have some benefit and may improve efficiency. • Signaling can make things better or worse. Each case has to be examined on its own merits.

29. Is education simply a signal? • There seems to be a discontinuous jump in wage. Earnings of high school graduates are much higher than the incomes of people who have only completed 3 years of high school.

30. This sheepskin effect, in reference to the fact that diplomas were often written on sheepskins, suggests graduation from high school is some kind of singal. • But what does it signal?

31. Data seems to suggest high school graduates had significantly lower quit and absentee rates than nongraduates.

32. Another interesting problem arising in the insurance market is known as the moral hazard. • This relates to the phenomenon that after contracting (insured), one transacting party may have the incentive to take less care (hidden action).

33. If no theft insurance is available, car owners may buy expensive locks. • On the other hand, after purchasing the theft insurance, care owners may not buy expensive locks.

34. Moral hazard could manifest in unusual forms. • Mountain climbers with better gear may take more challenges. This may expose them to greater risks. This is also a form of moral hazard.

35. When an insurance company sets its rates, it has to take into account the incentive change.

36. The tradeoffs involved are: • too little insurance means people bear too much risk • too much insurance means people will take inadequate care • So the whole point is on balancing these two.

37. Hence an insurance policy often includes a deductible, the amount that the insured party has to pay in any claim. (compared this with premium). • This is designed to make sure that consumers will take some care.

38. Now the whole problem becomes how can I get someone do something for me? • This naturally leads us to the incentives problems.

39. Suppose we have a worker (agent) who if exerting effort x can produce output y=f(x). • Efforts are not observable but outputs are.

40. effort x, output y=f(x). • Efforts are not observable but outputs are. • Let the cost of x be c(x) and the worker has some outside opportunity which gives him the utility of u.

41. effort x, output y=f(x). • Then the whole problem boils down to choosing the payment s(y)=s(f(x)) to the worker to max the profit of the Principal.

42. Now to make the worker participate, we have the participation constraint or the individual rationality IR constraint. • That is, s(f(x))-c(x)u.

43. If we can observe x, the principal simply maxx f(x)-s(f(x)) subject to s(f(x))-c(x)u. • This can be solved by maxx f(x)-c(x)-u (**). • So FOC is MP(x*)=MC(x*).

44. But if x is not observable, then we need to worry about whether agents will indeed choose x*.

45. This brings us to another constraint, called the incentive compatibility IC constraint. • It means that s(f(x*))-c(x*) s(f(x))-c(x) for all x.

46. There is a way to do this, that is, to sell the firm to the agents. • So s(f(x))=f(x)-R. • If the worker max s(f(x))-c(x)=f(x)-c(x)-R, then it looks just like (**). • So x* will be chosen if IR is OK.

47. To make IR OK, we just choose R so that f(x*)-c(x*)-R=u.

48. In short, the sell-out contract is to make the agents the residual claimant so that he will take the proper care.

49. However, this is good because we assume risk neutrality of agents. • If agents are risk averse, then this incentive scheme may entail too much risk on agents and for this reason, we do not see that every principal uses this kind of scheme to motivate his agents.

50. So sometimes we see sharecropping such as s(f(x))=af(x)+F. • The incentives to the agent are not exactly right. But this is something of a happy medium. The worker and the employer share the risk of output fluctuations. It also gives the worker an incentive to produce output but it does not leave him bearing all the risk.