Microeconomics
People are Different

John D. Hey, University of York and LUISS

Microeconomics: Lecture 34

ASYMMETRIC INFORMATION

The problem of asymmetric information

So far in this course we have assumed that all agents in the market have the same information about the good being traded. In this final chapter we consider the problems that arise if some agents have more information than others. The usual case is that

The market for lemons

We start with the simple case considered by Varian in his 'Market for Lemons' example. For those who do not know, a 'lemon' is a bad used car. The term apparently used for a good used car is a 'plum'. We assume that in the market for used cars there are Let us begin with an extremely simple case. Let us suppose the market has 100 people who want to buy a used car and 100 who want to sell one. Let us further suppose that 50 of the used cars on sale are lemons and 50 are plums and suppose further that al Let us suppose also that the various reservation prices are as follows: Seller of a plum: 2000 Seller of a lemon: 1000 Buyer of a (known) plum: 2400 Buyer of a (known) lemon: 1200 Note that an equilibrium is clearly possible - the sellers of lemons sell their cars at a price between 1000 and 1200, and the sellers of plums sell their cars at a price between 2000 and 2400. But obviously the sellers of lemons would like to pass off th We suppose that buyers are risk-neutral and, as we have already assumed, that they know that half the cars on offer are lemons and that half are plums If the buyer cannot tell the difference, the most that he or she would be willing to pay is . At this price, no sellers of plums would be willing to sell, so only sellers of lemons would be willing to sell. If buyers worked this out, they would know that just lemons were being offered and would therefore be at most willing to pay 1200. The obvio Now let us consider a more general case, where there is a continuum of qualities being offered. Let us suppose that the supply curve is where is the quantity supplied and the price. Suppose further that the reason that more are offered at higher prices is that the owners of higher quality units are being tempted out to sell. Thus the average quality on offer is also an increasing function of price. Let denote the average quality. We suppose that the average quality is related to the price by . Now suppose that demand depends on both the price and the average quality in the following way: , that is, where is the demand, and is a parameter reflecting how quality affects demand. Note that a is positive so that demand is positively affected by quality (and negatively affected by price). Let us take a particular value of and draw the implied demand and supply curves. We get:

In this case there is a unique equilibrium - but note that only the low quality cars are being traded - the equilibrium price is not sufficiently high to tempt out the high quality sellers. Note also there is a sort of subsidy - the higher quality cars ar Now let us ask what would happen if the quality effect outweighed the price effect earlier. Take a different value for the parameter .

In this case there would be no equilibrium price - the market would cease to exist - no cars at all would be traded. Finally consider the following case, again with a different value for .

Here there are apparently two equilibria. You might like to consider which is more realistic. The problem in all three cases is the asymmetry of information.

The market for insurance

Let us now consider a similar situation in a different market - the market for insurance. We covered this in chapter 25. As in that chapter we assume that preferences take the expected utility form. We begin with the symmetric information case - when bot riskiness of the risk being insured.

symmetric information

Let us suppose, as before, that there are two States of theWorld, State 1 and State 2. Let us assume that their respective probabilities are 0.4 and 0.6. With fair (or perfect) insurance, the budget line facing the person who is thinking about taking out where and are the probabilitities of the two states, in this case 0.4 and 0.6. So the fair insurance line has slope -0.4/0.6 = -2/3. Recall that along this line the insurance company expects to break even - on average the premium it collects when the company does ex ante uncertain income - 10 in State 1 and 70 in State 2. The budget line facing this individual under fair insurance is:

Suppose now that our indiviudal is a risk-averse expected utility maximiser. His or her indifference curves look as in the following graph. Remember the important result that along the certainty line the slope of expected-utility indifference curves are e .

If we put these two graphs together, we get the following optimising solution.

Because the slope of the budget line (under fair insurance) is equal to and the slope of the indifference curves along the certainty line are also equal to , we get the familiar result that the risk-averter chooses to become fully insured. The insurance company, of course, breaks even.

moral hazard

Now let us consider the case which is called moral hazard . This is a case in which the insured person, because he or she is insured , is less careful about the risk that he or she faces - and therefore the risk changes. In this case, we assume that, because the individual is effectively insured against State 1 happening moral hazard will make State 1 more likely. Let us assume that th but that the insurance company is unaware of this . We now have asymmetric information - the company thinks that the probability of State 1 happening is 0.4, whereas it is in fact 0.5. Now the indifference map of the individual changes - because he or she know that the probability of State 1 happening is now 0.5: the indifference curves now have a slope of -1 (= -0.5/0.5) along the certainty line.

Suppose the insurance company continues to think that the probability of State 1 happening is 0.4 and continues to offer fair insurance on that basis. Then we get the following situation.

The individual chooses the red asterisk point and the insurance company loses money. Why? Because the correct fair insurance line should be the red dashed line in the figure below.

Along the red dashed line the insurance company breaks even on average when the true probability of State 1 is 0.5. At the red asterisked point the insurance company is losing money. This is the problem of moral hazard and explains why insurance companies take measures to stop the probabilities changing - like insisting that people install fire alarms for example.

adverse selection

Another interesting problem of asymmetric information is that of adverse selection . This occurs in an insurance market, for example, when there are two types of people wanting to be insured - high risk people and low risk people. Let us assume that the high risk people have and the low risk people have . So the high risk people have the red indifference curves in figures 34.7, 34.8 and 34.9 above, while the low risk people have the blue indifference curves in figures 34.5 and 34.6 above. If the insurance company could distinguish between the two types then the solution would be easy, as we s

The company would simply offer the blue budget line to the low risk people and the red budget line to the high risk people. Both groups of people would end up fully insured and the insurance company would break even. But if the company could not distingui adverse selection . But if the insurance company cannot distinguish between the two groups - cannot tell whether someone is high or low risk - economics tells us that it may be able to do something quite clever: get the two groups to reveal which group they belong to by offering two types of insurance contract - one which would be attractive only to the low risk group and one that would be attractive only to the high risk group. How do they do this? Consider the figure below.

The two contracts are represented by the asterisks: the blue asterisk point is attractive to the low risk group, the red asterisk to the high risk group. The insurance company breaks even and the high risk people are completely covered by the insurance. separating equilibrium . Note that the only problem is that the low risk people are not completely covered (as they would like to be).

Other solutions

There are of course other ways round these asymmetric information problems. Some of these rely on the fact that most problems are not one-off problems (though many are - consider what happens to you if you just buy or sell once). If problems are repeated reputations, through brand names , through no-claims bonuses , through guarantees and so on. Agents can also use screening devices (you have been to job interviews?). Also people can obtain signals of their quality - a good example is the signal provided by having a degree. This may be be very one good reason why you are trying to get a degree - and obviously the better the degree the better the signal. But under one condition: that it is harder to this course is organised the way that it is. Are all?

Summary

Asymmetric Information could stop markets existing - the low quality goods drive out the high quality. Moral hazard makes insurance companies lose money. In cases of adverse selection, self-selection may be possible, leading to a separating equilibrium. But this may be inefficient. If decision problems are repeated then other ways round the asymmetric information problem may be possible. Signals may be important - but it should be more difficult to get a high quality signal.

And finally....

All the best in the future. I hope that you have enjoyed the course ... and that some of you become economists.

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