Chapter 37 Asymmetric Information In reality, it is often the case that one of the transacting party has less information than the other. 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.

The owner of a lemon is happy to part with his car for 1000 and that of a plum for The buyers are willing to pay 2400 for a plum and 1200 for a lemon. If information is symmetric, then the plum will sell at some price between 2000 and 2400 while the lemon between 1000 and However, if buyers do not know how much each car is worth, then they are willing to pay the expected value.

Since there are 50 lemons and 50 plums, thus buyers are willing to pay up to 0.5x x2400=1800. 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, they are willing to pay only Thus only lemons get sold while none of the plums do. This differs from the case when information is symmetric.

This is an example of adverse selection. There are some other examples like insurance, health insurance, (marriage market?) so market equilibrium is typically not efficient. There are ways evolved to alleviate this inefficiency. For instance, compulsory purchase plan, employee insurance as fringe benefits. (Talk a bit about reputation and standardization.)

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. Suppose we have two types of workers, able and unable. Able workers have MPL of a 2 while unable a 1 and a 2 >a 1.

The fraction of able workers is b. If firms can distinguish two types of workers, then they will offer wage a 2 to able and to a 1 unable. However, if they cannot, they can only offer ba 2 +(1-b)a 1. Now if under this wage, both types will work, then there is no problem of efficiency loss. Suppose now workers can acquire education to signal his type.

Let e 2 be the education acquired by able and e 1 by unable. Let c 2 e 2 be the cost for able and c 1 e 1 for unable. 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. Suppose further that c 2 <c 1.

Let e* satisfy (a 2 -a 1 )/c 1 < e*< (a 2 -a 1 )/c 2. Then we have an equilibrium where able workers get education e* and unable 0. Firms pay a 2 when they see e*and pay a 1 when they see 0. Does anyone have an incentive to deviate? Would unable mimic able? If he did, then the gain is a 2 -a 1 while the cost is c 1 e*. The first inequality guarantees that this is not profitable.

What about able workers? Would he deviate to acquire education of 0? If he did, the loss is a 2 -a 1 while the gain is c 2 e*. The second inequality guarantees that loss is bigger than gain and so it is not profitable to do so. Hence it is indeed an equilibrium. This is called a separating equilibrium where two types choose different signals to separate. In this setup it is a pure waste to signal.

However, when the competitive equilibrium is not efficient, though signaling has cost, it might have some benefit and may improve efficiency. 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. (talk about theft insurance)

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

Now the whole problem becomes how can I get someone do something for me? This naturally leads us to the incentives problems. Suppose we have a worker (agent) who if exerting effort x can produce 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. 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.

Now to make the worker participate, we have the participation constraint (individual rationality IR). That is, s(f(x))-c(x)  u. So if we can observe x, the principal simply does max x f(x)-s(f(x)) subject to s(f(x))-c(x)  u. This can be solved by max x f(x)-c(x)-u (**). So FOC is MP(x*)=MC(x*). But if x is not observable, then we need to worry about whether agents will indeed choose x*.

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

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

A final note on the voting right of a corporation. It is often the case that shareholders have the right to vote on various issues while bond holders do not. Why is that? The answer may lie in the incentives. If a corporation produces X dollars and total claim is B dollars of bond holders. Then the amount that goes to shareholders is X-B. So this makes sure the shareholders have the right incentives to max X.