Chapter 37 Asymmetric Information

1

• 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.

2

• 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 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 1200.
• However, if buyers do not know how much each car
  is worth, then they are willing to pay the
  expected value.

3

• Since there are 50 lemons and 50 plums, thus
  buyers are willing to pay up to 0.5x1200
  0.5x24001800.
• 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 1200. Thus only lemons get sold while
  none of the plums do. This differs from the case
  when information is symmetric.

4

• 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.)

5

• 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 a2 while unable
  a1 and a2gta1.

6

• The fraction of able workers is b.
• If firms can distinguish two types of workers,
  then they will offer wage a2 to able and to a1
  unable. 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.
• Suppose now workers can acquire education to
  signal his type.

7

• Let e2 be the education acquired by able and e1
  by unable. Let c2e2 be the cost for able and c1e1
  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 c2ltc1.

8

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

9

• What about able workers? Would he deviate to
  acquire education of 0? If he did, the loss is
  a2-a1 while the gain is c2e. 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.

10

• 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)

11

• 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.

12

• 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 yf(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.

13

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

14

• 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)-Ru.

15

• 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.

16

• 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.