1. Asymmetric Information
Chapter 18
Asymmetric Information
Nicholson and Snyder, Copyright ©2008 by Thomson South-Western. All rights reserved.

2. Asymmetric Information
Transactions can involve a considerable amount of uncertainty
can lead to inefficiency when one side has better information
The side with better information is said to have private information or asymmetric information

3. The Value of Contracts
Contractual provisions can be added in order to circumvent some of the inefficiencies associated with asymmetric information
rarely do they eliminate them

4. Principal-Agent Model
The party who proposes the contract is called the principal
The party who decides whether or not to accept the contract and then performs under the terms of the contract is the agent
typically the party with asymmetric information

5. Leading Models Two models of asymmetric information
the agent’s actions affect the principal, but the principal does not observe the actions directly
called a hidden-action model or a moral hazard model
the agent has private information before signing the contract (his type)
called a hidden-type model or an adverse selection model

6. First, Second, and Third Best
In a full-information environment, the principal could propose a contract that maximizes joint surplus
could capture all of the surplus for himself, leaving the agent just enough to make him indifferent between agreeing to the contract or not
This is called a first-best contract

7. First, Second, and Third Best
The contract that maximizes the principal’s surplus subject to the constraint that he is less well informed than the agent is called a second-best contract
Adding further constraints leads to the third best, fourth best, etc.

8. Hidden Actions
The principal would like the agent to take an action that maximizes their joint surplus
But, the agent’s actions may be unobservable to the principal
the agent will prefer to shirk
Contracts can mitigate shirking by tying compensation to observable outcomes

9. Hidden Actions
Often, the principal is more concerned with outcomes than actions anyway
may as well condition the contract on outcomes

10. Hidden Actions
The problem is that the outcome may depend in part on random factors outside of the agent’s control
tying the agent’s compensation to outcomes exposes the agent to risk
if the agent is risk averse, he may require the payment of a risk premium before he will accept the contract

11. Owner-Manager Relationship
Suppose a firm has one representative owner and one manager
the owner offers a contract to the manager
the manager decides whether to accept the contract and what action e  0 to take
an increase in e increases the firm’s gross profit but is personally costly to the manager

12. Owner-Manager Relationship
The firm’s gross profit is
g = e + 
where  represents demand, cost, and other economic factors outside of the agent’s control
assume  ~ (0,2)
c(e) is the manager’s personal disutility from effort
assume c’(e) > 0 and c’’(e) < 0

13. Owner-Manager Relationship
If s is the manager’s salary, the firm’s net profit is
n = n – s
The risk-neutral owner wishes to maximize the expected value of profit
E(n) = E(e +  – s) = e – E(s)

14. Owner-Manager Relationship
We will assume the manager is risk averse with a constant risk aversion parameter of A > 0
The manager’s expected utility will be

15. First-Best
With full information, it is relatively easy to design an optimal salary contract
the owner can pay the manager a salary if he exerts a first-best level of effort and nothing otherwise
for the manager to accept the contract
E(u) = s* - c(e*)  0

16. E(n) = e* - E(s*) = e* - c(e*)
First-Best
The owner will pay the lowest salary possible [s* = c(e*)]
The owner’s net profit will be
E(n) = e* - E(s*) = e* - c(e*)
at the optimum, the marginal cost of effort equals the marginal benefit

17. Second Best
If the owner cannot observe effort, the contract cannot be conditioned on e
the owner may still induce effort if some of the manager’s salary depends on gross profit
suppose the owner offers a salary such as
s(g) = a + bg
a is the fixed salary and b is the power of the incentive scheme

18. Second Best This relationship can be viewed as a three-stage game
owner sets the salary (choosing a and b)
the manager decides whether or not to accept the contract
the manager decides how much effort to put forth (conditional on accepting the contract)

19. Second Best
Because the owner cannot observe e directly and the manager is risk-averse, the second-best effort will be less than the first-best effort
the risk premium adds to the owner’s cost of inducing effort

20. First- versus Second-Best Effort
The owner’s MC is higher in the second best, leading to lower effort by the manager
MC in second best
c’(e) + risk term
MC in first best
c’(e) 1 MB e
e** e*

21. Moral Hazard in Insurance
If a person is fully insured, he will have a reduced incentive to undertake precautions
may increase the likelihood of a loss occurring

22. Moral Hazard in Insurance
The effect of insurance coverage on an individual’s precautions, which may change the likelihood or size of losses, is known as moral hazard

23. Mathematical Model
Suppose a risk-averse individual faces the possibility of a loss (l) that will reduce his initial wealth (W0)
the probability of loss is 
an individual can reduce this probability by spending more on preventive measures (e)

24. E[u(W)] = (1-)u(W0-e-p) + ()u(W0-e-p-l+x)
Mathematical Model
An insurance company offers a contract involving a payment of x to the individual if a loss occurs
the premium is p
If the individual takes the coverage, his expected utility is
E[u(W)] = (1-)u(W0-e-p) + ()u(W0-e-p-l+x)

25. First-Best Insurance Contract
In the first-best case, the insurance company can perfectly monitor e
should set the terms to maximize its expected profit subject to the participation constraint
the expected utility with insurance must be at least as large as the utility without the insurance
will result in full insurance with x = l
the individual will choose the socially efficient level of precaution

26. Second-Best Insurance Contract
Assume the insurance company cannot monitor e at all
an incentive compatibility constraint must be added
The second-best contract will typically not involve full insurance
exposing the individual to some risk induces him to take some precaution

27. Hidden Types
In the hidden-type model, the individual has private information about an innate characteristic he cannot choose
the agent’s private information at the time of signing the contract puts him in a better position

28. Hidden Types
The principal will try to extract as much surplus as possible from agents through clever contract design
include options targeted to every agent type

29. Nonlinear Pricing
Consider a monopolist who sells to a consumer with private information about his own valuation for the good
The monopolist offers a nonlinear price schedule
menu of different-sized bundles at different prices
larger bundles sell for lower per-unit price

30. Mathematical Model
Suppose a single consumer obtains surplus from consuming a bundle of q units for which he pays a total tariff of T
u = v(q) – T
assume that v’(q) > 0 and v’’(q) < 0
the consumer’s type is 
H is the “high” type (with probability of )
L is the “low” type (with probability of 1-)
0 < L < H

31. Mathematical Model
Suppose the monopolist has a constant average and marginal cost of c
The monopolist’s profit from selling q units is
 = T – cq

32. First-Best Nonlinear Pricing
In the first-best case, the monopolist observes 
At the optimum
v’(q) = c
the marginal social benefit of increased quantity is equal to the marginal social cost

33. First-Best Nonlinear Pricing
This graph shows the consumers’ indifference curves (by type) and the firm’s isoprofit curves T
U0H
U0L q

34. First-Best Nonlinear Pricing
A is the first-best contract offered to the “high” type and B is the first-best offer to the “low” type T
U0H A
U0L B q

35. Second-Best Nonlinear Pricing
Suppose the monopolist cannot observe 
knows the distribution
Choosing A is no longer incentive compatible for the high type
the monopolist must reduce the high-type’s tariff

36. Second-Best Nonlinear Pricing
The “high” type can reach a higher indifference curve by choosing B T
To keep him from choosing B, the monopolist must reduce the “high” type’s tariff by offering a point like C C
U0H A
U2H
U0L B q

37. Second-Best Nonlinear Pricing
The monopolist can also alter the “low” type’s bundle to make it less attractive to the high type T
U0H A E
U2H C
U0L B D q
q**L
q**H

38. Monopoly Coffee Shop The college has a single coffee shop
faces a marginal cost of 5 cents per ounce
The representative customer faces an equal probability of being one of two types
a coffee hound (H = 20)
a regular Joe (L = 15)
Assume v(q) = 2q0.5

39. First Best
Substituting such that marginal cost = marginal benefit, we get
q = (/c)2
q*L = q*H = 16
T*L = T*H = 160
E() = 62.5

40. Incentive Compatibility when Types Are Hidden
The first-best pricing scheme is not incentive compatible if the monopolist cannot observe type
keeping the cup sizes the same, the price for the large cup would have to be reduced by 30 cents
the shop’s expected profit falls to 47.5

41. Second Best
The shop can do better by reducing the size of the small cup
The size that is second best would be
LqL-0.5 = c + (H - L)qL-0.5
q**L = 4
T**L = 60
E() = 50

42. Adverse Selection in Insurance
Adverse selection is a problem facing insurers where the risky types are more likely to accept an insurance policy and are more expensive to serve
assume policy holders may be one of two types
H = high risk
L = low risk

43. First Best The insurer can observe the individual’s risk type
First best involves full insurance
different premiums are charged to each type to extract all surplus

44. First Best Without insurance each type finds himself at E
U0L
Without insurance each type finds himself at E
certainty line
U0H B
A and B represent full insurance A E W1

45. Second Best
If the insurer cannot observe type, first-best contracts will not be incentive compatible
if the insurer offered A and B, the high-risk type would choose B
the insurer must change the coverage offered to low-risk individuals to make it unattractive to high-risk individuals

46. First Best W2
The high-risk type is fully insured, but his premium is higher (than it would be at B) C
U0L
U1H
certainty line
U0H B
The low-risk type is only partially insured D A E W1

47. Market Signaling
If the informed player moves first, he can “signal” his type to the other party
the low-risk individual would benefit from providing his type to insurers
he should be willing to pay the difference between his equilibrium and his first-best surplus to issue such a signal

48. Market for Lemons
Sellers of used cars have more information on the condition of the car
but the act of offering the car for sale can serve as a signal of car quality
it must be below some threshold that would have induced the owner to keep it

49. Market for Lemons
Suppose there is a continuum of qualities from low-quality lemons to high-quality gems
only the owner knows a car’s type
Because buyers cannot determine the quality, all used cars sell for the same price
function of average car quality

50. Market for Lemons
A car’s owner will choose to keep a car that is in the upper end of the spectrum
reduces the average quality
reduces the market price
leads sellers of the high end of the remaining cars to keep their cars
reduces average quality and market price

51. Auctions
A seller can often do better if several buyers compete against each other
high-value consumers are pushed to bid high
Different formats may lead to different outcomes
sellers should think carefully about how to design the auction

52. First-Price Sealed Auction Bid
All bidders simultaneously submit secret bids
The auctioneer unseals the bids and awards the object to the highest bidder
The highest bidder pays his own bid

53. First-Price Sealed Auction Bid
In equilibrium, it is a weakly dominated strategy to submit a bid b greater than or equal to the buyer’s valuation v
a strategy is weakly dominated if there is another strategy that does at least as well against all rivals’ strategies and strictly better against at least one

54. First-Price Sealed Auction Bid
A buyer receives no surplus if he bids b=v no matter what his rivals bid
by bidding b < v, there is a chance for some positive surplus
Since players likely avoid weakly dominated strategies, we can expect bids to be lower then buyers’ valuations

55. Second-Price Sealed Auction Bid
The highest bidder pays the next highest bid rather than his own
All bidding strategies are weakly dominated by the strategy of bidding exactly one’s valuation
second-price auctions induce bidders to reveal their valuations

56. Second-Price Sealed Auction Bid
The reason that bidding one’s valuation is weakly dominant is that the winner’s bid does not affect the amount he has to pay
that depends on someone else’s bid

57. Common Values Auctions
In complicated economic environments, different auction formats do not necessarily yield the same revenue
Suppose the good has the same value to all bidders, but they do ot know exactly what that value is
common values auction

58. Common Values Auctions
The winning bidder realizes that every other bidder probably though the object was worth less
means that he probably overestimated the value when bidding
This is often referred to as the winner’s curse

59. Important Points to Note:
Asymmetric information is often studied using a principal-agent model in which a principal offers a contract to an agent who has private information
the two main variants of the model are the models of hidden actions and hidden types

60. Important Points to Note:
In a hidden-action model (called a moral hazard model), the principal tries to induce the agent to take appropriate actions by tying the agent’s payments to observable outcomes
doing so exposes the agent to random fluctuations, which is costly for a risk-averse agent

61. Important Points to Note:
In a hidden-type model (called an adverse selection model), the principal cannot extract all of the surplus from high types because they can always gain positive surplus by pretending to be a low type
the principal will offer a menu of contracts from which different types of agents can select

62. Important Points to Note:
In a hidden-type model, the principal will offer a menu of contracts from which different types of agents can select
the principal distorts the quantity offered to low types in order to make the contract less attractive to high types

63. Important Points to Note:
Most of the insights gained from the basic form of a principal-agent model, in which the principal is a monopolist, carry over to the case of competing principals
the main change is that agents obtain more surplus

64. Important Points to Note:
The lemons problem arises when sellers have private information about the quality of their goods
sellers whose goods are higher than average quality may refrain from selling
the market may collapse, with goods of only the lowest quality being offered for sale

65. Important Points to Note:
The principal can extract more surplus from agents if several of them are pitted against one another in an auction setting
in a simple economic environment, a variety of common auction formats generate the same revenue
differences in auction format may generate different levels of revenue in more complicated settings