CHAPTER 8
ADVERSE SELECTION: AKERLOF’S
MARKET FOR LEMONS
Econ3004/ Econ6039 Health Economics, 2023 Semester 2
Dr Yijuan Chen, Australian National University
Bhattacharya, Hyde and Tu – Health Economics
Intro
 A man walks into the office of a life insurance
company.
 He wants to buy a $1 million life insurance policy for
a term of one day. Your company will have to pay $1
million to his heirs if and only if he dies tomorrow.
 You know nothing else about this man.
 How much do you charge?
Bhattacharya, Hyde and Tu – Health Economics
Asymmetric information
 Definition: a situation in which agents in a
potential economic transaction do not have the
same information about the quality of the good
being transacted
 A major theme of this course, and the source of
many problems in health insurance markets
THE INTUITION BEHIND THE MARKET FOR
LEMONS
Bhattacharya, Hyde and Tu – Health Economics
First: symmetric information
 Imagine a well-functioning used car market
 Sellers advertise cars, and buyers can accurately
assess the condition of each car for sale
 Some buyers will be willing to pay more for cars in
good condition; others are happy to get a deal
 Symmetric information: buyers and sellers have
symmetric info about car quality. This is crucial.
 Outcome: each car sells for a different price,
depending on its quality
Bhattacharya, Hyde and Tu – Health Economics
First: symmetric information
 Pareto-improving transaction: a transaction that
leaves all parties at least no worse off
 One goal of a market is to make sure all Pareto-
improving transactions take place
 In the market we have described, there is nothing
to stop all Pareto-improving transactions from
taking place
 All the cars end up with the people who value them
the most
Bhattacharya, Hyde and Tu – Health Economics
Next: asymmetric information
 New assumption: sellers can determine car quality,
but buyers cannot
 All cars look identically good to the buyers
 This market will look different from the previous
one in several ways:
 any cars that sell, sell for the same price
 The best cars will not be offered on the market
 It is possible that the cars will not end up with the people
who value them most (buyers)
Bhattacharya, Hyde and Tu – Health Economics
Why is there only one price?
 Imagine that two cars are offered for different
prices in this market: P and P’ > P
 No buyer will want to buy the expensive car,
because both cars will seem the same
 All sellers will have to lower their prices to match
the lowest price on the market
Bhattacharya, Hyde and Tu – Health Economics
Why are some cars not offered?
 We know the market has one price P
 Consider the seller who owns the nicest car on the
market – it is probably worth way more than P
 That seller has no reason to remain in the market
 Why doesn’t he advertise the high quality of his vehicle
and charge a higher price?
 Remember, buyers can’t “see” quality
 Outcome: only the lower-quality cars stay on the
market. This is our first example of adverse selection.
Bhattacharya, Hyde and Tu – Health Economics
Adverse selection
Definition: the oversupply of low-quality
goods, products, or contracts that
results when there is asymmetric
information.
 This is one of the most important ideas in health
economics.
Bhattacharya, Hyde and Tu – Health Economics
What happens to our market?
 Recap
 Cars only sell at one price
 As a result, the best cars leave the market
 What do buyers do?
 They know the average car remaining on the market is of
low quality.
 Unless buyers value cars very highly, they will not want to
buy these cars.
 The market unravels, and potential Pareto-improving
transactions do not occur. This is a market failure.
A FORMAL STATEMENT OF THE AKERLOF
MODEL
Bhattacharya, Hyde and Tu – Health Economics
A formal treatment
 We will introduce a formal model of the market we
discussed in the previous slides.
 We will present explicit utility functions and a
specific distribution of car quality to make the
argument more concrete.
 But remember – the logic of the argument is the
same as what we just saw.
Bhattacharya, Hyde and Tu – Health Economics
Seller and buyer utility functions
 Sellers and buyers derive
utility from the cars they
own and other goods
 Buyers value cars 50%
more than sellers (that’s
why they are buyers in
the first place)
 Xj = quality of the jth car
owned
 M = utility from other
goods
Bhattacharya, Hyde and Tu – Health Economics
Distribution of car quality
 Car quality X is uniformly distributed between 0 and 100
 Cars are equally likely to have any quality level between 0 and 100
 You are equally likely to have a car of quality level 50 as you are to have a
car of quality 96, 17, π, 54.2828 or any real number between 0 and 100
 We use the term Xi to denote the quality of car i
Bhattacharya, Hyde and Tu – Health Economics
Information assumptions
 Buyers do not know the true quality of a
particular car, but they do know a lot.
 Buyers know the utility function of the
sellers and know the distribution of cars
available for sale
 They also understand that sellers will
withdraw highest-quality cars if the price
does not justify selling.
Bhattacharya, Hyde and Tu – Health Economics
Which cars will sellers offer?
 A seller will put a car on the market if selling it will
increase his utility.
 If a seller sells his car of quality X for P dollars, he
loses X units of utility but gains P dollars
 Hence, he will only put car j on the market if P > Xj
Bhattacharya, Hyde and Tu – Health Economics
When will buyers buy?
 Figuring out when buyers buy is trickier due to
uncertainty.
 Like sellers, buyers are trying to maximize utility.
But think about a buyer who is considering
buying a car of uncertain quality. How does she
know what will happen to her utility?
 Buyers have to think in terms of expected utility.
Bhattacharya, Hyde and Tu – Health Economics
When will buyers buy?
 Suppose a buyer buys a car in this market.
 She pays P dollars and thus loses P units of utility.
 She gains a car with expected value E[X|P], so she
gains 3/2 E[X|P] units of utility.
 Remember, E[X|P] means “expectation of X conditional
on P.” We need to think about P because it affects
sellers’ decisions, and hence affects the distribution of
quality X.
 Hence, buyers will buy if:
Bhattacharya, Hyde and Tu – Health Economics
When will buyers buy?
 We need to find E[X|P] to decide if buyers will buy
 Remember the distribution of cars now:
 The formula for expectation for a uniform
distribution is simply the average of the endpoints.
So E[X|P] = ½ P
Bhattacharya, Hyde and Tu – Health Economics
When will buyers buy?
 We found E[X|P] = ½ P
 We plug that into our condition for buying:
3/2 E[X|P] > P
3/2 * ½ P > P
¾ P > P
 This is impossible; hence buyers will not buy for
any P!
 No cars sell, no Pareto-improving trades take place,
the cars stay with sellers (who do not want them
as much as the buyers do). The market unravels.
Bhattacharya, Hyde and Tu – Health Economics
What just happened?
 To review:
 A single price P is somehow established in the market
 Sellers remove all cars of quality greater than P
Of the cars that remain, the average quality (E[X|P]) is
only ½ P
 Buyers do not like cars enough to buy a car of quality
½ P for a price of P
No cars sell, even though buyers like cars better than
sellers and all the cars “should” end up with buyers.
Ch 8 | Adverse Selection: Akerlof’s Market for
Lemons
THE ADVERSE SELECTION DEATH SPIRAL
Bhattacharya, Hyde and Tu – Health Economics
What does this used car market have to do
with health insurance?
 Let’s imagine a health insurance market that is similar
to the market we just discussed:
 Each customer i has an expected amount of health care
costs over the course of the year Xi.
 An insurance company offers a single policy with an annual
premium P. This full insurance policy covers all health care
costs incurred during the year.
 Customers are risk-neutral. Customer i will purchase
insurance if and only if P is less than his expected health
care costs Xi.
 The insurers cannot distinguish healthy and sick customers
 Expected customer health care costs Xi are distributed
uniformly in the population between $0 and $20,000.
Bhattacharya, Hyde and Tu – Health Economics
What does this used car market have to do
with health insurance?
 Analogy between these two markets
 The “cars” are customers’ bodies
 The “sellers” are customers
 The “buyers” are insurance companies
 The sellers try to convince the buyers that the “cars”
are healthy; just as a high-quality car is worth a lot to
buyers, a healthy customer is worth a lot to insurers
 Just like high-quality cars leave the market when a
universal price is set, high-quality bodies will leave the
market when a universal premium is set.
Bhattacharya, Hyde and Tu – Health Economics
Health insurance market
 Suppose the insurer offers a contract with
premium $10,000 for the year.
 What happens? Who stays in the market?
Bhattacharya, Hyde and Tu – Health Economics
Health insurance market
 Only the least healthy people buy insurance; their
average health expenditures are $15,000.
 The insurer raises premiums to $15,000 the next year.
Bhattacharya, Hyde and Tu – Health Economics
Adverse selection death spiral
 There is nothing to stop this cycle, which is called
an adverse selection death spiral.
 Definition: successive rounds of adverse selection
that destroy an insurance market.
 The heart of the problem is adverse selection: only
the worst customers stay in the market when the
insurer sets the premium.
 No way for the insurer to turn a profit in this very
simple model.
Ch 8 | Adverse Selection: Akerlof’s Market for
Lemons
WHEN CAN THE MARKET FOR LEMONS
WORK?
Bhattacharya, Hyde and Tu – Health Economics
What if buyers value cars very highly?
 Let’s assume new utility functions:
 Now buyers value cars much more than sellers.
Will this fix the market?
Bhattacharya, Hyde and Tu – Health Economics
What if buyers value cars very highly?
 We need a new condition for buyers:
 Recall that E[X|P] = ½ P. This is unaffected by the
buyers’ utility function – why?
 The condition now holds: buyers will be willing to
buy cars at price P. They know the remaining cars
are bad but they value them highly enough to
pay P for them.
Bhattacharya, Hyde and Tu – Health Economics
What if there is a minimum guaranteed car
quality?
 The condition for buyers is as it was before, but
now E[X|P] will be different because a different
subset of cars is on the market.
 This is promising: the worst cars were forced off
the market, so the remaining cars are better.
Bhattacharya, Hyde and Tu – Health Economics
What if there is a minimum guaranteed car
quality?
 When do buyers buy?
 If 3/2 E[X|P] > P
 What is E[X|P]
 Based on the formula for the expectation of a
uniform distribution, E[X|P] = ½ * (P + 10)
 Buyers buy if:
3/2 E[X|P] > P
3/2 * ½ * (P + 10) > P
3/4 P + 15/2 > P
 Buyers will buy if the price is below $30.
Bhattacharya, Hyde and Tu – Health Economics
Conclusion
 Asymmetric information causes parties to
misrepresent themselves
 Adverse selection removes high-quality goods from
the market, leaving only low-quality
 Generally, the market will unravel unless:
 Someone values a product highly enough to have a
positive change in utility
 Government regulation through a price floor promotes a
minimum standard of quality
 One major concept has been missing in this whole
analysis: risk aversion.
 The Rothschild-Stiglitz model combines asymmetric
information and risk aversion.