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. 51作业君版权所有
