These notes were prepared based on the lectures and supplemented by information from textbooks and tutorials where parts of the lecture were unclear. Graphs, equations, and bullet-point explanations included. Prepared by a first class Economics and Management student for the FHS Microeconomics pape...
MT7 Information Economics
Lecture 18: Adverse Selection and Screening
Outline:
Introduction
Adverse Selection
Insurance
Screening in insurance
Introduction
General equilibrium theory (1960s-1970s)
o If economic agents are rational (roughly: complete, transitive & continuous preferences,
ideally convex too), all market participants are non-strategic (price taker) and fully
informed, and all goods are traded (no externalities), then the market equilibrium is
efficient.
o Interventions, regulation cause distortions and efficiency loss
Government re-allocates for equity not efficiency purposes. Best to have lump-
sum approaches to minimise efficiency loss
Microeconomics since the 1980s: identify and propose 'fix' to market failures
o Failure of price taking: monopoly theory, Cournot and Bertrand oligopolies, other game-
theoretic models of imperfect competition
Fix: make markets contestable, or regulate natural monopolies
o Externalities: over- (respectively under-) production of negative (respectively positive)
externalities, missing public goods
Fix: create more markets (Coase), quantity v price regulation; mechanisms for
the public or private provision of public goods
o Asymmetric information: adverse selection and moral hazard
This week's content
Adverse selection
Agents in certain markets are heterogeneous: some “good” (highly productive), some “bad”
Agents privately know their Nature-given quality (type)
Adverse selection occurs when the wrong type of agent may make (offer or accept) a deal.
o Trade, or even an offer, may be bad news to one of the parties.
o Marx’s Maxim: I won’t belong to a club that will have me as a member”
Examples:
o Loan offered by bank may be accepted by high-risk borrowers who privately know that
they are unlikely to make payment
o Job offered by a firm at a wage equal to average productivity may be accepted by
below-average productivity workers
o Seller may offer used durable good (e.g., car) for sale only if its privately-known quality
is below average
o Individuals who know that they are careless or accident-prone may be more likely to
seek insurance
Goals of our analysis
, o Study the consequences, testable predictions of adverse selection
o Understand market solutions and develop guidelines for government intervention in
real-life situations
Akerlof’s market for lemons
Insight: adverse selection can shut markets
His model of the market for used cars, in words:
o the owner of a car has private information about its quality
o potential buyers realize this and may be reluctant to purchase for fear of buying a
“lemon”
o vicious circle: buyers are not willing to pay high price, at which sellers are not offering
good quality cars, and so on
o thin market for used cars; the market may even collapse
Numerical example
o The quality of a used car, q, is a random draw between 0 and 1, uniformly distributed
Pr[q ≤ x] = x
E[q|q ≤ x] = ½x
o The seller’s valuation for her car is its quality, q
o The buyer’s valuation for the same car is 1.5 × q (i.e., 50% more)
If there was perfect information trade would occur
o Only the seller knows q
o Both sides are price taker and risk neutral
o There is no trade that occurs
At price p ∈ [0, 1.5] sellers with cars of quality q ≤ p offer to sell
p ∈ [0, 1.5]: theoretically the maximum price buyers are willing to pay is
1.5 for cars q = 1 under perfect information
Buyers infer the average quality of used cars is E[q|q ≤ p] = ½p
Hence a buyer’s willingness to pay for an average used car is 1.5 × ½p = ¾p,
Since WTP < p, buyers will refuse to buy
There is no trade: the market unravels
o Cause: when an individual decides to sell a low-quality car, he affects the purchasers'
perceptions of the quality of the average car on the market
Subtleties: partial unravelling & multiple equilibria
Adverse selection does not necessarily cause a market to fully unravel and no trade to occur.
There can be partial unravelling of the market that produces multiple equilibria.
New example: assume three quality levels H = 100, M = 60, L = 20
o Seller’s valuation is q ∈ {H, M, L}; buyer’s is 50% more
o Seller knows q, buyer does not
o Assume Pr[H] = ½, Pr[M] = Pr[L] = ¼
o Assume that the seller, if indifferent, sells; the buyer, if indifferent, buys.
o Buyer is risk neutral (so we can just take WTP = EV*1.5)
There exists an equilibrium at p ∈ [100, 105], all q levels traded
o At p ≥ 100 all goods are supplied by sellers, since it is above their valuation
, o Since all goods are supplied, E[q] = ½*100 + ¼*60 + ¼*20 = 70
o Buyers’ WTP is 1.5 × 70 = 105
o If buyer's WTP ≥ p (105 ≥ p), they are happy to buy
Another equilibrium at p = 60 with q = L, M traded
o At p = 60, sellers supply L and M
o E[q|q ≤ p = 60] = ½*60 + ½*20 = 40
o Buyers’ WTP is 1.5 × 40 = 60 (buyers willing to buy only if 60 ≥ p)
o Hence, at p =60, sellers supply L and M, while buyers are willing to buy
Third set of equilibria at p ∈ [20, 30], only q = L traded
o At p ≤ 20, seller supplies L
o E[q|q ≤ p = 20] = 20
o Buyers’ WTP is 1.5 × 20 = 30 (buyers willing to buy only if 30 ≥ p)
o Hence, at p ∈ [20, 30], q = L is traded
Adverse selection FAQ
Does adverse selection always start at the top of the quality ladder? (Higher quality products
leave the market supply)
o Yes, if quality is ordered the same way with differing valuations
Who sets the market price?
o Nobody (or, if you like, the mythical “Walrasian auctioneer”)
o We ask, “what type of trades occur at a given price?”
o Need to manually check various price ranges: who sells, who buys
Any guidance on equilibrium price within a given range?
o If there are more sellers than buyers in the market, then presumably, they drive the
price to the bottom of the range
o If buyers outnumber sellers (at a given price) then vice versa
Quality choice
Unlike the lemons model, we consider a variation of the model where quality may be
determined by the producers.
If consumers value high-quality product at $14 and low-quality product at $8, and both the high-
and low-quality products costs producers $11.50. 3 possible cases:
o Only low-quality produced: no product sold, since cost of $11.50 > consumer WTP $8
o Only high-quality produced: product price is $11.50 due to competition, but consumer
WTP is $14, so there is consumer surplus. This is the socially optimal outcome/
o Both qualities produced (at least 7/12 is high-quality): 14q + 8(1-q) ≥ 11.5 (WTP > cost),
so 7/12 ≤ q ≤ 1
Same consumer WTP, but high-quality product costs $11.50 and low-quality product costs $11
o Each producer behaves competitively and believes that choosing to produce high/ low
quality has negligible effects on market price and perceived quality.
o All producers thus select the low-quality product, which means consumer WTP is $8 and
equilibrium is where no products are sold.
Adverse selection in insurance
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