Consumers may be incompletely informed about states. Difference between imperfect information and asymmetric information

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1 Chapter 10 Asymmetric information and agency Complete information versus incomplete information Consumers may be incompletely informed about states Difference between imperfect information and asymmetric information Various cases Symmetric information Asymmetric information Perfect information First best n/a Imperfect information Uncertainty Adverse selection Asymmetric information usually involves some strategic issue 1

2 State of nature: the central concern in the health model Common value vs private value Example of private value: how much does one enjoy the weather? Example of common value: what is the extent of loss? Similarly, what is the probability of loss Asymmetric information about common value: adverse selection problem 2

3 Ackerlof s lemons problem There are various quality levels of a used car. There are 200 cars; all of them similar although their qualities actually differ For each car, its quality is uniformly distributed on [0,2] Let q denote the quality. The number of cars with quality less than q is 100*q A quality-q car is worth q to the seller (who owns it) A quality-q car is worth 1.5q to the buyer (who considers buying it) Note that it is common knowledge that for a given level of quality, a buyer values the car higher than the seller 3

4 Suppose that the market work through an auctioneer A price is called out by the auctioneer All those buyers who want to buy at this price record their demands All those sellers who want to sell at this price record their supplies An equilibrium is a price such that demand equals supply The adverse selection problem: buyers infer quality from the market price Only those sellers with car quality below market price will want to sell 4

5 Can a price of 2 be an equilibrium? At 2 every owner wants to sell so supply is 200 But if every owner wants to sell, all cars are in the market, and therefore a buyer only gets a car of average quality: the market quality is 1 A buyer s willingness to pay is therefore 1.5 At price 2, there is no buyer 5

6 How about a price of 1.2? At price 1.2, owners of cars with quality less than q = 1.2 will sell The average quality of cars in the market becomes 0.6 But with the average quality at 0.6, the average car is worth 1.5*0.6 = 0.9 to a buyer Again, at price 1.2, there is no buyer 6

7 What about an equilibrium at price p? At price p, all sellers with quality less than p will sell Average quality of cars in market is p/2 The average value of a car in the market is p/2 * 1.5 < p Again, there is no buyer Although it is common knowledge that a trade is mutually beneficial if the value of q is known, no trade can occur when q is only known to the seller The seller makes sell decision on his valuation; a marginal decision Yet, the price measures the average quality in the market 7

8 How does it apply to health insurance? Let M be the expected medical expenditure of an insured M is uniformly distributed on [0,20,000], and there are many consumers Suppose an insurance plan covers all medical expenses when the insured become sick Suppose that consumers know their value of M, but not the insurance companies 8

9 Can there be an equilibrium premium where a plan breaks even? Can it be P? If the plan offers an insurance of P, those with M > P will join That means the average expenditure will be [ P]/2 = P/2 To cover that the premium will have to be P/2 That is, P = P/2, or P = But at P = 20000, no consumer will buy insurance 9

10 Ways to overcome adverse selection Groups Ultimate group: national health insurance---not health care reform in the US Experience ratings: premium adjusts according to outcomes Report cards: NCQA 10

11 Physician agency The physician acting on behalf of the patient Often the interaction involves asymmetric information: the physician learns about the patient s condition, in a way that is unknown to the patient Credence goods market 11