Asymmetric Information I

1. Asymmetric Information I The value of information, adverse selection, signaling

2. Invisible hand theory and information • Our general equilibrium models have assumes that buyers are fully informed. • Given that consumers are not fully informed, they must employ strategies for gathering information. • Financial Market Research • Geographic studies of potential oil fields • Market research for new products • Time invested educating oneself about expensive products, • Searching for the best price

3. Optimal Investment in Acquiring Information • Keep acquiring more information until the expected marginal benefit equals the marginal cost. I* = the optimal quantity of information.

4. Example of price search You know that different stores charge different prices for the particular HP calculator you have decided to buy. Should you buy from the first store you visit, or should you search all the stores in your area? Suppose you visit the first store and find that they charge $500. Should you buy or continue searching? To search further is costly. What are the expected benefits?

5. Prior Beliefs and the quality of the outcome- low marginal benefit • Suppose you have a good idea of the price distribution. 500 • If you think $500 is already near the low end of the price distribution, then you don't stand to gain much.

6. High marginal benefit of drawing another price • Additional search will be more attractive if you think $500 is near the high end of the distribution. 500

7. Buy it Continue to search Acceptance price Optimal Search Rule • Based on your estimate of the distribution of available prices and the cost of search, you should choose an “acceptance price.” • Then keep searching until you find a calculator priced at least as low as the “acceptance price.”

8. Illustration of the principle • There is a spinning wheel numbered from 0 to 100. • You have won the right to buy a new HP calculator for a price in dollars equal to 10 multiplied by the number you get on the spinning wheel when you spin the pointer. • You spin and get 50, i.e., 500 dollars for the calculator A spin is like “randomly visiting a store”.

9. Constant Marginal Search Cost • Now suppose someone offers you a chance to spin again for a fee of $100. • If you end up with a higher number, you still pay only $500. • But if you get a lower number, you pay the lower amount. The chance to spin again is like “the chance of randomly visiting another store”.

10. The economic calculations • If you accept this offer, will you end up better off on the average? C = cost of spinning again = $100 B = expected benefits of spinning again • 50% of the time, the number you get will be greater than 50. • In those cases your benefit is zero. • 50% of the time, the number you draw is less than 50. • In these cases your benefit will lie between 0 and $500, for an average savings of $250. • On the average, your benefit from spinning again will therefore be • B = .5(0) + .5($250) = $125 > C = $100. So it is worth your while to spin again.

11. Search is a Gamble • The fact that you will do better on the average by searching further does not guarantee that your next search will make you better off. • For example, suppose you spin again and get 60, i.e., $600. Then you will have incurred a $100 cost and gotten nothing in return. • Should you spin for a cost of $100 again? • You should view the cost of your previous search as a sunk cost. So, yes, you should search again. • You made a good decision, but just happened to get a bad outcome.

12. Optimal stopping rule • Equate marginal benefit to marginal cost • For a price p, the probability of getting a lower price is 1- (p/1000), which results in a benefit of zero • The probability of getting a lower price is p/1000, and the conditional expected price is p/2 which yields a consumer surplus improvement of p/2. • equate MB and MC (p/2)*(p/1000) =100 => p2 =20000 or approximate 447

13. Observational learning, informational cascades and herding behavior • Sometimes we can gather “free” information by observing the actions of others • You are in a new town and you want to find a good place to eat, what do you do? • Should you invest in the stock market or not? • Should you buy real estate? • Which major do you choose at the university?

14. Example • I will need eight student volunteers, and I will place them in a random order. • Each student will have a chance to buy an single unit of an asset from me at a price of 6 RMB. • Prior to my “IPO” I toss a coin out of sight If it is heads each asset is worth 10 RMB, otherwise it is worth zero. I will not show you the result until after each of the 8 students makes a choice. • However, I will give each of you a hint. If the asset value is 10 I will put 2 red chips and 1 black chip in a bag. If the value is 0 I will put 1 red chip and 2 black chips in a bag. • Prior to making a decision a student to selects 1 chip from the bag at random, inspects the color prior to returning it to the bag. The other students can’t see the draw and the student is forbidden to share his info. • The student then makes a decision to buy or not buy the asset. Everyone observes this decision

15. Asset Valuation • If you observe the chips you can use Baye’s rule to calculate the posterior expected value. #Red - #Black Value #Red - #Black Value -4 0.58 1 6.67 -3 1.11 2 8.00 -2 2.00 3 8.89 -1 3.33 4 9.41 0 5.00

16. What if we learn from others • If the first student buys we know they observed a red chip, if no buy then it was a black chip – Assume it was a buy • If the second student receives a red chip as well he updates the value to $8, and buys as well • The third student knows the first two draws are red, notice if he observes red the value is $8.89 and if its black it’s $6.67. Both cases he buy, and there is no information sent to the market • Each subsequent student should also buy regardless of their private information – this is herding or an informational cascade

17. Adverse Selection -The Lemons Problem • Asymmetric information • A situation in which one side of the market—either buyers or sellers—has better information than the other. • Mixed market • A market in which goods of different qualities are sold for the same price.

18. THE LEMONS PROBLEM Uninformed Buyers and Knowledgeable Sellers • How much is a consumer willing to pay for a used car that could be either a lemon or a plum? To determine willingness to pay in a mixed market with both lemons and plums, we must answer three questions: • How much is the consumer willing to pay for a plum? • How much is the consumer willing to pay for a lemon? • What is the chance that a used car purchased in the mixed market will be of low quality? Consumer expectations play a key role in determining the market outcome when there is imperfect information.

19. Uninformed Buyers and Knowledgeable Sellers If buyers assume here is a %50 chance of getting a lemon, they are willing to pay $3,000 for a used car. At this price, 20 plums are supplied (point a) along with 80 lemons (point b). This is not an equilibrium because consumers’ expectations of a 50–50 split are not realized. If buyers assume all cars on the market are lemons, they are willing to pay $2,000 At this price, only lemons will be supplied (point c). Consumer expectations are realized, so the equilibrium is shown by point c, with an equilibrium price of $2,000.

20. Equilibrium with All Low-Quality Goods

21. Equilibrium with All Low-Quality Goods • The asymmetric information in the market generates a downward spiral of price and quality: • • The presence of low-quality goods on the market pulls down the price consumers are willing to pay. • • A decrease in price decreases the number of high-quality goods supplied, decreasing the average quality of goods on the market. • • The decrease in the average quality of goods on the market pulls down the price consumers are willing to pay again.

22. A Thin Market: Equilibrium with Some High-Quality Goods If buyers are pessimistic and assume that only lemons will be sold, they are willing to pay $2,000 for a used car. At this price, 5 plums are supplied (point a), along with 45 lemons (point b). This is not an equilibrium because 10 percent of consumers get plums, contraryto their expectations. If consumers assume that there is a 25 percent chance of getting a plum, they are willing to pay $2,500 for a used car. At this price, 20 plums are supplied (point c), along with 60 lemons (point d). This is an equilibrium because 25 percent of consumers get plums, consistent with their expectations. Consumer expectations are realized, so the equilibrium is shown by points c and d.

23. A Thin Market: Equilibrium with Some High-Quality Goods

24. Evidence of the Lemons Problem • The lemons model makes two predictions about markets with asymmetric information. • First, the presence of low-quality goods in a market will at least reduce the number of high-quality goods in the market and may even eliminate them. • Second, buyers and sellers will respond to the lemons problem by investing in information and other means of distinguishing between low-quality and high-quality goods.

25. Buyers Invest in Information The more information a buyer has, the greater the chance of picking a plum from the cars in the mixed market. Consumer Reports publishes information on repair histories of different models and computes a “Trouble” index, scoring each model on a scale of 1 to 5. By consulting these information sources, a buyer improves the chances of getting a high-quality car. Another information source is Carfax.com, which provides information on individual cars, including their accident histories. Reputation systems on auction sites like E-bay