Chapter 6:The Economics of Information and Choice Under Uncertainty Chapter Outline The Economics Of Information Choice Under Uncertainty Insuring Against Bad Outcomes Until this chapter, we assumed perfect information but in practice, decisions are made w/o such, i.e. under asymmetric information and uncertainty. Two issues in Chapter 6 1. how we gather and evaluate relevant information 2. Include uncertainty to Chapter 3 Consumer Choice Model. 1

Signaling A toad’s croak at night is a signal between potential advesaries –conveying information about its size Signaling: communication that conveys information. Two properties of signaling: between potential adversaries: Signals must be costly to fake (Costly-to-Fake Principle) If some individuals use signals that convey favorable information about themselves, others will be forced to reveal information even when it is considerably less favorable (The Full-disclosure Principle) 2

Costly-to-Fake Principle Costly-to-fake principle: for a signal to an adversary to be credible, it must be costly to fake, i.e. if a small toad could costlessly imitate the deep croak of big toads, then a deep croak is no longer the characteristic of big toads. Problem: Big toads have a natural advantage - the deepness of a croak alone emerges as a reliable signal. The Costly-to-Fake Principle has applications to signals between people in economic applications. Economic applications: Product Quality Assurance Choosing a Trustworthy Employee Choosing a Hard-Working, Smart Employee 3

Economic Applications of the Costly-to-Fake Principle Product Quality Assurance – products are so complex for the average consumer to determine the quality. To producers of high quality products who need to communicating such quality and hence charge higher prices, need to communicate via heavy advertising. The basis of such evidence that it works is that most consumers surveyed at purchase state “– as seen on TV.” Choosing a Trustworthy Employee – most employees steal or cheat their employers. Solution: choose from people who belong to a certain group whose behavior is difficult to fake over a long period. For example . Recruit New York nannies who belong to a group that would find it to fake –membership of a Mormon tradition! : Choosing a Hard-Working, and Smart Employee –choose graduates from an lite university and those who graduate with honors! But recall the recent story about cheating by undergraduates at Harvard. Problem – it is not clear how graduates from such institutions contribute to high productivity!

The Full-Disclosure Principle Figure 6.1: The Information Implicit in Silence The Full-disclosure Principle-individuals must disclose even unfavorable qualities about themselves, lest their silence be taken to mean that they have something even worse to hide. Explains smaller toads croak at all since their low pitch reveals their size or inadequacy in croaking! All toads crock to keep them from appearing smaller than they really are. The Full-Disclosure principle derives from asymmetric information – a silent toad knows its size BUT the rival can only make an informed guess.

Applications of Costly-to-Fake Principle Product Warranties Producers know much more than consumers about how good their products are. Producers of high quality products issue long and comprehensive warrants (liberal guarantees), e.g. Hyundai cars in the US. Henceforth, all Hyundai products might be deemed of credible quality. Regulating the Employment Interviewer Lack of evidence that something resides in a favored category will often suggest that it belongs to a less favored one. For example, laws prohibit asking the candidate his/her marital status. Reason – prevent employers from discriminating on basis of demographic information. Problem: smart candidates volunteer this information to get into the favorable pool! The Lemons Principle Cars offered for sale, taken as a group, are simply of lower average quality than cars not offered for sale. The Stigma of the Newcomer--- used to avoid ‘local bad reputation’ by relocating. Thus, a newcomer was often viewed as having bad reputation. Those deemed trustworthy in their locale, chose to reap those rewards. 6

Probability And Expected Value Economic decisions made under uncertainty are essentially gambles Expected value: the sum of all possible outcomes, weighted by its respective probability of occurrence. In addition to the expected value of a gamble (EV), most people also consider how they feel about each of its possible outcomes. People choose the alternative that has the highest expected utility. Expected utility: the expected utility of a gamble is the expected value of utility over all possible outcomes. The expected values of the outcomes of a set of alternatives need not have the same ranking as the expected utilities of the alternatives. 7

Probability And Expected Value Diminishing marginal utility: for a utility function defined on wealth, one in which the marginal utility declines as wealth rises. Fair gamble: a gamble whose expected value is zero. Type of Risk Preferences Risk averse: preferences described by a utility function with diminishing marginal utility of wealth. Risk seeking: preferences described by a utility function with increasing marginal utility of wealth. Risk neutral: preferences described by a utility function with constant marginal utility of wealth. 8

Figure 6.2: A Concave Utility Function The Von Neumann-Morgenstern Expected Utility Model – model of choice between uncertain alternatives Central Premise – people choose the alternative that has the highest expected utility (EU). Assume a utility function with numerical values to satisfaction associated with different outcomes. That is, the expected utility of a gamble is the expected value of utility over ALL possible outcomes. Concave Utility function – U(M)( where M= total wealth) is concave if for any pairs of M1 and M2, the function lies above the chord that joins [M1, U(M1)] and [M2, U(M2)] U(M) also exhibits diminishing marginal utility of wealth. People with a concave U(M) are Risk Averse – always refuse a gamble whose EV =0 Gambles with EV =0 are termed Fair Gambles (tossing a coin) 9

Figure 6.3: A Risk-Averse Person Will Always Refuse a Fair Gamble U(M) is concave in wealth (M) EU = ½ (18) + ½ (38) = 28 Note that 28 lies on the chord between 18 and 32 BUT under the gamble= 40 The EU of refusing the gamble is U(40) =32 >28 = EV It clear that a risk-averse consumer will reject not only fair gambles but even those with EV>0 Winning endpoint Losing endpoint For U(M), all gambles with EV wealth <52 yield lower EU than that of keeping initial wealth level at 40. Note: The arc between A and C = EV lies above the chord AC = EU. Thus, EV between A and C lies above the EU 10

Figure 6.4: The Utility Function of a Risk-Seeking Person is Convex in Total Wealth 11

Figure 6.5: Risk Neutrality 12

Figure 6.6: The Value of Reducing Uncertainty 13

Risk Pooling Law of large numbers: a statistical law that says that if an event happens independently with probability p in each of N instances, the proportion of cases in which the event occurs approaches p as N grows larger. Makes it possible for people to reduce their risk exposure through pooling arrangements. 14

Adverse Selection and Moral Hazard Adverse selection: process by which the less desirable potential trading partners volunteer to exchange. Moral hazard: incentives that lead people to file fraudulent claims or to be negligent in their care of goods insured against theft or damage. 15

Figure 6.9: The Reservation Price for Insurance 16

Figure A6.1: A Hypothetical Uniform Wage Distribution 17

Figure A6.2: The Expected Value of an Offer that is Greater than $150 18

Figure A6.3: The Acceptance Wage 19

Figure A6.4: A Hypothetical Price Distribution 20

Figure A6.5: The Acceptance Price as a Function of the Cost of Search 21

Figure A6.6: An Unbiased Estimate with a Uniform Distribution 22

Figure A6.7: The Expected Value of The Highest Estimate N = 1,2,3 & 4 23