复旦大学本科微观经济学lectu.ppt

Main topics Consumption under risk Decision-making under uncertainty Gambling and avoiding risk Demand for insurance Value of information Behavioral Economics Probability distribution relates probability of occurrence to each possible outcome first of two following examples is less certain fig. 1 Calculations Expected values Variance Concepts/Terms Fair bet Risk averse vs. risk neutral vs. risk loving Value of information You should know Fair bet wager with an expected value of zero flip a coin for a dollar: (1) + (-1) = 0 Gambling Why would a risk-averse person gamble when the bet is unfair? enjoys the game makes a mistake: cant calculate odds correctly has Friedman-Savage utility fig. 5 Avoiding risk just say no: dont participate in optional risky activities obtain information diversify risk pooling diversification can eliminate risk if two events are perfectly negatively correlated LOTTERIES A “lottery” is the prospect with known (monetary) payoffs, each one with a known probability of occurring Can represent a lottery by a list of payoffs and their corresponding probabilities * payoffs given by: Xn , n = 1,N * probabilities given by: prn , n = 1,N where 0 prn 1 such that: pr1 + + prN = 1 A REAL LOTTERY CALIFORNIA MEGA MILLIONS LOTTERY “Match”PrizeOdds /Probabilities Prob*Prize - 5+Mega Ball Grand Prize 1 in 175,711,536 (e.g., $10M) 0.0000000057 $0.0 5$175,0001 in 3,904,7010.0000002561$0.04 4+Mega Ball$5,0001 in 689,0650.0000014512 $0.01 $1501 in 15,3130.0000653040$0.01 3+Mega Ball$1501 in 13,7810.0000725637 $0.01 2+Mega Ball$101 in 8440.0011848341 $0.01 3$71 in 3060.0032679739$0.02 1+Mega Ball$31 in 1410.0070921986 $0.02 Mega Ball$21 in 750.0133333333 $0.03 Nothing$097.5 in 1000.9749820794$0.00 Expected Prize$0.21 Note: payoffs are made at one time or over many years. Source: Expected payoff = Expected Prize Cost of ticket =$0.21 - $1.00 =- $0.79 A LITTLE STATISTICS RANDOM VARIABLE - Takes on values Xn with probabilities prn - Frequency distribution, e.g., bell-shaped grade distribution Probability 1.0 .90 .80 .70 .60 .50 .40 .30 .20 .10 0 A LITTLE STATISTICS EXPECTED UTILITY Utility of Income RISK PREFERENCES Q. Is the decision maker willing to take a “fair bet”? Where a “fair bet” is a lottery for which the expected payoff is zero: E(X) = pr1*X1 + pr2*X2 + + prN*XN = 0 If no, then they are “risk averse.” A. If yes, then they are either “risk neutral” or “risk loving” RISK AVERSE DECISION MAKER RISK AVERSE DECISION MAKER OTHER RISK PREFERENCES RISK PREMIUM The “risk premium” of a lottery is the amount the decision maker would give up to have certain outcome rather than the lottery. Mathematically, “risk premium” equates the expected utility to the utility of the expect value. RISK PREMIUM RISK PREFERENCES USING INDIFFERENCE CURVES RISK PREFERENCES USING INDIFFERENCE CURVES MRS WITH RISK MRS WITH RISK Insurance risk-averse people will pay moneyrisk premiumto avoid risk worldwide insurance premiums in 1998: $2.2 trillion Lloyd Building House insurance Scott is risk-averse wants to insure his $80 (thousand) house 25% chance of fire next year if fire occurs, house worth $40 With no insurance expected value of house is $70 = ( $40) + ( $80) variance $300 = ($40 - $70)2 + ($80 - $70)2 With insurance suppose insurance company offers fair insurance lets Scott trade $1 if no fire for $3 if fire insurance is fair bet because expected value is $0 = ( -$3) + ( $1) Scott fully insurances: eliminates all risk pays $10 if no fire receives $30 if fire net wealth in both states of nature is $70 Commercial insurance is not fair available only for diversifiable risks Many important sources of risk are not diversifiable natural disasters terrorism No insurance for terrorism and natural disasters major natural disasters and terrorism are nondiversifiable risks because such catastrophic events cause many insured people to suffer losses at the same time more homes have built where damage from storms or earthquakes is likely, larger potential losses to insurers from nondiversifiable risks insurance companies major losses in 1990s: $12.5 billion for losses in the 1994 Los Angeles earthquake $15.5 billion for Hurricane Andrew in 1992 (total damages were $26.5 billion) $3.2 billion for damage from Hurricane Fran in 1995 Dropping insurance coverage Farmers Insurance Group reported that it paid out three times as much for the Los Angeles earthquake as it collected in earthquake premiums over 30 years. insurance companies now refuse to offer hurricane or earthquake insurance in many parts of the country for these relatively nondiversifiable risks Nationwide Insurance Company announced in 1996 that it was sharply curtailing sales of new policies along the Gulf of Mexico and the eastern seaboard from Texas to Maine a Nationwide official explained, “Prudence requires us to diligently manage our exposure to catastrophic losses.” Government steps in in some areas, state-run pools provide insurance coverage Florida Joint Underwriting Association California Earthquake Authority worse deal: these policies extend less protection rates are often 3x more than the previously available commercial rates require large deductibles The Value of Information Risk often exists because we dont know all the information surrounding a decision Because of this, information is valuable and people are willing to pay for it The Value of Information The value of complete information The difference between the expected value of a choice with complete information and the expected value when information is incomplete The Value of Information Example Per capita milk consumption has fallen over the years The milk producers engaged in market research to develop new sales strategies to encourage the consumption of milk The Value of Information Example Findings Milk demand is seasonal with the greatest demand in the spring Price elasticity of demand is negative and small Income elasticity is positive and large The Value of Information Example Milk advertising increases sales most in the spring Allocating advertising based on this information in New York increased profits by 9% or $14 million The cost of the information was relatively low, while the value was substantial (increased profits) Behavioral Economics Sometimes individuals behavior contradicts basic assumptions of consumer choice More information about human behavior might lead to better understanding This is the objective of behavioral economics Improving understanding of consumer choice by incorporating more realistic and detailed assumptions regarding human behavior Behavioral Economics There are a number of examples of consumer choice contradictions You take at trip and stop at a restaurant that you will most likely never stop at again. You still think it fair to leave a 15% tip rewarding the good service. You choose to buy a lottery ticket even though the expected value is less than the price of the ticket Behavioral Economics Reference Points Economists assume that consumers place a unique value on the goods/services purchased Psychologists have found that perceived value can depend on circumstances You are able to buy a ticket to the sold out Cher concert for the published price of $125. You find out you can sell the ticket for $500 but you choose not to, even though you would never have paid more than $250 for the ticket. Behavioral Economics Reference Points (cont.) The point from which an individual makes a consumption decision From the example, owning the Cher ticket is the reference point Individuals dislike losing things they own They value items more when they own them than when they do not Losses are valued more than gains Utility loss from selling the ticket is greater than original utility gain from purchasing it Behavioral Economics Experimental Economics Students were divided into two groups Group one was given a mug with a market value of $5.00 Group two received nothing Students with mugs were asked how much they would take to sell the mug back Lowest price for mugs, on average, was $7.00 Behavioral Economics Experimental Economics (cont.) Group