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Berkeley ECON 100A - Lecture Notes

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Main topicsProbability distributionYou should know…Fair betGamblingAvoiding riskLOTTERIES A REAL LOTTERY A LITTLE STATISTICS A LITTLE STATISTICS EXPECTED UTILITY Utility of IncomeRISK PREFERENCES RISK AVERSE DECISION MAKER RISK AVERSE DECISION MAKEROTHER RISK PREFERENCESRISK PREMIUM RISK PREMIUMRISK PREFERENCES USING INDIFFERENCE CURVES RISK PREFERENCES USING INDIFFERENCE CURVESMRS WITH RISK MRS WITH RISKInsuranceHouse insuranceWith no insuranceWith insuranceCommercial insurance No insurance for terrorism and natural disastersDropping insurance coverageGovernment steps inThe Value of InformationThe Value of InformationThe Value of Information – ExampleThe Value of Information – ExampleThe Value of Information – ExampleBehavioral EconomicsBehavioral EconomicsBehavioral EconomicsBehavioral EconomicsBehavioral EconomicsBehavioral EconomicsBehavioral EconomicsBehavioral EconomicsMain topics1. Consumption under risk2. Decision-making under uncertainty3. Gambling and avoiding risk4. Demand for insurance5. Value of information6. Behavioral EconomicsProbability distribution• relates probability of occurrence to each possible outcome• first of two following examples is less certainfig. 1• Calculations• Expected values• Variance• Concepts/Terms• Fair bet• Risk averse vs. risk neutral vs. risk loving• Value of informationYou should know…Fair bet• wager with an expected value of zero• flip a coin for a dollar:[½ × (1)] + [½ × (-1)] = 0GamblingWhy would a risk-averse person gamble when the bet is unfair?• enjoys the game• makes a mistake: can’t calculate odds correctly• has Friedman-Savage utilityfig. 5Avoiding risk• just say no: don’t participate in optional risky activities• obtain information•diversify • risk pooling• diversification can eliminate risk if two events are perfectly negatively correlatedLOTTERIES • 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 payoffsand their corresponding probabilities* payoffs given by: Xn, n = 1,…,N * probabilities given by: prn, n = 1,…,Nwhere 0 < prn< 1 such that:pr1+ … + prN= 1A REAL LOTTERYCALIFORNIA MEGA MILLIONS LOTTERY“Match” Prize Odds / Probabilities Prob*Prize--------------------------------------------------------------------------------------------------------------------------------------------5+Mega Ball Grand Prize 1 in 175,711,536(e.g., $10M) 0.0000000057 $0.05 $175,000 1 in 3,904,701 0.0000002561 $0.044+Mega Ball $5,000 1 in 689,065 0.0000014512 $0.014 $150 1 in 15,313 0.0000653040 $0.013+Mega Ball $150 1 in 13,781 0.0000725637 $0.012+Mega Ball $10 1 in 844 0.0011848341 $0.013 $7 1 in 306 0.0032679739 $0.021+Mega Ball $3 1 in 141 0.0070921986 $0.02Mega Ball $2 1 in 75 0.0133333333 $0.03Nothing $0 97.5 in 100 0.9749820794 $0.00Expected Prize $0.21Note: payoffs are made at one time or over many years. Source: www.calottery.comExpected payoff = Expected Prize – Cost of ticket= $0.21 - $1.00= - $0.79A LITTLE STATISTICS• RANDOM VARIABLE• - Takes on values Xnwith probabilities prn• - Frequency distribution, e.g., bell-shaped grade distributionProbability1.0.90.80.70.60.50.40.30.20.100A LITTLE STATISTICSEXPECTED UTILITYUtility of IncomeRISK PREFERENCESQ. 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= 0A. If no, then they are “risk averse.” A. If yes, then they are either “risk neutral” or “risk loving”RISK AVERSE DECISION MAKERRISK AVERSE DECISION MAKEROTHER RISK PREFERENCESRISK PREMIUMThe “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 PREMIUMRISK PREFERENCES USING INDIFFERENCE CURVESRISK PREFERENCES USING INDIFFERENCE CURVESMRS WITH RISKMRS WITH RISKInsurance• risk-averse people will pay money—risk premium—to avoid risk• worldwide insurance premiums in 1998: $2.2 trillionLloyd BuildingHouse insurance• Scott is risk-averse• wants to insure his $80 (thousand) house• 25% chance of fire next year• if fire occurs, house worth $40With no insurance• expected value of house is$70 = (¼ × $40) + (¾ × $80) • variance$300 = [¼ × ($40 - $70)2] + [¾ × ($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 = (¼ × [-$3]) + (¾ × $1)• Scott fully insurances: eliminates all risk• pays $10 if no fire• receives $30 if fire• net wealth in both states of nature is $70Commercial insurance • is not fair• available only for diversifiable risks• Many important sources of risk are not diversifiable• natural disasters• terrorismNo insurance for terrorism and natural disasters• major natural disasters and terrorism are nondiversifiablerisks 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 1995Dropping 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


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Berkeley ECON 100A - Lecture Notes

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