《健康经济学》课件Chapter7.ppt

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1、Why buy insurance?,Demand for insurance driven by the fear of the unknown Hedge against risk-the possibility of bad outcomes Purchasing insurance means forfeiting income in good times to get money in bad timesIf bad times avoided,then money lost Ex:The individual who buys health insurance but never

2、visits the hospital might have been better off spending that income elsewhere.,Risk aversion,Hence,risk aversion drives demand for insurance We can model risk aversion through utility from income U(I)Utility increases with income:U(I)0Marginal utility for income is declining:U(I)0,Income and utility

3、,Graphically,Utility increasing with income U(I)0Marginal utility decreasing U(I)0,Adding uncertainty to the model,An individual does not know whether she will become sick,but she knows the probability of sickness is p between 0 and 1Probability of sickness is p Probability of staying healthy is 1-p

4、If she gets sick,medical bills and missed work will reduce her income IS=income if she does get sickIH IS=income if she remains healthy,Expected value,The expected value of a random variable X,EX,is the sum of all the possible outcomes of X weighted by each outcomes probability If the outcomes are x

5、1,x2,.,xn,and the probabilities for each outcome are p1,p2,.,pn respectively,then:EX=p1 x1+p2 x2+pn xn In our individuals case,the formula for expected value of income EI:EI=p IS+(1-p)IH,Example:expected value,Suppose we offer a starving graduate student a choice between two possible options,a lotte

6、ry and a certain payout:A:a lottery that awards$500 with probability 0.5 and$0 with probability 0.5.B:a check for$250 with probability 1.The expected value of both the lottery and the certain payout is$250:EI=p IS+(1-p)IH EA=.5(500)+.5(0)=$250EB=1(250)=$250,People prefer certain outcomes,Studies fin

7、d that most people prefer certain payouts over uncertain scenarios If a student says he prefers uncertain option,what does that imply about his utility function?To answer this question,we need to define expected utility for a lottery or uncertain outcome.,Expected Utility,The expected utility from a

8、 random payout X EU(X)is the sum of the utility from each of the possible outcomes,weighted by each outcomes probability.If the outcomes are x1,x2,.,xn,and the probabilities for each outcome are p1,p2,.,pn respectively,then:EU(X)=p1 U(x1)+p2 U(x2)+pn U(xn),Example,The students preference for option

9、B over option A implies that his expected utility from B,is greater than his expected utility from A:EU(B)EU(A)U($250)0.5 U($500)+0.5 U($0)In this case,even though the expected values of both options are equal,the student prefers the certain payout over the less certain one.This student is acting in

10、 a risk-averse manner over the choices available.,Expected utility without insurance,Lottery scenario similar to case of insurance customerShe gains a high income IH if healthy,and low income IS if sick.Uncertainty about which outcome will happen,though she knows the probability of becoming sick is

11、p Expected utility EU(I)is:EU(I)=p U(IS)+(1-p)U(IH),Consider a case where the person is sick with certainty(p=1):EU=U(IS)equals the utility from certain income IS(Point S)Consider case where person has no chance of becoming sick(p=0):EU=U(IH)equals utility from certain income IH(Point H),EU(I)and pr

12、obability of sickness,What if p lies between 0 and 1?,For p between 0 and 1,expected utility falls on a line segment between S and H,Ex:p=0.25,For p=0.25,persons expected income is:EI=0.25IS+(1-.25)IH Utility at that expected income is EU(I)(Point A),Expected utility and expected income,Crucial dist

13、inction betweenExpected utility EU(I)Utility from expected income U(EI)For risk-averse people,U(EI)EU(I),Risk-averse individuals,Synonymous definitions of risk-aversion:Prefer certain outcomes to uncertain ones with the same expected income.Prefers the utility from expected income to the expected ut

14、ility from uncertain income U(EI)EU(I)Concave utility functionU(I)0U(I)0,A basic health insurance contract,Customer pays an upfront feePayment r is known as the insurance premiumIf ill,customer receives q-the insurance payout If healthy,customer receives nothingEither way,customer loses the upfront

15、feeCustomers final income is:Sick:IH+q rHealthy:IS+0 r,Income with insurance,Let IH and IS be income with insuranceSick:IH=IH+q rHealthy:IS=IS+0 r Remember that risk-averse consumers want to avoid uncertaintyFor them,optimallyIH=IS,Full insurance,Full insurance means no income uncertaintyIS=IHFinal

16、income is state-independentRegardless of healthy or sick,final income is the sameRisk-averse individuals prefer full insurance to partial insurance(given the same price),Full insurance payout,State independence impliesIH=ISSoIH+0 r=IS+q rIH=IS+qq=IH ISThe payout from a full insurance contract is dif

17、ference between incomes without insurance,Actuarially fair insurance,Actuarially fair means that insurance is a fair beti.e.the premium equals the expected payoutr=p qInsurer makes zero profit/loss from actuarially fair insurance in expectation,Actuarially fair,full insurance,Notice consumers with a

18、ctuarially fair,fullinsurance achieve their expected income withcertainty!,Insurance and risk aversion,As we have seen,simply by reducing uncertainty,insurance can make this risk-averse individual better off.Relative to the state of no insurance,with insurance she loses income in the healthy state(I

19、H IH)and gains income in the sick state(IS IS).In other words,the risk-averse individual willingly sacrifices some good times in the healthy state to ease the bad times in the sick state.,Insurer profits,Now consider the same insurance contract from the point of view of the insurerPremium rPayout qP

20、robability of sickness pE=Expected profits,Fair and unfair insurance,In a perfectly competitive insurance market,profits will equal zeroSame definition as actuarially fair!An insurance contract which yields positive profits is called unfair insurance:An insurer would never offer a contract with nega

21、tive profits,Full vs.partial insurance,Partial insurance does not achieve state-independenceSize of the payout q determines the fullness of the contract Closer q is to IH IS,the fuller the contract,Comparing insurance contracts,AF-Actuarially fair&fullAP-Actuarially fair&partialA-UninsuranceU(AF)U(A

22、P)U(A),The ideal insurance contract,For anyone risk-averse,actuarially fair&full insurance contract offers the most utilityHence,it is called the ideal insurance contractIdeal and non-ideal insurance contracts:,Comparing non-ideal contracts,AF Full but actuarially unfair contractAP Partial but actua

23、rially fair contract,Comparing non-ideal contracts,In this case,U(AF)U(AP)Even though AF is actuarially unfair,its relative fullness(i.e.higher payout)makes it more desirableBut notice if contract AF became more unfair,then expected income EI fallsIf too unfair,AF may generate less utility than APSi

24、milarly,AP may become more full by increasing its payoutUncertainty falls,so point AP movesAt some point,this consumer will be indifferent between the two contracts,Conclusion,Demand for insurance driven by risk aversionDesire to reduce uncertaintyDiminishing marginal utility from incomeU(I)is concave,so U(I)EU(I)Risk aversion can explain not only demand for insurance but can also help explainLarge family sizesPortfolio diversificationFarmers scattering their crops and land holdings,