See image 4. AUTO INSURANCE. Consider a standard auto insurance problem in which we assumewealth levels XG0OD =100 and XBAD=0, probabilities Pr[x600D]=Pr[O]=0.7 andPr[XBAD]=Pr[6]=0.3, administrative costs of 9, the utility function U[x]= Vx , and an insurancepolicy price set exactly halfway between the Insurer's willingness to accept and the Driver'swillingness to pay. TIP: Sketch the diagram and follow the lecture slides.a) Find the expected utility if the Driver is uninsured. Remember that EU is a weighted averageof the two utility levels, U[xc00D] and U[X®AD], based on their probabilities.b) Find the certainty equivalent, which is thexCE such that U[xCE] = sqrt[xCE] = EU.c) Find the expected claim, which is how much an insurer expects (on average) to pay to fix orreplace the car. EClaim = Pr[ OJ(xc00D – x600D) + Pr[®](x©00D – XBAD)d) What is the Driver's willingness to pay for an insurance policy? WTP = XG0OD – xCEe) How much of that WTP is a risk premium (the extra amount the Driver will pay “because hehates risk")? WTP = EClaim + Risk Premium.f) What is the Insurer's willingness to accept? This is the lowest amount the Insurer mustcharge in order to break even, on average. Remember that there are two expenses the Insurermust cover: WTA = E[Claim] + Adming) Find the insurance policy price, assumed to split the economic pie equally between theDriver and the Insurer (i.e., a price halfway between WTP and WTA sets consumer surplusequal to producer surplus).h) Find the insurer's expected profit (or PS) and its actual profit if there is an accident.i) MORAL HAZARD REDO! Show the effect on the Insurer's profit if, after the insurancepolicy price has been set and an insurance policy purchased, the fully insured Driver behavesrecklessly, resulting in Pr[XG00D] = ½. Ie., the Insurer thinks an accident occurs 30% of thetime, but it actually occurs 50% of the time. TIP: You essentially have to redo parts (a)-(h)with the new probabilities, but then assume the uninformed Insurer still sets the price foundin part (g).= 1/GOOD„GOOD

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4. AUTO INSURANCE. Consider a standard auto insurance problem in which we assume wealth levels XGOOD=100 and x BAD=0, probabilities Pr[xGOOD]=Pr[]=0.7 and Pr[xBAD]=Pr[]=0.3, administrative costs of 9, the utility function U[x] = √x, and an insurance policy price set exactly halfway between the Insurer's willingness to accept and the Driver's willingness to pay. TIP: Sketch the diagram and follow the lecture slides. a) Find the expected utility if the Driver is uninsured. Remember that EU is a weighted average of the two utility levels, U[x GOOD] and U[xBAD], based on their probabilities. b) Find the certainty equivalent, which is the xCE such that U[xCE] = sqrt[xCE] = EU. c) Find the expected claim, which is how much an insurer expects (on average) to pay to fix or replace the car. EClaim = Pr[](xGOOD – XGOOD) + Pr[](xGOOD – xBAD)

4. AUTO INSURANCE. Consider a standard auto insurance problem in which we assume wealth levels XGOOD=100 and x BAD=0, probabilities Pr[xGOOD]=Pr[]=0.7 and Pr[xBAD]=Pr[]=0.3, administrative costs of 9, the utility function U[x] = √x, and an insurance policy price set exactly halfway between the Insurer's willingness to accept and the Driver's willingness to pay. TIP: Sketch the diagram and follow the lecture slides. a) Find the expected utility if the Driver is uninsured. Remember that EU is a weighted average of the two utility levels, U[x GOOD] and U[xBAD], based on their probabilities. b) Find the certainty equivalent, which is the xCE such that U[xCE] = sqrt[xCE] = EU. c) Find the expected claim, which is how much an insurer expects (on average) to pay to fix or replace the car. EClaim = Pr[](xGOOD – XGOOD) + Pr[](xGOOD – xBAD)

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter16: Information, Risk, And Insurance

Section: Chapter Questions

Problem 10RQ: In an insurance system, would you expect each person to receive in benefits pretty much what they...

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In an insurance system, would you expect each person to receive in benefits pretty much what they pay in premiums or is it just that the average benefits paid will equal the average premiums paid?