Question

2) (15 points) Suppose that Peter is an expected-utility maximizer who derives utility from his disposable income according to the function: U(I) = V1001, where I, measured in US dollars, represents his disposable income. Currently, Peter's disposable income is $90,000. There is a 1% chance that his Audi will be stolen. If this happens, his disposable income will be reduced to $10,000, since he will be spending $80,000 getting a new car. a) If Peter does not purchase auto insurance, what is his expected utility? b) Peter is given an option of buying an insurance policy priced at $500, which will fully insures him against his loss. What is his expected utility? Should Peter buy the insurance? c) What is Peter's maximum willingness to pay for an insurance policy that fully insures him against the car theft, i.e., paying him the entire amount if his car gets stolen?

Answer 1

10 T Dis pos able imceme in case of theft IT -$10.000 INT EDisposable inceme in caue of n0 theft -$90,000 Pr Probability of theft Probability s mo thaft PT PNT 0.49 a Expected uhuity uithout Tnsurana (Eu 99 x (10 INTto.01 (10I 0.99x 10 X90000 - 0.99 x 3 000 + 0.01X 1000 +0.01 X10 L0000 2930 t 10 2980

b) Prca imsuramteCx) s00 Se uith Insuranco, Inieme im case of tholt (I gooo0-80000 +80000 S00 89.500 case of No-Theft lINT) 900o0-s00 89,500 Incame in ane his epected uhlily ith full insurante LEu')- Pur T+ Pr UT +0.01X10 XI D:99x 10 xIT 9.4 XJ89500 83 500 1OX 29 91.66 Sine Eu Peter Should buy the insuramte Eu'

( ut be the maximum pnce Peter u fex full insurance uilling to bay Then, Income incase d theft (I) 900oo-g0000 tfoc00 goo0o-y 17 Iniome im caie f no thaft Tw 90000-4 tena hs enpected uhility (EU") 1 +Pr U PNT UNT + 0.01 X1OI INT -0.99 X10 x +0.1190000y 9.9 J90000-y 9cc0 -५ । o 190000-y Goc00y 9.4 +0.1)

Se. Petu wiu t and this insuaanio EU t0190000-y Jo000-y 2980 298 90000-4 2 88804 g0000 illorynes manimum tull insurane $1196 Hence Peter's pay tos