Question

5. Green likes to speed and has an expected cost of speeding of $21.25. a. A ticket for going 20 miles per hour over the speed limit is $425. What is Green's perceived probability of getting caught at this speed if Green is risk neutral? (Hint, consider the expected cost formula EC = P1*Sticket + PNT*$no ticket, which is a version of the expected value formula.) b. What is Green's expected wealth if his initial wealth is $2.025 and he speeds? (Expected, not actual wealth.) c. Suppose Green has a utility function U=w12, where w is wealth, which is currently $2,025. What is the decrease in Green's utility if he gets a speeding ticket? d. What is Green's expected utility of speeding? Use the probability you found in part a. e. What is the certainty equivalent of wealth for Green's speeding activity? f. What is the maximum Green would be willing to pay for speeding insurance"? That is, how much would Green pay for insurance that would pay for his speeding tickets if he were caught speeding?

Answer 1

ANSWER

a)

As given in hint

EC = P_T*$ticket + P_NT*$no ticket

We have

EC=$21.25, $ticket=$425, $noticket=0.

Plug in given values in above relation

21.25 = P_T*425 + P_NT*0

P_T=0.05 (perceived probability)

b)

Wealth in case, he is caught=2025-425=$1600

Wealth in case, he is not caught=$2025

Expected wealth=P_T*wealth if caught+(1-P_T)*wealth if not caught

Expected wealth=0.05*1600+(1-0.05)*2025=$2003.75

c)

Utility in case he is not caught=U(2025)=2025^0.5=45 utils

Utility in case he is caught=U(1600)=1600^0.5=40 utils

Decrease in utility=45-40=5 utils

d)

Expected utility=PT*U(1600)+(1-PT)*U(2025)=0.05*40+0.95*45=44.75 utils

e)

Certainty equivalent will be equal to wealth level (say Y) such that utility at Y is equal to expected utility of speeding.

U(Y)=44.75

Y^0.5=44.75

X=44.75²=2002.56

f)

Maximum willingness to pay for insurance=2025-2002.56=$22.44