Question

1. Michelle wants to hike the West Coast Trail and plans to take $900. With probability 1/10 she will loose $500 on her way. Thus she will spend $900 on her way is she is lucky, and only $400 is she is not lucky. Her utility form the trip is given by U(E) = E/?, where E is the amount of money she spends on the trip. (a) What is the Michelle's expected utility form the trip? (b) Suppose Michelle can buy an insurance policy that will cover the en- tire $500 loss. Will she buy it if the price is $60? $59? $50? (c) What is Michelle's reservation price for this insurance policy? (d) What is the competitive equilibrium price of the policy is the insurance companies have perfect information and incur no transaction costs?

Answer 1

a)

Probability of loss=p=1/10=0.10

Spending in case of loss=$400

Utility in case of loss=U(400)=400^1/2=20 utils

Probability of no loss=1-p=1-1/10=0.90

Spending in case of no loss=$900

Utility in case of no loss=U(900)=900^1/2=30 utils

Expected utility=p*U(400)+(1-p)*U(900)=0.10*20+0.9*30=29 utils

b)

Let the person's maximum willingness to pay for insurance is X, then in case of insurance

U(900-X)=Expected utility without insurance=29

(900-X)^1/2=29

900-X=29²=841

X=$59

Michelle would pay a maximum of $59 to avoid uncertainty.

So, Michelle will buy insurance if price of insurance is $59 or $50. He will not buy insurance at a price of $60.

c)

Reservation price=X=$59

d)

Competitive price of insurance=p*insured amount=0.10*500=$50