Question

Moe owns jewelry that would cost $10,000 to replace if lost. There is a 0.1% chance that it would be lost or stolen in a given year. Moe’s utility function is U = W0.5, where W is wealth. Sketch a graph showing your answers to the following questions.

a.

How much would fair insurance cost that completely replaces the loss of the jewelry being stolen?

b.

What is Moe’s expected utility (incurring the risk)without insurance?

c.

To achieve the same level of utility in part (b), how much income with certainty (i.e., income amount with no risk of loss, or risk-free income) must Moe need?(Hint: you need to do a little mathematical manipulation. Set the utility level you found in part (b) equal to W0.5 and solve for W.)

d.

How much would Moe be willing to pay for an insurance policy that completely reimburses her in the event that the jewelry is lost or stolen?

e.

Why the difference between Moe’s willingness to pay and the actuarily fair insurance price?

Answer 1

Probability of loosing = p = 0.01

Probability of not loosing = 1-p = 0.99

Answer-a :-

fair insurance cost that completely replaces the loss of the jewelry being stolen

            = probability of losing * amount of loss

            = 0.01 * 10000 = 100 doller

Answer–b :-

Expected utility without insurance

            = p*u(w-10000) + (1-p)*u(w)

            =0.01*(w-10000)*0.5 + 0.99*w*0.5 = 0.005w-50 + 0.495w

            = 0.5w -500

Answer-c :-

            0.5w -500 = 0.5w ( w cannot be determine)

Answer-d :- cannot be determine

Answer-e :- cannot be determine