Question

4) A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year.

a. (5) What is the consumer’s expected wealth one year from now?

b. (5) An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? Explain.

c. (5) Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the above described uncertain situation. What is the maximum premium that the insurance company will be able to charge this consumer for its full insurance policy? Explain.

Answer 1

Q4) a) in good state wealth , = 100,000

Cg = 100,000, Cb = 50,000

Pg = .9, Pb = .1

Expected wealth = Cg*Pg + Cb*Pb

= 100,000*.9 + 50,000*.1

= 90,000 + 5000

= $ 95,000

b) the required premium value = loss in bad state* probability of loss

= 50,000*.1

= $ 5000

C) the maximum premium = Initial wealth - certainty equivalent of the risky gamble

= 100,000 - 85,000

= $ 15,000