Question

NEED HELP!!!!!PLZ!

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

A) when lost half of wealth, then bad state wealth = 100,000/2

= 50,000

So Expected wealth = .9*100,000+ .1*50,000

= 90,000+5,000

= 95,000

b)

as when an insurance firm breaks even

then, net expected loss = net expected gain

πM = (1-π)*(B-M)

π: probability of good state

M : premium, B: promised benefit in bad state

πM = B-M - πB + πM

M = B-πB

M = B*(1-π)

B = 50,000

since full insurance, so entire loss is compensated in bad state

π= .9

so premium = .1*50,000

= 5000

C) now Maximum premium , willing to pay

= Initial wealth - Certainty Equivalent

= 100,000-85,000

= $ 15,000

​​​​​