Question

Suppose the Ajax Insurance Company provides insurance for skydivers whose wealth before diving is $400. An accident will leave divers with a wealth of $100. The company divides the divers into two classes: safe (probability of an accident = 0.2) and unsafe (probability of an accident = 0.5). The utility of wealth for all divers is given by the function: U(w) = w^0.5. Can someone explain how they got the following answers, thanks.

1.1) The utility of wealth for all divers is given by the function: U(w) = w^0.5. If only the unsafe divers buy the insurance and the premium is $100, the insurance company will:

a.	earn a profit of $100 per unsafe diver.
b.	break even.
c.	incur a loss of $200 per unsafe diver.
d.	incur a loss of $300 per unsafe diver.
e.	experience none of the above.

ANS: C

1.2) Given this information, the divers are:

a.	risk-averse.
b.	risk seeking.
c.	risk-neutral.
d.	indifferent to risk.
e.	risk-averse, risk seeking, or risk-neutral; we cannot tell from this information.

ANS: A

Answer 1

1.1) Loss in case of accident = 400-100 = 300
Insurance premium = 100
loss per unsafe driver = 300-100 = 200

1.2) If utility increases more than the increase in money, then risk loving. If utility increases less than the increase in money, then risk averse.
W = 100, U(W) = 10
W = 400, U(W) = 20
W = 900, U(W) = 30
Therefore the rate of increase in utility decreases with the increase in wealth. Therefore, risk-averse.