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.If only the unsafe divers buy insurance and the premium is $100,the insurance company will:

Question

Quizplus · Accepted Answer

Firstly, let's calculate the expected utility of wealth for an unsafe diver without insurance:
U(400) = 400^(0.5) = 20

Now, let's calculate the expected utility of wealth for an unsafe diver with insurance:
U(300) = 300^(0.5) = 17.32 (wealth after deducting the premium)
U(100) = 100^(0.5) = 10 (wealth after accident)

EU(insured) = 0.5*U(300) + 0.5*U(100) = 13.66

By buying insurance, the expected utility of wealth for an unsafe diver decreases from 20 to 13.66. Hence, unsafe divers have no incentive to purchase insurance.

Since no unsafe diver will buy insurance, the company can only earn premiums from the safe divers. However, the premiums collected will be insufficient to compensate for the claims made by unsafe divers. The expected cost of claims per unsafe diver is (0.5)*(300-100) = $100. Hence, for every unsafe diver, the company will incur an expected loss of $100 - $100 (premium) = -$200.

Therefore, the insurance company will incur a loss of $200 per unsafe diver.

Suppose the Ajax Insurance Company Provides Insurance for Skydivers Whose