A risk-averse individual who maximizes the expectation of the utility function U has an initial wealth W. he faces the possibility of an accident that occurs with probability p > 0 (which he cannot affect). The accident would result in damages d> 0. An insurance company offers him the following deal: if he pays an initial premium of k+px where k> 0 the company will pay him x in the event of an accident. He can choose any nonnegative value of x.

a; is this deal actuarially fair or unfair? Explain

for the rest of the problem, suppose that he decides to buy a strictly positive amount of insurance

b; find his FOC for an interior maximizer

c; will he fully insure himself? Why or why not?

d; discuss the relationship of your answers to a and c.