Consider the model of insurance: an expected-utility-maximising decision-maker has

wealth w = 4, faces a risk 0 < q < 1 of damages d = 2, and has access to insurance

contracts of the form (P, R) = ( (q/2)R, R), where P is the premium the decision-maker pays

to the insurance company and 0 R d is the reimbursement the insurance company delivers to the decision maker if she suffers damages. Finally, assume that the decision- maker's utility function over money consequences C = R is such that u(c) = C

(a) [2] Given any 0 R d, is the insurance contract (P, R) = ( 2q R, R) actuarially fair?

Explain why or why not.

b)Given any 0 R d, derive the decision-maker's expected utility from the insurance contract (P, R) = ( (q/2)* R, R).

(c)[2] What is the decision-maker's optimal choice of insurance coverage R*?