A family's wealth w has utility u(w) = w^1/2 and the family has VNM utility relative to choices under uncertainty. The family's initial wealth is w₁ = 100 and there is a p = 50% probability of a damage L = 64, which would reduce wealth to w₂ = 36.

(a)Determine the expected value E(w) of the family's wealth without insurance.

(b)Determine the expected utility of the lottery describing the two possible wealths of the family if no insurance is purchased.

(c) Determine the maximum price P the family is ready to pay for complete insurance, and

the associated risk avoidance price R i.e. benefit from elimination of risk, and show that

P=d+R (where d is the expected value of the damage reimbursement with complete insurance).