Problem 3 [20 points]. Connor is a strictly risk-loving expected utility maximizer. He possesses treasure in the amount of w > 0, but with probability it > O he suffers a loss D > O. He can buy insurance. A policy that pays off $1 in case of loss costs p > 0, so if he buys a units of insurance he pays pa dollars. He cannot buy negative insurance, nor can he spend more than w on insurance. He can afford full insurance. Connor's Bernoulli utility function is increasing and twice continuously differentiable. 1) [5 points] Write out Connor's expected utility maximization problem and the associated first order conditions. 2) [4 points] Show that if p = it, then there is a solution to the first-order conditions where the amount of insurance that Connor purchases is equal to D (that is, full insurance). 3) [6 points] Show, however, that if p = it, then full insurance does NOT maximize Connor's expected utility. (HINT: Show that when p = It, expected utility increases when a > D). Explain in words why Connor prefers being over-insured (a > D) to having full insurance (a = D) when p = It. 4) [5 points] Show that if p = It, Connor prefers no insurance (a = 0) to a small positive amount. Provide an intuitive explanation