Hi...my professor sent me this problem set with answers, but I am bit confused with the steps. Can you please explain me the STEPS.... thank you.

Ben is a proud owner of a romantic mansion facing the lake Mendota worth $500,000. The location attractive as it is, however has one drawback. Occa- sionally in the spring heavy rains raise the water level in the lake, flooding the house. When this happens, the value of the house drops to $50,000. The flood occurs with probability 10%. Ben finds the situation too stressful and therefore he is going to sell the house in the summer (after the potential flood).

Ben has the utility function U(x) =w , where w represents his wealth after the season (value of the house, plus any insurance, minus insurance payments, we usually assume).

(a) Based on Ben's utility function, is he risk loving, risk averse, or risk neutral? Explain how you can tell.

(b) Without insurance, what is Ben's certainty equivalent wealth? What is the expected value of Ben's wealth? Which is bigger and how does this relate to the answer in part (a)?

(c) Suppose Ben can buy insurance. The insurance company provides X dollars of coverage for a premium of .11X. Does Ben buy insurance, and if so, how much coverage does he purchase?

(d) Extra: Suppose instead of charging as in (c), the insurance company charge .1X plus a fixed fee of $4,500. Will the consumer buy more, less, or the same level of coverage (X) as you found in part (d)? Hint: You don't have to compute this analytically, but rather pro- vide an intuitive explanation. Of course, you can always calculate it analytically if you are unsure.

Answer.

(a) Risk averse. U = 1/2w.5. and so. U"= 1/4w1.5 <0. (or state that utility function is concave)

(b) EU = 658.76 so CE = 433,961.

The expected value is EV = 455,000.

Can you pls show the steps

He is risk averse which means he would accept less than the EV with certainty.

(c) The objective:

max.9500, 000 .11X + .150, 000 + .89X X)

The FOC yields a solution of X = 361, 794.

Please show me the steps

(d) If he buys insurance, he will buy full insurance. A risk averse con- sumer will buy full insurance if the price is fair. The fixed fee is less than the difference between the EV and CE.

THANK YOU