Stephen has wealth of $200 and faces a possible loss of $100. The probability of the loss is 1/8. Stephen is risk averse and has the following utility of wealth function. u(w) = w 1/2 Stephens brother Lucas on the other hand, is risk neutral with utility of wealth u(w) = w. a. Show that, whatever his wealth level, Lucas is indifferent between offering Stephen insurance that is actuarially fair and doing nothing. In other words, show that Lucass expected utility of offering fair insurance is equal to his expected utility if he does nothing. b. Find Stephens Arrow-Pratt coefficient of absolute risk aversion. c. Show that if Lucas offers Stephen fair insurance, Stephen will insure completely. d. Unfortunately, one day Lucas lands himself in jail and is no longer able to offer Stephen insurance. Stephen is forced to turn to Mr. Big for his insurance now and Mr. Big charges $0.80 for each dollar of insurance he provides. How much insurance does Stephen buy now?