Question 7 (a) Suppose that Jane is an expected utility maximizer with u(x) = -e-0.0027, and has initial wealth is $50,000. Derive how Jane feels about the following bets: (i) Jane will accept (-100, 3;X, ) if and only if X >???? (ii) Jane will accept (-150, };X, ) if and only if X >???? (iii) Jane will accept (-200, }; X, ) if and only if X >???? (iv) Jane will accept (-300, }; X, }) if and only if X > ???? (b) Like Jane, Charles has initial wealth $50,000. But unlike Jane, Charles evaluates gambles according to prospect theory with x(p) = p and X if x 2 0 v (x ) = ax if x 5 0. If we observe that Charles accepts (-100, ;; X, ) if and only if X > 185, what can we conclude about Charles's a? (c) Suppose that Charles has the 2 that you found in part (b), and derive how he feels about the following bets: (i) Charles will accept (-150, };X, ) if and only if X >???? (ii) Charles will accept (-200, }; X, ) if and only if X > ???? (iii) Charles will accept (-300, };X, ) if and only if X &gt