Annie is considering a bet with a 60% chance of winning $7,000 and a 40% chance of losing $6,000.

Annie's utility function is:

u(w)= 1 e^w/10,000

where e 2.7183 and w is equal to wealth. Her current wealth is $8,000.

(a) Will she accept the bet in order to maximize her expected utility? Provide complete solutions.

(b) Assume that Annie's behavior is consistent with prospect theory, the value function of which is the following:

v(x) = {x^0.5 if x 0, 2(x)^0.5if x < 0}

Will Annie accept the bet? Provide a complete solution.