Maurice faces the following options. He must first choose between (1a) and (1b), and then choose between (2a) and (2b).

(1a) $25 for sure

(1b) $36 with probability 20%, $25 with probability 79%, $0 with probability 1%

(2a) $36 with probability 20%, $0 with probability 80%

(2b) $25 with probability 21%, $0 with probability 79%

Suppose Maurice chooses (1a) and (2a).

1. Show that Maurice's choices are inconsistent with the Expected Utility Theory. Assume Maurice's initial wealth is 0.

2. Consider the Prospect Theory. Assume Maurice takes his endowment before choosing as his reference point. His value function is v(x) = x when x 0 and 2 x when x < 0 . His probability-weighting function () satisfies the following conditions: (0.2) = 0.2, (0.21) = 0.21, and (1) = 1. In order to explain Maurice's choices with the above v() and () functions, what additional condition does () (specifically, (0.79)) need to satisfy?