Ann is a participant in an experiment. Her value function is

v(x) =x/2 when x 0 and3x when x < 0

and her probability-weighting function is (p) = p for any p [0, 1]. In the experiment, Ann is asked to choose between

Option 1: receiving a sure $10, and Option 2: a lottery that pays $20 and $0 with equal probability.

1. (12 points) If Ann takes her endowment before participating in the experiment as her reference point, which option would she choose according to the prospect theory?

2. (12 points) Suppose Ann has participated in a different experiment before, and from that experiment, she earned $25. If Ann takes her earnings from the previous experiment as her reference point, which option would she choose according to the prospect theory?

3. (6 points) From your answers to Questions (2.1) and (2.2), what can you say about Ann's risk preference? Explain.