This question asks you to think about the mug experiments discussed in class in terms of actual utility functions. Let two dimensions of choice be mugs and money, with mugs being dimension 1 and money being dimension 2. Denote outcomes in mugs and money by c1 and c2, respectively, and reference points in the two dimensions by r1 and r2, respectively. The person's utility is given by:

4c1 + c2 + v(4c1 4r1)+ v(c2 r2),

where v(x) = 0.5x for x 0, and v(x) = 2x for x < 0. You can think of the first part of the utility function (4c1 + c2) as standard "consumption utility," and the second part (v(4c1 4r1)+ v(c2 r2)) as the reference-dependent "gain-loss utility."

a) Consider a variation on the mug-trade experiments. Some subjects (called the "choosers") are initially not given a mug or any money. Then, they are told that they can either have the mug or money, and are asked for the minimum amount of money which they would be willing to accept instead of the mug. Solve for this "choosing price."