2. 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) Does this formulation capture loss aversion? Does it capture diminishing sensitivity?

(b) Argue that the reference point of an owner of the mug is r1 = 1 and r2 = 0. Given this reference point, solve for the “selling price”, the mini-mum price at which an owner is willing to part with her mug.

(c) What is the reference point of a non-owner of a mug? Give both r1 and r2. Solve for the “buying price”, the maximum price at which a non-owner is willing to buy a mug.

(d) In a graph with mugs on the horizontal axis and money on the vertical axis, draw indifference curves for non-owners. In a second graph draw indifference curves for mug owners. Indicate how to read off the buying and selling prices from the graph. Hint: the indifference curves will be piecewise linear

(e) Consider a variation on the mug-trade experiments discussed in class. 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 willingto accept instead of the mug. Solve for this “choosing price.”

(f) Suppose a non-owner finds $2 on the street just before her buying price is elicited, and does not adjust her reference point in money to this find. What would her buying price be? Explain the intuition.