1 Solve

Suppose Fox has reference-dependent preferences over money, stickers, and airplanes. Let

his consumption in money, stickers, and airplanes be c1, c2, and c3, respectively, and let his

reference points in money, stickers, and airplanes be r1, r2, and r3, respectively. Then, Fox's

utility is given by

v(c1 r1) + v(4c2 4r2) + v(4c3 4r3),

where v(x) = x for x 0, and v(x) = 2x for x < 0. Normalize Fox's initial amount of money

to zero, and suppose he starts off with zero stickers and zero airplanes.

1. What will be Fox's utility from losing two stickers, gaining one airplane, and gaining

$6?

2. Fox arrives at the experiment, and it turns out that he receives an $8 show-up bonus,

which he does not incorporate into his reference point for money. Suppose Fox is given

a sticker (and he does incorporate this into his reference point). Calculate his selling

price by (i) writing down his reference point; and (ii) solving for the price pS that

makes him indifferent between keeping his sticker and receiving nothing and giving up

his sticker and getting pS.

3. Now suppose Fox is not given a sticker. Calculate his buying price by (i) writing down

his reference point; and (ii) solving for the price pB such that he is indifferent between

getting a sticker for pB and not getting or paying anything.

4. Identify which of the prices pS and pB is different from the one we calculated in class.

Explain intuitively (and briefly) what drives the difference.

5. Argue briefly that Fox's buying and selling prices for airplanes are the same as for

stickers.

For the rest of the question, suppose that Fox has two options in the experiment: to buy

a sticker for $7, and to buy an airplane for $6.

6. Suppose Fox arrives at the experiment with a reference point of having one sticker and

one airplane (perhaps because he was told he could get these as gifts). His reference

point in money is still $0, and he still receives the $8 show-up bonus. Would he buy a

sticker for $7 if that was the only choice he was offered? Would he buy an airplane for

$6 if that was the only choice he was offered? Would he make both purchases? Briefly

explain the intuition.

7. Now suppose Fox can choose whether to enter the above experiment with a reference

point of getting the sticker or a reference point of getting the airplane, knowing the

prices in advance. (He still cannot choose his reference point in money, which is $0, and

he knows he will get $8.) Which one would he choose? Briefly explain the intuition.