Fox has reference-dependent preferences over money. Let his realized outcome in money bec1, and his reference point in money ber1. Then, Fox's utility is given by

v(c1r1),

wherev(x) =xforx0, andv(x) = 2xforx <0. Normalize Fox's initial amount of money

to zero.

1. What will be Fox's utility from gaining $7?
2. What will be Fox's utility from losing $7?
3. Fox has just agreed to take part in an experiment, and he was told by the organizers that hemightreceive $14 for his participation. Suppose Fox canchoosewhether to incorporate these $14 into his reference point. Calculate his utility with a reference point of $0 and a reference point of $14 if he receives $14 for his participation. Calculate his utility with a reference point of $0 and a reference point of $14 if he receives $0 for his participation. Which reference point yields higher utility? Explain the intuition.

Now suppose Fox has reference-dependent preferences over money and stickers. Let his consumption in money and stickers bec1andc2, respectively, and let his reference points in money and stickers ber1andr2respectively. Then, Fox's utility is given by

v(c1r1) +v(4c24r2),1

wherev(x) =xforx0, andv(x) = 2xforx <0. Normalize Fox's initial amount of money to zero, and suppose he starts off with zero stickers.

1. What will be Fox's utility from gaining three stickers?
2. What will be Fox's utility from losing two stickers?
3. What will be Fox's utility from gaining four stickers and losing $7?
4. What is Fox's choosing price for one sticker. That is, what is the amount of moneypCthat would make Fox indifferent between gaining one sticker and gainingpC? (You can follow these steps:)
5. (a) What is Fox's utility from gaining one sticker?
6. (b) What is Fox's utility from gainingpC(as a function ofpC).
7. (c) Set these two equal, and solve forpC.
8. What is Fox's buying price for one sticker. That is, what is the pricepBthat makes Fox indifferent between gaining one sticker and losingpBand not getting or paying anything?
9. (a) What is Fox's utility from buying one sticker forpB(as a function ofpB)? (b) What is Fox's utility from not buying anything?
10. (c) Set these two equal, and solve forpB.

Now suppose Fox has reference-dependent preferences not just over money and stickers, but over money, stickers, and airplanes. Let his consumption in money, stickers, and airplanes bec1,c2, andc3, respectively, and let his reference points in money, stickers, and airplanes ber1,r2, andr3, respectively. Then, Fox's utility is given by

v(c1r1) +v(4c24r2) +v(4c34r3),

wherev(x) =xforx0, andv(x) = 2xforx <0. Normalize Fox's initial amount of money

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

9. What will be Fox's utility from gaining two stickers, losing one airplane, and gaining $4?