This problem is a simplified version of section IV in Ko szegi and Rabin (2006). Consider the follo- wing example. We consider an individual named Ben. There are two goods that Ben likes, money and shoes. The consumption utilities are m1(x) = sx for shoes, and m2(y) = x for money. Ben has reference-dependent preferences with reference-dependent utility that is piece-wise linear, with slope in gains, and in losses, where > 0, > 1.

(a) It's a Saturday morning, and Ben wakes up with his mind set on buying shoes, as many people do on Saturdays. What is the highest price pmax Ben is willing to pay for a pair of shoes ? I.e., what is the highest price at which buying is a personal equilibrium ?

(b) What is the interpretation that pmax > s ?

(c) Now suppose that before shopping, Ben reads in the Straits Times that the store selling the shoes plays the following lottery : If you decide to buy the shoes, they will flip a coin. If it comes up heads, you get the shoes for free. If it comes up heads, they cost pmax. Is Ben still willing to buy the shoes at pmax ? What is the highest price Ben is willing to pay in this case ?

(d) Now suppose that it's a Wednesday, and Ben wakes up not expecting to buy shoes. Again, he reads the newspaper and it has the same ad in it. What is the highest price at which not buying is not a personal equilibrium ?

(e) Why is the price in (d) lower than pmax ?