**1.** Michaela has reference-dependent preferences over mugs, c1 and money, c2 – with reference points r1 and r2, respectively -represented by the following utility function

where

Suppose that Michaelaís initial endowment of money is zero, and that she starts o§ with zero mugs.

**(a)** What feature(s) of the prospect theory value function does *v* capture? What feature(s) does it not capture?

**(b)** According to the above utility function, who is better o§: a person whose reference point is to get nothing and gets nothing, or one whose reference point is to get $1,000 and gets $1,000? Is there something weird about this? If so, how could you modify the utility function to make it more realistic (while still capturing the same features of prospect theory)?

Use the original utility function for the rest of the problem.

**(c)** What is Michaelaís buying price, pb, for a mug?

**(d)** What is Michaelaís selling price, ps, for a mug?

**2.** Now consider Vera who has reference-dependent preferences over mugs, c1 and money, c2 ó with reference points r1 and r2, respectively ó represented by the following utility function

where

That is, Vera does not evaluate gains and losses in mugs and money separately, but looks at gains and losses from her overall consumption relative to the reference point. Suppose that Veraís initial endowment of money is zero, and that she starts o§ with zero mugs.

**(a)** What is Veraís buying price, Pb, for a mug?

**(b)** What is Veraís selling price, Ps, for a mug?

**(c)** What does this say about how to think about specifying models of reference-dependent preferences?

**3.** Barack has reference-dependent preferences over the number of hours he gets to spend with his family each day, F1, and his personal fame, F2, which is measured by the number of New York Times articles written about him each day. (For simplicity we will assume that all articles are positive to Barack, so that more articles is always better than fewer.) His preferences are represented by the following utility function, in which R1 and R2 represent Barackís reference points for family time and fame, respectively:

where

Currently, Barack holds a job in which he spends no time with his family, F1 = 0, but gets two articles each day, F2 = 2. We’ll call this “job A”. He likes his job, but he is considering the possibility of changing jobs next year.

**(a)** Suppose that Barack’s only other job option is a job that would give him no New York Times articles, but that would allow him to spend more time with his family. If we assume that Barackís reference point is determined by the status quo, how many hours of family time would the new job need to have in order to make Barack willing to change jobs? Explain the psychological intuition for your answer.

**(b)** Now suppose that Barack’s alternative job option actually has 3 hours of family time and no articles. We’ll call this “job B”. And now, assume that Barack’s reference point is determined by his expectations of future family time and future fame, in whatever job he expects to hold next year. Would it be possible under rational expectations for Barack to plan to switch from job A to job B?

**(c)** Compare your answer in (b) to the answer you gave for (a) above. Explain the psychological intuition for the similarities or differences between your answers to these two questions.

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