Joanna is playing blackjack for real money. She has reference-dependent preferences over money: if her earnings are m and her reference point is r, then her utility is v(m r), where the value function v satisfies v(x) = ln(x + 1) for x 0, and v(x) = 2 ln(x + 1) for x 0.

(a) Graph Joanna's utility function as a function of m r.

(b) Does Joanna's utility function satisfy loss aversion? Does it satisfy

diminishing sensitivity?

Suppose that Joanna has linear probability weights (that is, she does NOT have prospect theory's non-linear probability weighting function). Hence, if she has a fifty-fifty chance of getting amounts m and m0, and her reference point is r, her expected utility is 1/2v(m r)+ 1/2v(m' r). For parts (c), (d), and (e), assume that Joanna's reference point is $0 (that is, no wins or losses) and for the given situation, answer the 3 following questions: (i) What is the g for which Joanna would be indifferent between not gambling and taking a fifty-fifty win $g or lose $5 gamble?(ii) Does this reflect risk loving or risk averse behavior? (iii)What feature of Joanna's reference-dependent preferences is driving this choice?

(c) This is the first round and Joanna has not won or lost any money

yet.

(d) Joanna is $10 down.

(e) Joanna is $10 ahead.

(f) What does the process of gamblingi.e. winning or losingdo to

Joanna's risk attitudes? Explain the intuition.