Joanna is playing blackjack for real money. She has reference- dependent preferences over money: if her earnings aremand her ref- erence point isr, then her utility isv(mr), where the value functionvsatisfiesv(x) = ln(x+1) forx0, andv(x) =2ln(x+1) forx0.

(a)Graph Joanna's utility function as a function ofmr.

(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 amountsmandm, and her reference point isr, her expected utility is1/2v(mr) +1/2v(mr).

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

following questions: (i) What is thegfor which Joanna would be indif- ferent between not gambling and taking a fifty-fifty win$gor 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.