1. [35pts] This question asks you to think about narrow bracketing and risky choice using actual referencedependent utility functions from earlier in the class. Suppose an investor has a utility function given by v(w r), where w is money and r is her reference point in money. Her reference point is her current wealth, normalized to zero. The function '0 satises 19(53) = r for a: > 0 and "0(a) = 2.53 for a: S 0. (a) Would the investor reject a fty-fty gain $200 or lose $100 gamble? What about two independent plays of the same gamble? Explain the intuition behind the result. (b) Now suppose that the investor is already facing some contemporaneous risk; for example, she might own stocks that could go up or down today. Specically, she has an equal probability of losing $100 or gaining $100 in her nancial investments today. In this case, would she accept an additional independent fty-fty gain $200 or lose $100 gamble? [Note: In fact, with a mere $10,000 invested in the stock market, there is a greater than 85% chance that one's wealth swings by more than $100 in a single day. So many people face far more nancial risk than the above]