4. Ana has reference-dependent preferences over money. Let her utility over money arm“,y

be given by: a: if s: > O

U=v e—rmme wherevm: _’

(C’m’y 3") H {25: ifar<0.

Let Ana start with no income, and a reference point of zero money. Every day, Ana has the option to invest in stocks. The stock price changes over the course of the day

such that with 50% chance, Ana earns $100 and with 50% chance, Ana loses $60. (a) Suppose Ana plans on checking her stock portfolio at the end of each day. She

will experience gain / loss utility depending on whether the stock went up or down.

What is her expected utility if she invests? What is her expected utility if she

does not invest? Will Ana invest in stocks? (b) Suppose Ana plans on checking her stock portfolio every two days instead. At the end of two days, what are the possible money outcomes that Ana can end up

with? What is the likelihood of each? (c) If she checks her stock portfolio every two days, what is her expected utility if

she invests? What is her expected utility if she does not invest? Will Ana invest in stocks? ((1) Explain why ﬁnancial advisors give advice saying to check stock balance every

once in a while. (e) Now suppose Ana starts with -$40, and a reference point of zero money. Ana

plans to checks her stock portfolio at the end of that day. What is her expected

utility if she invests? What is her expected utility if she does not invest? Will

Ana invest in stocks? (f) Explain the intuition as to why your answer here differs from part (a).