This question asks you to think about narrow bracketing and risky choice using actual reference-dependent utility functi

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This question asks you to think about narrow bracketing and
risky choice
using actual reference-dependent 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 v satisfies v(x) = x for x > 0 and v(x) = 2.5x for
x ≤ 0.
(a) Would the investor reject a fifty-fifty 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.
Specifically, she
has an equal probability of losing $100 or gaining $100 in her
financial investments
today. In this case, would she accept an additional independent
fifty-fifty 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
financial risk than
the above.]
(c) What is the minimum gain $x such that the above investor
with stocks accepts
a 50-50 gain $x or lose $100 gamble? What does this imply about the
investor’s
risk preferences over gambles?
(d) In fact, many people are risk averse over small stakes gambles
while simultane-
ously owning stock. Carefully explain how narrow bracketing relates
to this this
phenomenon.