4. Lya has reference-dependent preferences over money and clothes. She goes shopping on Black Friday. The outcomes are money $c_1$ and clothes consumed $c_2$. Lya's reference point in money and clothes are $r_1$ and $r_2$. Lya's utility is given by
$u(c|r) = c_1 + 100c_2 + v(c_1 - r_1) + v(100c_2 - 100r_2)$,
where $v(x) = 0.5x$ for $x \ge 0$, and $v(x) = x$ for $x < 0$.
(a) Calculate Lya's reservation price for purchasing clothes when she does not expect to buy any.
(b) Calculate Lya's reservation price for purchasing clothes when she expects to purchase one unit of clothes.
(c) What is Lya's preferred personal equilibrium?
(d) Now suppose Lya expects to purchase one unit of clothes on sale for $z < 100$. Suppose, however, that when Lya shows up to the store she discovers that the sale expired. What's the most Lya is now willing to pay for the clothes?
(e) What is the intuition for your answer in part (d)?
