Let $u_{g}(x)$ be Julie's utility function over gains and $u_{l}(x)$ her utility function over losses. If Julie's preferences are best described with Prospect Theory, which of the following is an example of Julie's value function? A) $\quad v(x \mid 0)= \begin{cases}\ln (x), & x0 \ 0, & x=0 \ -x, & x0 \ 0, & x=0 \ -\ln (-x), & x0 \ x, x=0 \ x, x0 \ -\left(x^{2}\right), \quad x \leq 0\end{array}\right.$

Question

Let $u_{g}(x)$ be Julie's utility function over gains and $u_{l}(x)$ her utility function over losses. If Julie's preferences are best described with Prospect Theory, which of the following is an example of Julie's value function? A) $\quad v(x \mid 0)= \begin{cases}\ln (x), & x>0 \ 0, & x=0 \ -x, & x<0\end{cases}$ B) $\quad v(x \mid 0)= \begin{cases}\mathrm{X}, & x>0 \ 0, & x=0 \ -\ln (-x), & x<0\end{cases}$ C) $\quad v(x \mid 0)=\left\{\begin{array}{l}x, x>0 \ x, x=0 \ x, x<0\end{array}\right.$ D) $\quad(x \mid 0)=\left\{\begin{array}{c}\ln (x), x>0 \ -\left(x^{2}\right), \quad x \leq 0\end{array}\right.$

Quizplus · Accepted Answer

Prospect Theory suggests that people value gains and losses differently, showing diminishing sensitivity for both, but with losses being felt more intensely than gains. Choice A reflects this by using a logarithmic function for gains ($x > 0$), indicating diminishing sensitivity, and a linear function for losses ($x < 0$), which can represent the stronger impact of losses, aligning with Prospect Theory's principles.

Let ug(x)u_{g}(x)ug​(x) Be Julie's Utility Function Over Gains And ul(x)u_{l}(x)ul​(x) Her Utility Function Over Losses

Let $u_{g}(x)$ Be Julie's Utility Function Over Gains And $u_{l}(x)$ Her Utility Function Over Losses