### 4. [16 points] Consider the reference-dependent model of Tversky and Kahneman. Let two dimensions of choice be mug ( (mathrm{M}) ) and money (d), and [ U_{r}(x)=v_{M}left(x_{M}-r_{M}right)+2 v_{d}left(x_{d}-r_{d}right) ] where [ begin{array}{c} v_{M}(x)=left{begin{array}{ll} 2 x & x geq 0 \ 3 x & x<0 end{array}right. \

4. [16 points] Consider the reference-dependent model of Tversky and Kahneman. Let two dimensions of choice be mug ( (mathrm{M}) ) and money (d), and [ U_{r}(x)=v_{M}left(x_{M}-r_{M}right)+2 v_{d}left(x_{d}-r_{d}right) ] where [ begin{array}{c} v_{M}(x)=left{begin{array}{ll} 2 x & x geq 0 \ 3 x & x<0 end{array}right. \