Suppose an individual has a utility function $U\left(x_{1}, x_{2}\right)$ and budget constraint $p_{1} x_{1}+p_{2} x_{2} \leq$ $y$. He employs the rule-of-thumb that says buy $x_{2}$ if and only if $p_{2}

Question

Suppose an individual has a utility function $U\left(x_{1}, x_{2}\right)$ and budget constraint $p_{1} x_{1}+p_{2} x_{2} \leq$ $y$. He employs the rule-of-thumb that says buy $x_{2}$ if and only if $p_{2}<p_{1}$. If $p_{1}<p_{2}$, then the individual's rule-of-thumb results in optimal demand if he has the following utility function:
A) $U\left(x_{1}, x_{2}\right)=2 \mathrm{x}_{1}+2 x_{2}$
B) $U\left(x_{1}, x_{2}\right)=\ln \left(x_{1}\right)+\sqrt{ }\left(x_{2}\right)$
C) $U\left(x_{1}, x_{2}\right)=\mathrm{x}_{1}^{\frac{1}{3}} x_{2}^{\frac{2}{3}}$
D) $U\left(x_{1}, x_{2}\right)=\ln \left(x_{1}\right)+\ln \left(x_{2}\right)$

Quizplus · Accepted Answer

The utility function $U(x_{1}, x_{2})=2x_{1}+2x_{2}$ is linear, meaning the individual is indifferent between $x_1$ and $x_2$ when prices are equal, and will choose the cheaper good when prices differ, aligning with the rule-of-thumb.

Suppose an Individual Has a Utility Function U(x1,x2)U\left(x_{1}, x_{2}\right)U(x1​,x2​) And Budget Constraint

Suppose an Individual Has a Utility Function $U\left(x_{1}, x_{2}\right)$ And Budget Constraint