A consumer has a budget constraint given by $p_{0} \widehat{x_{1}}+p_{1} x_{1}+p_{2} x_{2} \leq y$ where $p_{0}0$ and $\widehat{x_{1}}=1$ if positive amounts of $x_{1}$ are purchased and 0 otherwise. If the consumer has a utility function given by $U\left(x_{1}, x_{2}\right)=x_{1}+x_{2}$ and $p_{1}=p_{2}$ then he will not purchase $x_{1}$.

Question

A consumer has a budget constraint given by $p_{0} \widehat{x_{1}}+p_{1} x_{1}+p_{2} x_{2} \leq y$ where $p_{0}>0$ and $\widehat{x_{1}}=1$ if positive amounts of $x_{1}$ are purchased and 0 otherwise. If the consumer has a utility function given by $U\left(x_{1}, x_{2}\right)=x_{1}+x_{2}$ and $p_{1}=p_{2}$ then he will not purchase $x_{1}$.

Quizplus · Accepted Answer

With this utility function, the two goods are perfect substitutes (the consumer gets the same utility from consuming a bundle of any composition of $x_{1}$ and $x_{2}$ ) and they are the same price. This means he will choose only to buy $x_{2}$ and avoid paying $p_{0}$.

A Consumer Has a Budget Constraint Given By p0x1^+p1x1+p2x2≤yp_{0} \widehat{x_{1}}+p_{1} x_{1}+p_{2} x_{2} \leq yp0​x1​​+p1​x1​+p2​x2​≤y

A Consumer Has a Budget Constraint Given By $p_{0} \widehat{x_{1}}+p_{1} x_{1}+p_{2} x_{2} \leq y$