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

True/False

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 $x_{1}$ .