这是一份stanford斯坦福大学学院ECON 141作业代写的成功案
Alternatively, one could normalize on some standard private good. To illustrate, consider A’s budget constraint with an earnings tax and a pair of net commodity taxes, as discussed earlier:
$$
\left(1+t n_{x}\right) x_{A}+\left(1+t n_{y}\right) y_{A}=\left(1-\tau_{A}\right) w_{A} l_{A}-\operatorname{Tan}_{A} .
$$
Suppose we were to take good $X$ as numeraire. Then the normalized budget constraint would be
$$
x_{A}+\frac{1+t n_{y}}{1+t n_{x}} y_{A}=\frac{1-\tau_{A}}{1+t n_{x}} w_{A} l_{A}-\frac{\operatorname{Tan}{A}}{1+t n{x}} .
$$
ECON 141 COURSE NOTES ：
$$
x_{A}+\left(1+\operatorname{tn}{y}^{x}\right) y{A}=\left(1-\tau_{A}^{x}\right) w_{A} l_{A}-\operatorname{Tan}{A}^{x} \text {, } $$ where $$ t n{y}^{x} \equiv \frac{1+t n_{y}}{1+t n_{x}}-1,
$$
$$
\tau_{A}^{x} \equiv 1-\frac{1-\tau_{A}}{1+t n_{x}},
$$
$$
\operatorname{Tan}{A}^{x} \equiv \frac{\operatorname{Tan}{A}}{1+t n_{x}} .
$$