求解一道高微习题，急急急！

\[MU_{c} = (c - \varphi N^{\alpha}c^{\beta})^{-\sigma} (1 - \varphi \beta N^{\alpha} c^{\beta - 1})\]
\[MU_{N} = (c - \varphi N^{\alpha}c^{\beta})^{-\sigma} (c - \varphi\alpha N^{\alpha - 1} c^{\beta}) \]
\[\frac{MU_{c}}{MU_{N}} = \frac{1 - \varphi \beta N^{\alpha} c^{\beta - 1}}{c - \varphi\alpha N^{\alpha - 1} c^{\beta}}\]
令其等于
\[\frac{MU_{c}}{MU_{N}} = \frac{P}{W}\]
再会代入之前的预算函数中。接下来就是计算的问题了。