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$5.(15$ points$)$ Suppose households choose consumption $C$ and the fraction of their time spent working $N$ to

max$\frac{C^{1-\frac{1}{}}}{1-\frac{1}{}}+\frac{(1-N{)}^{1-\frac{1}{}}}{1-\frac{1}{}}$ subject to $pC=wN(1-).$ Assume

$($a$)$ What is the $\%$ change in leisure $(1-N)$ when there is a $1\%$ change in consumption, holding the after$-$tax real wage fixed?

$($b$)$ What is the $\%$ change in leisure when there is a $1\%$ change in the net tax rate $(1-),$ holding consumption and the before$-$tax real wage fixed?

$[$Use natural logs to calculate elasticities in $($a$)$ and $($b$).]$

$($c$)$ Which is bigger, $($a$)$ or $($b$)?$