Chapter $8$ Comparative$-$Static Analysis of General$-$Function Models

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$5.$ How do the two partial elasticities in Prob. $4$ vary with $P$ and $R?$ In a strictly monotonic fashion $($assuming positive $P$ and $R)?$

$6.$ The foreign demand for our exports $x$ depends on the foreign income $Y_f$ and our price level $P$:$x={}_1^{\frac{1}{2}}+p-2.$ Find the partial elasticity of foreign demand for our exports with respect to our price level.

$7.$ Find the total differential for each of the following functions:

$($a$)U=-5x^3-12xy-6y^5$

$($b$)U=7x^2{y}^3$

$($c$)U=3x^3(8x-7y)$

$($d$)U=(5x^2+7y)(2x-4y^3)$

$($e$)u=\frac{9y^3}{x-y}$

$($f$)U=(x-3y{)}^3$