I am given two equations:
$x=\frac{u}{v}(1- \frac{1-y+py}{p})$ and $y\frac{x}{2}= a\frac{p}{1-y+py}$
where $p$, $a$, $u$ and $v$ are parameters. I am asked to provide $\frac{\delta x}{\delta y}$ and $\frac{\delta y}{\delta x}$
I derived the corresponding partial derivatives to find:
$\frac{\delta x}{\delta y}=\frac{u}{v}\frac{1-p}{p}$ and $\frac{\delta y}{\delta x}=\frac{-2a}{x^2}\frac{1}{2p-1}$ (using implicit differentiation for $\frac{\delta y}{\delta x}$)
My question is whether this approach is correct or I need to apply total differentiation. If I need to apply total differentiation, I have only seen that one finds the compartive statics with respect to the parameters by finding, for example, dx/da and then setting du,dv,dp=0 via Cramers rule. Nevertheless, how would one find dx/dy?
Any help is mega appreciated.