$5\mathrm{.}5$

Suppose the utility function for goods $x$ and $y$ is given by

utility $=U(x,y)=xy+y.$

a$.$ Calculate the uncompensated $($Marshallian$)$ demand functions for $x$ and $y,$ and describe how the demand curves for $x$ and $y$ are shifted by changes in I or the price of the other good.

b$.$ Calculate the expenditure function for $x$ and $y.$

c$.$ Use the expenditure function calculated in part $($b$)$ to compute the compensated demand functions for goods $x$ and $y.$ Describe how the compensated demand curves for $x$ and $y$ are shifted by changes in income or by changes in the price of the other good.