Consider the utility function of fixed proportions $($perfect complements$)U=$min$(x,4y).$ Let $Px,Py,$I denote price of $x,$ price of $y$ and income respectively.

a$.$ Find demand function for good $x$ and demand function for good $y.$

b$.$ Find indirect utility function.

c$.$ Find the expenditure function.

Utility function is given by $U(x,y)=xy$ where $>0,>0$;$+=1.$

a$.$ Find Marshallian demand function.

b$.$ Find indirect utility function.

c$.$ Find the compensated demand function and expenditure function.

d$.$ Draw the Marshallian and compensated demand function.

e$.$ What is the effect of a price increase on Marshallian demand function? Can you decompose this effect into substitution and income effects? You can assume $==0\mathrm{.}5$ if it will make derivition anond