Question

May I get any assistance with these following questions please? U(x,y)=min(4x,2y) Prices: px,py Incme : I 1)Find Marshallian demand. 2) Find Hicksian demand, indirect utility function and expenditure function.

Answer 1

In a min function, the optimal is when both the arguments are equal. So 4x=2y. So y=2x. In the budget constraint, px.x+py.y=I. So px.x+py.2x=I. So X=I/(px+2py)

y=2I/(px+2py)

Indirect utility function is derived by substituting the demands. So V=4I/(px+2py). Hicksian demand function is same as marshallian demand function as there is no substitution effect and the optimal is always at the kink.

For expenditure function, just use the indirect utility function.

E=U(px+2py)/4.