Consider the utility function U(x, y) = x0.3y0.7, with budget constraint I = xpx + ypy.

a) Derive the uncompensated demand functions (for x, y), the indirect utility function, and the expenditure

function for this case.

b) Derive the compensated demand functions (for x, y).

c) What is the budget share for good x in this case? Use the elasticity representation of the Slutsky equation

to show that the Slutsky equantion holds for the uncompensated demand for good x.

d) Show in general the budget share spent on good x can be derived as sx = dlnE

dlnpx , where E = xpx + ypy.