Problem 2 (25 points)
Suppose that a consumer has the utility function given by:
U(x,y) = x^a y^b
with prices p^x, p^y and income M, and where a > 0,? > 0.
a. Maximize this consumer's utility. Derive Marshallian demand for both goods.
b. Show that at the optimum, the share of income spent on each good does not
depend on prices or income.
c. Show that the elasticity of Marshallian demand for x is constant.
d. For good x, use your answer to (b), the elasticity of Marshallian demand you
found in (c), and the relationship between the elasticities of Marshallian and
Hicksian demand derived from Slutsky's equation to solve for the elasticity of
Hicksian demand.
e. Which of Marshallian and Hicksian demands for x is more elastic? How could
you have answered this question without calculating elasticities, based only
on knowing the Marshallian demand function for x.
