Question

Suppose that a consumer has the utility function given by:

U(x,y)= (x^a)*(y^b)

With prices p^x, p^y and the income M, and where a>0, b>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 answers to b) the elasticities of Marshallian and Hicksian demand derived from Slutsky's equation to solve for the elasticity of Hickisian demand.

e) Which of Marshallian and Hickisian demands for x is more elastic? How could you have answered this question without calculating elasticities, based only on knowing the Marshallian demand function of x.

Answer 1