5.3 As defined in Chapter 3, a utility function is homothetic if any straight line through the origin cuts all indifference curves at points of equal slope: the MRS depends on the ratio y/x.

a. Prove that, in this case, ∂x/∂I is constant.

b. Prove that if an individual’s tastes can be represented by a homothetic indifference map then price and quantity must move in opposite directions; that is, prove that Giffen’s paradox cannot occur.