5.10 Suppose the individual’s utility function for three goods, X1, X2, and X3, is “separable”; that is, assume that U(X1, X2, X3)
U1(X1) U2(X2) U3(X3)

and U i  0 U i  0 for i
1, 2, or 3.

Show that

a. None of the goods can be inferior;

b. Xi/Pi must be  0.

In the Chapter 6 extensions we examine this separable utility case in more detail.