6.8 Hicks’s “second law” of demand states that the predominant relationship among goods is net substitutability (see footnote 3 of Chapter 6). To prove this result:

a. Show why compensated demand functions Xi
hi(P1, . . . , Pn, V )

are homogeneous of degree zero in P1 ... Pn for a given level of V.

b. Use Euler’s theorem for homogeneous functions (for a statement of this theorem, see footnote 5 of Chapter 7) to show that



n j
1 Pj
U
constant
0 (for all i
1, n).

c. Use the “first law of demand”

that
U
constant

 0

to conclude that



j
1 Pj
U
constant

 0, that is, net substitution must prevail, on average.