Value & Capital, CHAPTER III -- COMPLEMENTARITY, Section 6

In this section Hicks deals with a couple of additional points about the effect of a change in the price of one good on the demands for other goods.

The first point is that the principles he has been discussing in preceding sections are "just as applicable to market demand as to the demand of the individual consumer."  Thus, two goods X and Y can be regarded as complementary for a group of consumers (or substitutes, for the group as a whole), depending on whether the total substitution effect causes the total demand for Y to increase when the price of X falls (or, in the case of substitutes, the total demand for Y falls when the price of X falls).

Another important principle is that "when the relative prices of a group of commodities can be assumed to remain unchanged, they can be treated as a single commodity."  This means that substitution effects can exist between the group as a whole and a single commodity X that is not in the group.  Thus a fall in the price of X relative to the prices of the other goods gives rise to a substitution in favor of X and away from the other commodities (although Hicks reminds the reader that the expenditure on these other commodities may be rearranged such that the expenditure on some of them is increased).  Similarly, if the price of X remains fixed and the prices of the commodities in the group all fall in the same proportion, this must cause a substitution in favor of the group as a whole.

Hicks gives us a hint of things to come by noting that, "We shall find, as we go on, that this proposition is a distinctly useful one."  But he closes this section by clarifying the limits of the proposition.  He notes that

It does not mean that there must be a substitution effect in favour of each commodity in the group taken separately, so that (apart from income effects) the demand for each commodity separately must increase.  It is always possible that the demands for some goods in the group may diminish, since they are substituted by other goods in the group.

Finally, regarding income effects, Hicks notes that when the group is large, so that the consumer spends a significant fraction of his income on it, the income effect will be large.  But negative income effects for a large group are not likely;  in other words, "it is unlikely that the consumer will spend less money upon a whole large group of goods when his income increases."  Therefore, regarding the demand for the group of goods, he concludes that "we should expect the income effect to pull in the same direction as the substitution effect."