Substitution Terms

As Hicks points out in the first book of Value and Capital, substitution is the only relationship possible in a two-good economy. In an economy having more than two goods, the relationship between pairs of goods need no longer be that of substitution. Complementarity, as defined by Hicks, then becomes possible. The own substitution term (g,rr) for the rt' good involves an increase in the price of the rth good, the other prices remaining unchanged, but with a compensatory increase in money income (to enable the original purchases to be chosen despite the higher price). Since all other goods at fixed prices may be treated as a single good, this is equivalent to substitution in the two-good case and the resultant change in the purchase of the rth good is unambiguously negative. On the other hand, if we follow Professor Hadar and take the own substitution term as requiring, instead, compensatory changes in the price of at least one other good (again treating the remaining goods together at unchanged prices) we are operating once more in an economy of at least three goods. The complementarity relationship again becomes possible and, therefore, the signs between pairs of goods, on the indifference surface, is no longer unambiguous. We agree that it is useful to be reminded of this implication of an alternative conception of the own substitution term. However, rather than allege that the substitution term has ambiguous implications it would seem more precise to assert that the term, substitution term, is ambiguous in that the underlying concept, entailing constant real income, may be realised in the case of a rise in the price of the rth good in two different ways: (1) through a compensatory increase in money income, the traditional way; and (2) through compensatory reductions in at least one other price, the possibility suggested by Hadar. It would therefore be more precise to say: (1) a money-incomecompensated rise in the price of the rth good always reduces the quantity demanded; while (2) a prices-compensated rise in the price of r (a) reduces its quantity only if those goods, whose prices are reduced in compensation, are all substitutes for r, although (b) the quantity of r demanded may increase if one or more of these goods are complementary with r. As for empirical relevance, since little empirical work at this level has been done, compensation through other price changes may be said to be perhaps empirically just as relevant. Conceptually, however, the traditional definition of the own substitution effect based on money income compensation is much the simpler. Moreover, with

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