On the Hicks–Allen Definition of Complements and Substitutes with Discrete Changes in Prices

For discrete price changes, compensated cross‐price effects for two goods need not be equal if the household consumes three or more goods. In this paper I ask whether compensated cross‐price effects must have the same sign even if they differ in magnitude. I show that with three or more goods, the answer to this question is ‘no’. For discrete price changes, with more than two goods, the signs of the compensated cross‐price effects for two goods can differ depending on which price changes. Hence, the Hicks–Allen definition of complements and substitutes can also differ depending on which price changes.