On behavioral complementarity and its implications

We study the behavioral definition of complementary goods: if the price of one good increases, demand for a complementary good must decrease. We obtain its full implications for observable demand behavior (its testable implications), and for the consumer's underlying preferences. We characterize those data sets which can be generated by rational preferences exhibiting complementarities. In a model in which income results from selling an endowment (as in general equilibrium models of exchange economies), the notion is surprisingly strong and is essentially equivalent to Leontief preferences. In the model of nominal income, the notion describes a class of preferences whose extreme cases are Leontief and Cobb-Douglas respectively.