On the determinants of complementarity: Elasticities of substitution, income shares, and relative prices

This paper extends an example due to Samuelson (1974) to develop the relationship between possible compensated complementarity between two goods and the two elasticities of substitution in an extended three good CES utility function. It also uses the same utility function to develop the implications of a generalized income share parameter and two different relative prices for possible complementarity between goods. Finally, it explores possible complementarity in a more general utility function with non-constant elasticities of substitution.