Complementarity and Substitutability: A Dual Approach Based on Luenberger's Benefit Function

This paper presents another definition of substitutes and complements. It follows a dual approach using the Luenberger's benefit function. The benefit function measures the amount of a reference bundle that an individual would be willing to give up to move from a given utility level to any bundle. Therefore the benefit function associates to any bundle of goods another bundle that lies on a given indifference curve. This enables one to derive an inverse demand function which is defined as the support price of this associated bundle. The classification of goods between complements and substitutes is then obtained by the comparative static properties of the support price. We present some examples which show that the proposed classification is different from the one obtained with another dual approach based on Deaton's distance function.