The Benefit Function Approach to Modeling Price-Dependent Demand Systems: An Application of Duality Theory

In this article we advocate more extensive use of the benefit function in specifying price-dependent or inverse demand models. In particular, we demonstrate how duality theory may be used to establish the inter-relationships between the Marshallian (or Hicksian) inverse demands and Luenberger's adjusted price functions, allowing estimable inverse demands to be derived directly from a benefit function. We also make use of a numerical inversion estimation method to rectify the "unobservability of utility problem" encountered in the empirical analysis of these inverse demands. To illustrate the usefulness of the proposed methods, we estimate two systems of inverse demands for Japanese quarterly fish consumption. Results generally indicate that the proposed methods are promising and operationally feasible so that we have opened up a wider range of empirical inverse demand specifications that can be subjected to tight theoretical restrictions.