Preference Conditions for Linear Demand Functions

Abstract

The present study takes consumer preferences as the primitive and a most general formulation of a linear demand system as the desideratum. To investigate how the two are related, I take a novel approach to demand integrability that relies on some recent results in Diasakos and Gerasimou (2020). The methodology applies for either of the two possible price-normalization regimes (with respect to the price of a numeraire commodity or income); in either case, it leads to a complete characterization of linear demand systems in terms of the properties for the underlying rationalizing preference relation, and analytical solutions for the corresponding (direct) utility function. My results provide a proper microfoundation for linear demand systems-in a way that addresses knowledge gaps in the extant literature on linear demand that leave space for fundamental misunderstanding. JEL Classifications: C02, D01, D11 An earlier version was presented at a session of the 20th annual SAET conference; I wish to thank the participants for helpful comments.