The Uncompensated Law of Demand: A 'Revealed Preference' approach

•New necessary and sufficient conditions for the Uncompensated Law of Demand are developed.•These conditions have the desirable feature that they do not rely on information about unobservable consumer data, such as preferences.•The conditions exploit properties of new objects, 'the Giffen commodity vector' and its dual 'the Giffen price vector'.•In addition to being based on observables, our conditions are amenable to direct and parsimonious econometric and experimental estimation.

Milleron and Malinvaud (1974), Mityushin and Polterovich (1978) and others, provide conditions under which the Uncompensated Law of Demand (ULD) holds. These conditions are based on properties of the consumer's (unobservable) utility function. In this paper we introduce the new idea of a 'Giffen commodity vector' and show how, in terms of it and the derivative of a consumer's inverse demand, a new necessary and sufficient condition for the ULD may be obtained. As both the Giffen vector and a consumer's inverse demand are observable, this allows us to obtain a 'Revealed Preference' style necessary and sufficient condition for the ULD without relying on conditions based on unobservables such as differential or curvature properties of a consumer's utility function.