Revealed Preference and the Utility Function

Professor Samuelson's approach' has proved to be a useful basis for deriving a considerable part of the static theory of consumer's choice. Its exisLing versions are not sufficient, however, to determine whether or not consumer's preferences can be described by a utility function of the customary type (the problem of integrability),2 except in the unrealistic case of two commodities. In this note Samuelson's fundamental hypothesis will be generalised so as to imply integrability while continuing to satisfy the methodological requirements of the revealed preference approach and without losing its plausibility. An attempt will be made to stress the logical, as distinct from the technically mathematical, aspects of the subtle problem of integrability, and to assess its importance.