ABSTRACT
In 1906, Pareto sent to press the Italian edition of his Manuale di economia politica. Immediately afterwards, the eminent mathematician Vito Volterra (1906) reviewed the work favourably; in particular, he dwelt upon the Paretian analysis of consumer behaviour in terms of indifference curves (or, more generally, of indifference varieties). On this subject Volterra noted that Pareto, in the mathematical appendix of the Manuale, implicitly supposed that every differential form, even in three or more variables, always has an integrating factor and therefore that a total utility (or ophelimity) function always exists, representing the tastes of a given consumer. After some months, Pareto (1906b) replied to Volterra, admitting the reasonableness of this remark, and expounded for the first time his theory of non-closed cycles and of the order of consumption, which he closely connected with the lack of integrability. He later expounded an enlarged and improved version of the same theory in the mathematical appendix of the Manuel d’économie politique (1909).
