The Paretian theory of ophelimity in closed and open cycles

Pareto deals with the theory of ophelimity in closed and open cycles on two main occasions: in the article in the Giornale degli Economisti (1906) following Volterra’s observations (1906) to the first edition of the Manuale; and in the Appendix to the Manuel (1909). In the Economie mathématique (1911) there is only a brief paragraph (§6) in which the question of closed and open cycles is barely introduced. Although Volterra’s observations were oriented towards identification of the integrability condition (moreover already introduced by Antonelli, 1886),1 Pareto shows no interest in them, but in the problem of the measurement of the elementary ophelimities (i.e. of the marginal utilities) starting from the empirical data (of an ideal experiment) represented by the marginal rates of substitution and by the indifference varieties.