Pareto Optimum

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Pareto Optimum


In further developing French economist Léon Walrass 1874 demonstration of the optimality of free competition, at first Italian economist Vilfredo Pareto studied the problem of optimal allocation of resources in terms of maximization of utility for a representative agent, which he described in his 1892 article Considerazioni sui principi fondamentali delleconomia politica pura. In a later article titled Il massimo di utilità dato dalla libera con-correnza.I (1894a), he re-analysed the question by determining the production coefficients that maximize the utility of a collectivistic society and demonstrated that they are exactly those of free competition (this is the real origin of the story of the second theorem of economic welfare). It was only at an even later stage, and as a consequence of some criticisms by Italian economists Maffeo Pantaleoni and Enrico Barone, that this theorem was redemonstrated by Pareto in 1894 and 1909. To reconfirm his theorem, Pareto started from the hypothesis of the incomparability of individual ophelimities, in flagrant contrast with his methodological position according to which every scienceand therefore economics as wellis a science of averages. From this there directly ensues the proposition that an allocation of resources is optimal (i.e., it is a pareto optimal point), if, as one moves away from it, the ophelimity of at least one individual increases and the ophelimity of at least one other individual decreases. On the other hand, this proposition cannot obviously be made operational from the point of view of economic policy, because the entire availability of resources of a society can be allocated in an infinite number of Pareto optimal points (described by the contract curve), from which the maximum maximorum (i.e., the best of the pareto optimal points) cannot therefore be extracted. Pareto more or less understood this difficulty and resolved it by stating in a 1913 article that if one wishes to give indications in terms of economic policy, one has to move into the realm of sociology, where the optimal allocation of resources can be univocally identified starting from a comparison between personal ophelimities arbitrarily carried out by the government.

The question of the economic unclassifiability of Pareto optimal points was authoritatively tackled in later years. As a solution, John Hicks and Nicholas Kaldor both published articles in 1939 that proposed a criterion of compensation that is conceptually similar to Paretos sociological criterion. Abram Bergson in his 1938 article A Reformulation of Certain Aspects of Welfare Economics and Paul Anthony Samuelson in his 1947 publication Foundations of Economic Analysis attempted to solve the problem by maximizing a social well-being function that was constructed, however, starting from cardinal individual functions of utility made comparable by resorting to value judgments.

While giving rise to outstanding formal analyses by such economists as Aldo Montesano (1990), Maurice Allais (1989), and Mark Blaug (1992), the subsequent literature developed around the theme of the either positive or normative nature of the Pareto optimum. While P. Hennipmann in his 1976 article Pareto Optimality: Value Judgement or Analitical Tool and G. C. Archibald in his 1959 article Welfare Economics, Ethics, and Essentialism defended the thesis that Paretos postulates do not reflect value judgments, Alan T. Peacock and Charles K. Rowley, in their 1972 and 1974 articles, weakened it by differentiating between economic liberalism and Pareto optimality, even though they attempted to portray the latter as a simple tool of economic reasoning. The normative thesis was taken to its extreme andconsidering Paretos unwavering political-intellectual militancyparadoxical consequences by Amartya Sen in 1970 and 1971 in articles where he demonstrated that in order to be logically consistent social choice cannot at the same time be liberal (respect of other peoples preferences, once ones own have been reaffirmed) and Paretian (incomparability of individual preferences and therefore necessary unanimity of social choices). Sen has been criticized in the literature for his too narrow definition of liberalism. By relaxing it, the compatibility between Paretos principle and liberalism would be restored. On the other hand, it should be pointed out that no ordinalistic theory of economic welfare based on a definition different from Paretos has yet been developed.

SEE ALSO Income Distribution; Pareto, Vilfredo


Allais, Maurice. 1989. La théorie générale des surplus. Grenoble, France: Presses Universitaires.

Archibald, G. C. 1959. Welfare Economics, Ethics, and Essentialism. Economica 26 (104): 316327.

Bergson, Abram. 1938. A Reformulation of Certain Aspects of Welfare Economics. Quarterly Journal of Economics 52 (2): 310334.

Blaug, Mark. 1992. The Methodology of Economics, or, How Economists Explain. 2nd ed. Cambridge, U.K.: Cambridge University Press.

Fine, Ben. 1975. Individual Liberalism in a Paretian Society. Journal of Political Economy 83 (6): 12771281.

Hennipman, P. 1976. Pareto Optimality: Value Judgement or Analitical Tool. In Relevance and Precision: From Quantitative Analysis to Economic Policy, eds. J.S. Cramer, A. Heertje, and P. Venekamp, 3969. New York: North-Holland.

Hicks, John. 1939. The Foundations of Welfare Economics. Economic Journal 69: 696712.

Hillinger, Claude, and Victoria Lapham. 1971. The Impossibility of a Paretian Liberal: Comment by Two Who are Unreconstructed. Journal of Political Economy 79 (6): 14031405.

Kaldor, Nicholas. 1939. Welfare Propositions of Economics and Intertemporal Comparisons of Utility. Economic Journal 49: 549552.

Montesano, Aldo. 1991. Il massimo di ofelimità per la collettività: definizioni, analisi, interpretazioni di Pareto e loro generalizzazione. In Pareto oggi, ed. G. Busino, 115138. Bologna, Italy: Il Mulino.

Ng, Yew-Kwang. 1971.The Possibility of a Paretian Liberal: Impossibility Theorems and Cardinal Utility. Journal of Political Economy 79 (6): 13971402.

Osborne, D. K. 1975. On Liberalism and the Pareto Principle. Journal of Political Economy 8 (6): 12831287.

Pareto, Vilfredo. 1892. Considerazioni sui principi fondamentali delleconomia politica pura. Giornale degli Economisti (August): 151157.

Pareto, Vilfredo. 1894a. Il massimo di utilità dato dalla libera concorrenza.I. Giornale degli Economisti (July): 4857.

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Pareto, Vilfredo. 1909. Manuel déconomie politique. Paris: Giard et Brière.

Pareto, Vilfredo. 1913. Il massimo di utilità per una collettività in sociologia. Giornale degli Economisti (avril): 338341.

Peacock, Alan T., and Charles K. Rowley. 1972. Pareto Optimality and the Political Economy of Liberalism. Journal of Political Economy 80 (3): 476490.

Rowley, Charles K., and Alan T. Peacock. 1975. Welfare Economics: A Liberal Restatement. London: Martin Robertson.

Samuelson, Paul Anthony. 1947. Foundations of Economic Analysis. Cambridge, MA: Harvard University Press.

Sen, Amartya. 1970. The Impossibility of a Paretian Liberal. Journal of Political Economy 78 (1): 152157.

Sen, Amartya. 1971. The Impossibility of a Paretian Liberal: Reply. Journal of Political Economy 79 (6): 14061407.

Walras, Léon. 1874. Eléments déconomie politique pure ou thèorie de la richesse sociale. Lausanne, Switzerland: Rouge.

Fiorenzo Mornati