The Limits of the Usual Interpretation of Walras’s Maximization of Social Satisfaction

Jaffe (1977/1983), Steiner (1994) and Beraud (2011) reconsidered the critiques addressed by Pareto (see Steiner, 1994), Launhardt (1885), Bortkiewicz (1889), Edgeworth (1889), Wicksell (1899), Samuelson (1947) and Baumol (1952) to Walras’s approach of the maximization of social satisfaction.

In the first edition of the Elements d'Economie Pure, Walras indeed considered the problem of social satisfaction maximization in a production economy while in the second edition (see his correspondence [Walras, 1965] with Bortkiewicz and Edgeworth in 1889) the results were extended to the theory of capitalization. In both cases, he tried to show that free competition yields a higher social maximum of satisfaction for the agents of the economy. Most of Walras’s critical commentators denied this result. Some of them were not convinced by the apparent logical consistency of Walras’s demonstration and they were right: more than one hundred years after, in spite of some differences of interpretation, Van Daal and Jolink (1993) and above all Mouchot (1994) confirmed and agreed that a solution to the problem raised by Walras’s theorem of maximal satisfaction (at least in the case of the theory of capitalization in the second and subsequent editions of the Elements dEconomie Pure) was impossible. Other commen­tators pointed out noncompetitive systems that offer to agents a superior maximal satisfaction. They considered however that Walras’s demonstra­tion of the existence of a social satisfaction maximum was an essential first step toward the elaboration of the first social welfare theorem (Baumol, 1952, for instance).

The problem is that most of all these commentators underestimated the importance of two specific assumptions made by Walras in this context, namely the zero profit and the price uniformity ones. Now, the consider­ation of these assumptions deeply changes the real meaning of Walras’s attempt and paves the way to a rather different conception of social welfare.

Uniformity of competitively determined price represented for Walras not only an analytical ideal, but an ethical ideal as well, constituting an indispensable pillar of social justice. In the “Theorie de la propriete,” Walras defined justice in exchange (or “commutative justice”) in terms of two conditions: first, the complete freedom of every trader to pursue his own advantage in the market; and second, the complete elimination from the market of any chance for a trader to profit by exchange at the expense of his counterpart or anyone else. The first condition is satisfied by the assumed perfection of the market mechanism, and the second by the stipulated universality of the budget restraint from which no trader is exempt in the Walrasian general equilibrium schema. (Jaffe, 1977/1983: 330)

Beraud (2011: 366, 367) also emphasized the importance of these two conditions and Jaffe’s, Beraud’s and RebeyroFs contributions certainly help to highlight the meaning of the following remark of Leon Walras:

Production in a market ruled by free competition is an operation by which services can be combined and converted into products of such a nature and in such quantities as will give the greatest possible satisfaction of wants within the limits of the double condition: [1] that each service and each product have only one price in the market, namely the price at which the quantity supplied equals the quantity demanded and [2] that the selling price of the products be equal to the cost of the services employed in making them. (Walras quoted and translated into English by Jaffe [1977/1983: 331])

Now, condition (1) expresses the principle of commutative justice, which excludes the possibility of distributional effects or redistributional back­wash from exchange, while condition (2) is related to distributional justice, which excludes injustices of the existing distribution of property. If we accept this interpretation first advanced by Jaffe, it is clear that we cannot consider Walras’s maximization of social satisfaction as a first formulation of the first welfare theorem but as a genuine and specific analysis of the conditions that allow to match justice, pure competition and social efficiency in a market economy.

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