The problem for Walras's exposition is that the equations that he wrote out have parameters that are actually endogenous variables in the tatonnement process in his model. He explained that production and exchange occur in disequilibrium in the mature comprehensive model, varying as prices change during the course of the adjustment of the markets toward their equilibrium set of variables (see, for example, 1889, pp. 235, 238, 294; 1988, §§209-12, pp. 315-19, §258, pp. 399401). The phenomena that change as a result include the asset holdings of the participants, which alter as a function of the variations in hiring, production and sales that occur as entrepreneurs adjust levels of output in order to maximize profits; and they include the amounts of each type of capital good, which vary in accordance with changes in the amount and composition of investment, which in turn varies with changes of the prices, costs, and incomes of capital goods, and with the rate of interest and changing levels of saving. Other variables that are affected are the incomes of the participants. Since consumer demand functions depend on both asset holdings and income, they also change during the tatonnement. Consequently, the equations that Walras presented as relating to the mature model of general equilibrium do not in fact describe it. Their solutions - prices, rates of employment of resources, incomes, outputs, and quantities traded - are not the values toward which the model actually converges.
In 1899 and in the fourth edition of the Eléments (1900), Walras tried to design a virtual model that would eliminate this problem, thus abandoning his objective and method of trying to construct a realistic model. A virtual model is one in which no economic activities occur in disequilibrium, except for the quotation of prices and the manifestation of the associated desired supply and demand quantities. In that way he hoped that the parameters of his equations would represent conditions that are truly constant during the equilibrating process of his model. He thought that he could achieve the virtual property by assuming that suppliers of resources and other commodities do not produce disequilibrium amounts but, instead, make written pledges to provide the commodities. Walras stated that they vary the amounts offered as a function of a series of suggested prices until the set is found at which the desired supply and demand of every commodity become simultaneously equal in every market. Only then are other economic activities allowed to take place (1900, pp. VIII, 215, 224, 260, 298, 302; 1988, pp. 5-7, §§207, 213-14, 251, 273, 274; pp. 309, 323, 377, 441, 447). The written pledges construction, however, is an incomplete sketch, notably because would-be demanders of consumption goods do not make pledges and so have no means of expressing their desires (Walker, 1996, pp. 372-95). Of course, Walras asserted that there is a tatonnement and that equilibrium is found, but those were just unsupported statements, not a consequence of his assumptions, not an outcome of the structure of the sketch and the behavior of its participants. Furthermore, he did not carry out his plan (1900, p. VIII; 1988, pp. 5, 7) to convert into written pledges markets all the older sub-models that are supposed to play a role in the 1899 design - sub-models dating from his mature period of theorizing but that he left unchanged in the fourth edition of the Eléments. He therefore presented disequilibrium production and exchange as occurring in some markets but not in others, a situation contradicted by his equation system, which allows only for virtual behavior. Thus Walras did not construct a general equilibrium model in his last phase of theorizing. Neither the written pledges sketch alone, nor it and the collection of sub-models associated with it, contain a pricing process or any other economic activities. It does not constitute a functioning system and therefore has no dynamic path and no equilibrium.
Nevertheless, by 1889 Walras had a fully formed conception of the interrelat-edness of economic phenomena and well-constructed sub-models of the important parts of a competitive economic system. The vitality of those contributions to economic theory was manifested by the strength of their influence on Vilfredo Pareto, to whose ideas we now turn.
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