Leon Walras

5.3.1. Walras's vision of the working of the economic system

The major contribution of Leon Walras to economic analysis was his theory of the general economic equilibrium. Although the theme of the relationships among different markets had been studied by preceding economists, no one before Walras had managed to construct a general theoretical structure capable of accounting for the multiplicity of relationships linking one market to another.

The markets must be interrelated so as to make the choices of all the economic subjects compatible. A subject who is unable to achieve the goal of maximizing his satisfaction will have excess demands for some goods and excess supplies for others. By means of exchange, the individual will use the excess supplies to eliminate the excess demands. A state of general eco­nomic equilibrium is one in which the prices are such as to allow all indi­viduals to maximize simultaneously their own objectives, with excess demand vanishing.

The free play of competition leads to a distribution of the factors among the productions of the various goods so as to satisfy the consumers’ demands. The scarcity of productive resources in respect to the demand for goods will decisively influence relative prices. Walras rejected the classical, and especially the Ricardian, distinction between scarce and reproducible goods. He stated in the Elements of Pure Economics:

There are no products which can be multiplied without limit. All things which form part of social wealth... exist only in limited quantities... In the production of some things like fruit, wild animals, surface ores and mineral waters, land-services play the predominant part. In the production of other things like legal and medical services, professors’ lectures, songs and dances, labour preponderates.

This passage, which is important for an understanding of the neoclassical concept of scarcity, shows a serious misunderstanding of the classical theory. In fact, Ricardo maintained that it is the single good that can be reproduced without limits, not the total of goods. The structure of the means of pro­duction, in other words, can be modified to produce any combination of products provided there is freedom of entry in all industries. Competition, intended as a process unfolding through time and not as a static situation in which the amount of each factor is fixed and unchangeable, will induce the capitalists to transfer their own capital from the sectors in which the rate of profit is low to those in which it is high. In this way the structure of supply will adjust to that of demand, while the quantities of capital goods will tend to settle at levels that guarantee a uniform profit rate.

In Walras’s conception, the economy is made up of a plurality of agents who are present on the market either as consumers or as suppliers of pro­ductive services or as entrepreneurs. The economic process originates from the meeting, in the market, of these various agents. The productive services are transformed into goods which are bought, either by other entrepreneurs, who need them for productive uses, or by the final consumers. The latter, who have supplied the productive services to the entrepreneurs, buy pro­duced goods from them by spending the income received in return for their productive services.

Clearly, there is no place in this model for the notion of social class. On the contrary, there are just two groups of individuals: the consumers and the entrepreneurs, distinguished solely by the different decisions they are called upon to take.

At the beginning of each period, let us say one year, the economy has an initial endowment made up of a certain quantity of goods and resources, including natural resources and the goods produced in the preceding period. Each agent owns a certain quantity of goods and services: as a worker he can offer a certain number of working hours, whilst as an entrepreneur he can supply services relating to the organization and control of the productive activity. Each agent tries to attain the best results from exchange. The consumers try, in the first place, to determine that division of their own income between consumption and savings which will provide them with the ratio of maximum satisfaction between present and future consumption. Sec­ond, they determine the way in which their consumable income is to be shared out in the purchasing of various goods so as to obtain the maximum utility. Those who supply productive services try to obtain the best balance between the income received in payment for these services and the sacrifice involved in their supply. Finally, the entrepreneurs try to attain the maximum profit from their own activity, by endeavouring to maximize the difference between the value of the goods produced and the costs sustained in producing them.

The pursuit of their own individual objectives ‘obliges’ the agents to enter into exchange relationships.

Let us now consider the firm. In order to fulfil its production plan, the firm uses, besides the reserves and stocks of fixed factors it already possesses at the beginning of the period, other inputs it buys from other firms and consumers. The output sold gives rise to revenues. The difference between revenues and costs represents the firm’s profit, which is either distributed to the owners of the firm (i.e. to the savers-consumers) or used to buy new plant so as to increase the endowment in future periods. The total production of the system is obtained by summing the production of all the firms. Inter­mediate goods are clearly included in this amount. These are the goods produced by a firm and used by another. If the value of intermediate con­sumption is subtracted from the value of total production, the value of the final output (or the gross national product, in the terminology of national accounting) is obtained. Naturally, the value of the gross national product is equal to the value of the gross national income. In fact, if the value of the intermediate consumption is subtracted from the value of the production of the single firm, the result is the amount the firm has paid for the factors employed or, rather, the income earned from these factors.

The factors of production are the same as the stocks of goods, natural resources, and services that make up the initial endowment of the system. These are owned by the consumers or by the firms; but the firms are in turn owned by the consumers. This means that the consumers possess, directly or indirectly, all the factors, so that the final remunerations only go to them. If the profits of a firm are entirely distributed, and therefore are not stocked to provide for the needs of capital accumulation, the national income is the real purchasing power in the hands of the consumers.

5.3.2. General economic equilibrium

The central aim of Walras’s theory is to show how the voluntary exchanges among individuals who are well-informed (each is perfectly aware of the terms of his own choices), self-interested (each thinks about himself), and rational (each tries to maximize his goals) will lead to an organization of the production and the distribution of income which is efficient and mutually beneficial. The peculiarity of the problem is this: that the sole form of social interaction which is admitted is that realized on the market by means of anonymous and impersonal exchanges. Neither trade unions nor pressure groups nor cartels nor other types of social groupings are allowed, as this would violate a fundamental requirement of the general-equilibrium model, that of perfect competition.

In order to account for the fact that the actions of the individual agents are co-ordinated on the market, it is necessary to demonstrate that prices exist that render advantageous to each individual precisely those activities and choices which satisfy his needs in an efficient way. This is why the theory of prices occupies a central position in the general-equilibrium system.

On the other hand, a complex relationship is established between the prices of goods and the prices of factors.

(1) in each market the demand equals the supply;

(2) each agent is able to buy and sell exactly what he planned to do;

(3) all the firms and consumers are able to exchange precisely those quantities of goods which maximize, respectively, profits and utilities.

It is worth nothing that, in order to obtain this result, it is only necessary to know, as initial data, the number of consumers, the number of firms, the initial endowments of resources, the consumers’ preferences, and the tech­niques available. All the rest is left to the maximizing behaviour of the agents and to the competitive mechanism. In reality, however, two dei ex machina are necessary for the general equilibrium to be reached: the ‘auctioneer’ and the ‘Sisyphus entrepreneur’.

The model of price-formation underlying Walras’s theory of exchange is one of competitive bargaining. According to this model, markets are conceptualized as auctions (one is led to think of an hold French-type stock exchange), in which there are, on the one hand, stockbrokers and, on the other, the auctioneer. At the beginning of the bargaining the auctioneer ‘shouts’ a price for each good and leaves the agents to formulate their buying and selling proposals. If, in correspondence to the shouted prices, the auc­tioneer notices that, for each good, the supply and demand are equal, he will declare bargaining closed, and that price vector will be the equilibrium vector. If this does not happen, the auctioneer will adjust the prices according to the rule: increasing the prices of goods in excess demand and decreasing the prices of goods in excess supply. This trial and error process, which Walras called tatonnement, will continue until all excesses of supply and demand have been eliminated. At this point the auction ends; the final quotations are registered as the equilibrium prices, and the supply and demand declared at such prices become binding contracts; exchanges are carried out on these terms. This is the single-agreed-price bargaining; the prices shouted by the auctioneer during the adjustment process are virtual prices; only the equilibrium ones are the prices at which exchanges actually take place. Such a peculiar way of describing the market process is crucial if one wants to reach a Walrasian general equilibrium. If, in fact, in the course of the process of convergence to equilibrium, the agents were allowed to exchange goods at disequilibrium prices, the individual’s endowments would vary in continuation, and it would never be possible to reach a Walrasian equilibrium, which, by definition, refers to the given initial allocation of resources.

Walras was certainly aware of the strong structural differences between his model and a real market economy. His main objective was to construct a model of an ideal economy which could be used as a solid base for political applications. He knew that this objective would hardly be realized in an authentic market economy. However, he nurtured the hope that the latter could be reformed along the lines of the model.

Let us now turn to the ‘Sisyphus entrepreneur’. Walras considered that a firm is in equilibrium when the profit is reduced to zero owing to the competition among entrepreneurs. In effect, in the Walrasian system there is only one category of maximizers: the consumers. The entrepreneurs, like the auctioneer, are mere co-ordinators who organize the productive activity, taking techniques and prices as given. The Walrasian entrepreneur buys the inputs at the prices fixed by the auctioneer, who looks after the adjustment process in the way described above. If the revenues are above the costs, the entrepreneur registers a profit. The existence of a profit or a loss is a sign of disequilibrium. The entrepreneur reacts to such a signal according to the rule: increase the scale of production when there is a profit and decrease it when there is a loss; ‘Thus, in a state of equilibrium in production, entrepreneurs make neither profit nor loss’, writes Walras (p. 225). Profit depends on exceptional circumstances; from a theoretical point of view it must be considered as a signal of disequilibrium.

Walras argued, therefore, that the choice to become an entrepreneur is purely accidental. The entrepreneur could be a capitalist who pays for the services of labour and land to the respective owners, keeping for himself a residue which is equal, in equilibrium, to the interest on the services given by his capital. Or he could be a worker who, after having paid for the services of the capital and land, obtains a residue equal, in equilibrium, to his wage. The same is true with a landowner who decides to become an entrepreneur. As profits are zero in equilibrium, the socioeconomic identity of the entrepre­neur is completely irrelevant. ‘They [the entrepreneurs] make their living not as entrepreneurs, but as land-owners, labourers and capitalists’ (p. 225). As we will see, the absence of a theory of the entrepreneur in Walras’s theory induced Schumpeter to say that he had built a brilliant theory which however was incapable of dealing with reality.

Walras constructed a system of simultaneous equations to describe the interaction between consumers and sellers. There are as many markets as there are goods, including the productive factors and their services. For each market, three types of equation are defined: one for demand, one for supply, and one for equilibrium. In each market of produced goods, the number of demand equations is equal to the number of consumers, while the number of supply equations is equal to the number of firms producing the good. In each factor market, the number of demand equations is equal to the number of firms multiplied by the number of goods produced by each of them, while the number of supply equations equals the number of owners of the factors. Furthermore, the ‘production equations’ are defined in such a way that the price of each product is equal to its cost of pro­duction, so that in equilibrium the entrepreneurs make ‘neither profits nor losses’. The costs of production depend on the input prices and the technique in use. The latter is represented by some technical coefficients, assumed fixed, which express the proportion in which each input is com­bined with the output. Then, in the ‘capitalization equations’, it is assumed that the purchase price of each capital good is equal to its ‘net income’ discounted at the current rate of interest. And this implies an equilibrium configuration in which the rates of returns of all capital goods are uniform and equal to the rate of interest. Finally, there is an equation that determines the rate of interest with the forces of supply and demand of the new capital goods.

Now, a necessary but not sufficient condition for such a system of equa­tions to have a solution is that the number of unknowns is equal to the number of equations. This raises three orders of problems of which Walras was not perfectly aware. The first originates from the capitalization equa­tions which—to the extent that they impose a uniform rate of return on capital goods, a purchase price equal to the production price, and the equality between supply and demand of each capital good—introduce into the model an over-determination of a degree equal to the number of production equations of the new capital goods minus one. It is possible to avoid this problem by renouncing the uniformity requirement for the rate of returns and by interpreting the model in terms of temporary equilibrium. We will discuss this further below.

The second order of problems originates from the fact that one of the equations in Walras’s system functionally depends on the others, so that the number of independent equations is lower than the number of unknowns. Intuitively, the matter can be explained in the following terms. If there is equilibrium in all the markets except one, this means that consumers have spent a sum of money equal to the value of the goods offered. But, given that the total value of the goods produced (the national product) equals by definition the total income earned by the consumers (the national income), there will also be equality between supply and demand in the last market. In 1942 Oscar Lange called this circumstance ‘Walras’s Law’: in a general equilibrium system, if all the markets, except one, are in equilibrium and the budgets of all the agents break even, then the remaining market must also be in equilibrium. This law is the ultimate consequence of the fact that, in the Walrasian conception of the economic system, the act of demanding goods on the part of an individual presupposes that he offers goods of equal value. But Walras did not grasp the mathematical implications of this fact.

Finally, we come to a third order of problems which is perhaps the most important. Walras did not take into account the fact that having ‘counted’ as many equations, even if independent, as there are unknowns is not enough to ensure the existence of a solution. A system of equations may have no solution at all, or may have many, even an infinity. Even in the case in which a solution exists, this may have no economic meaning, as would happen if some prices or some quantities were negative. Almost a century was to pass before the neoclassical economists managed to find the solution to this problem. We will see their results in Chapter 10.

5.3.3. Walras and the articulation of economic science

Walras’s impact on the evolution of economic theory has been enormous. No other economist before him had managed to construct a theoretical model and an analytical method which was so vast and versatile. Others, such as Quesnay and Cournot, had formulated the idea of interdependence among economic facts. But while Cournot maintained that the problem of general equilibrium was outside the scope of mathematics, Walras proved that, at least in principle, the problem could be resolved.

Notwithstanding this, his work passed almost unnoticed in France during the twenty-five years following its publication, and it was really only in the 1950s that the attitude of French scholars towards him began to change radically. But also outside France the reception of his work was, initially, somewhat cold, if not hostile. The relationships between Walras, on the one hand, and Jevons, Edgeworth, Wicksteed, and Menger, on the other, were certainly not the most cordial. Marshall, in his Principles, quoted Walras only three times and in brief passages. An exception should be made for the Italians; Pantaleoni, Barone, and especially Pareto held him in great respect, and were fervent propagandists of his work.

Walras, as Menger had done, always endeavoured to maintain a clear distinction between moral values and science. He believed that pure science had nothing to do with value judgements: ‘The distinguishing characteristic of a science is the complete indifference to consequences, good or bad, with which it carries on the pursuit of pure truth’ (p. 52). And Walras added, following Bentham: ‘From other points of view the question of whether a drug is wanted by a doctor to cure a patient, or by a murderer to kill his family, is a very serious matter, but from our point of view, it is totally irrelevant. So far as we are concerned, the drug is useful in both cases, and may even be more so in the latter case than in the former’ (p. 65). It is this radical dualism between technical and ethical judgements that was to dominate developments in economic thought.

Walras had always intended to write another two systematic treatises, one on applied and one on social economics, which would in some way have supplemented his fundamental work on pure theory. But the debilitating rhythm of work as professor in Lausanne, a position he had gained, not without difficulty, in 1870, absorbed all his energies until 1892, when he left teaching. After this, he contented himself with publishing two collections of papers, entitled ILtudes d’economie sociale (1896) and Istudes d’economie politique appliquee (1898).

Walras was a close observer of contemporary economic problems, favouring moderate reformism in socioeconomic matters. His political position, which he derived from Kant’s moral philosophy and the ration­alism of his times, was a mixture of traditional liberalism and the doctrine of State intervention. It is interesting that, while in regard to questions of justice he was a convinced supporter of the natural-law approach, he com­pletely expelled the notion of natural law from economics. He never believed that, beyond observable facts, there could be a structure of eco­nomic laws capable of mirroring some natural order. As we already know, Walras was a severe critic of the classical dichotomy between natural and market prices and of everything derived from that distinction. Finally, he believed that economic analysis could not have any intrinsic connection with the measures of economic policy; he always kept the normative and positive analyses clearly separated. Walras divided economics into three different fields: pure economics, which is based on the principle of truth, and concerned with the relationships among things; applied eco­nomics, which is based on the principle of utility and concerned with the relationships between persons and things; and social economics, which is based on the principle of justice and concerned with the relationships among persons.

Walras put forward numerous articulate recommendations for economic policy. His favourite subjects were the nationalization of natural monopol­ies, the stabilization of prices by the monetary authorities, the capital market, whose efficiency and reliability should be ensured by the State, and the acquisition of land by the State and its concession in use to private agents in order to increase government revenues. It is worth noting the curious fact that Walras considered himself a ‘scientific socialist’.

5.4.