Economic Equilibrium: The Pre-Walrasian Background
A recurrent theme in economics was, well before Walras and already developed by Adam Smith (1776), the notion that somehow out of the disparate activities of many relatively disconnected individuals a great deal of coordination emerges.
This is the idea behind the often quoted and frequently misinterpreted phrase of Smith in which he refers to the “invisible hand”. There are a number of aspects of this vision that are worth examining. The usual idea, attributed to Smith, is that the result of the unconscious coordination of individuals leads to some sort of social optimum. Even a casual reading of Smith reveals that this is not what he had in mind but once again this is a projection of ideas developed subsequent to Walras. Nevertheless there was clearly present in Smith’s work the ideathat an economy self-organizes into states, which have, possibly positive, attributes. However, the underlying argument in Smith was that capital would flow from activities with low rates of profit to those yielding higher rates and that this would finally result in a uniform rate of profit (that is, zero extra profit) situation, which could now, with hindsight, be thought of as some sort of long-period position or equilibrium. David Ricardo developed the analysis and also included demographic changes and emphasized the importance of land but also envisaged a point of gravitation (see Kurz and Salvadori 1995: ch. 1).
If one accepts the idea that the simple process of interpersonal trading would lead to a situation in which there was no more extra profit to be made from trade and that this could be considered as an equilibrium, then this had much earlier origins as Arrow observed:
The idea that traders will respond to profit opportunities by increasing their activities and, by doing so, tend to wipe them out must have been recognized whenever there was trade.
A 12th century rabbinical commentary argues that if someone charges “too high a price”, others will offer the good at a lower price and thereby bring it down. (Arrow 2007: 1)This idea was developed by Antoine-Augustin Cournot (1838), who defined markets as being places, not necessarily geographically defined, where all units of the same good are sold at the same price. How this would happen was not specified but the argument that the gains from trade would be arbitraged away had a direct influence on Walras who was familiar with, and influenced by, Cournot’s work. Thus Cournot had this early sort of equilibrium notion in mind.
Yet the problem that Walras addressed, and which has come to be called the general equilibrium problem, was not whether economies would settle to some sort of general state from which individuals would not want to deviate, but whether in an economy with many goods it was possible that all these markets would clear simultaneously. He also posed the important but different question: would there be some natural tendency for this to happen? The first and less ambitious question can be phrased as: could one find prices for each of the goods even when the demand and supply for each good depends on the prices of the other goods, such that there would be no excess demand or supply for any good? That is, if you could write down the aggregate demand and supply for the goods as a function of the prices of all goods could you solve this system for an equilibrium?
In this respect there is, it has been suggested, some evidence that Walras was influenced by Achilles-Nicolas Isnard (1781), a French engineer and economist who defined an equilibrium notion and was considered to be a follower (whereas, he was more of a critic) of Quesnay. Isnard has been credited by Ingrao and Israel (1990) with seeing economic equilibrium as a solution of a system of equations and claiming that a solution could be found if the number of equations were equal to the number of unknowns.
The same claim was made by Jaffe (1969: 25), who went as far as to say, “Walras worked out the mathematical framework of his general equilibrium theory with Isnard’s Traite des Richesses at his elbow”. (See also Screpanti and Zamagni 1993.) What is suggested by Jaffe is that the essential framework for Walras’s work was already laid out by Isnard, and that what was lacking was the derivation of demand from the maximization of utility and it was this that Walras added to move the theory forward. Indeed, it has also been suggested that Isnard, as an engineer, was not particularly interested by what motivated individuals to make their choices and that Walras’s contribution was a natural way to fill the gap. All of this is an ex post construction. As Misaki (2009) points out, there is little concrete evidence that Walras actually studied Isnard’s work in detail, contrary to Jaffe’s assertion, and furthermore, as van den Berg (2007) indicates, Isnard developed, at some length, arguments as to the psychological factors influencing people’s choices. As van den Berg (2007: 94) says,Isnard developed sophisticated views about human decision-making processes. While he claimed that producers and consumers make decisions on the basis of personal interests, he qualified these as being supported by unreflective, impulsive, or habitual action and concluded that only conduct motivated by an “interested” choice that is “fortified by virtuous habits” leads to socially desirable outcomes. This concern with the motivations of humans engaged in social transactions stands in strong contrast with modern economic equilibrium theory.
The point here is a simple one, in order to trace a direct progressive path in the development of theory we tend to ignore the other possible routes that could have been taken. If Walras had been more interested in the alternative ways of formulating motivations, for example, by taking various psychological considerations into account, his theory might have evolved quite differently.
However, there are good reasons as to why he took the path he did. Walras had three projects, which he referred to as pure economics, applied economics and social economics. The only one of these that was pursued fully was the first. While, as he himself insisted, no theory has any value if not consistent with empirical evidence, his pure economics and those who followed in that tradition reflect little concern for the inductive approach.
Walras himself was persuaded by the idea that, even though we are dealing with internal feelings and sentiments when talking about what satisfies people, once we establish what these preferences are we can have full recourse to the weapons of the natural sciences. Indeed, in a letter to Hermann Laurent he said:
All these results are marvels of the simple application of the language of mathematics to the quantitative notion of need or utility. Refine this application as much as you will but you can be sure that the economic laws that result from it are just as rational, just as precise and just as incontrovertible as were the laws of astronomy at the end of the 17th century. (Letter no. 1454 to Hermann Laurent, in Jaffe 1965)
In this connection, Mirowski (1989) has developed a complete account of the dependence of Walras on the physics of the time. It is not surprising therefore that he insisted on developing what he came to call l,economie mathematique at the expense of a more general framework. Indeed, Walras continually manifested the desire to be appreciated and approved of by mathematicians. Yet, Walras was far from convincing the mathematicians on many points. For example, late in his life Walras, unjustifiably claimed the unqualified support of Henri Poincare and wrote, “in 1906 I was in contact with certain eminent French mathematicians who had seen at first glance that my mathematical economics was well founded and who made a declaration to this effect at the St. Louis Exhibition” (Walras letter 1642 to Charles Gide, in Jaffe 1965) - this, as Jaffe remarks, despite the explicit denial by Henri Poincare that he had mentioned mathematical economics in the address to which Walras referred (Poincare letter no. 1639, in Jaffe 1965).
Thus there were many forces at play in the evolution of Walras’s work, and although he claimed that the only economists to whom he owed anything were Cournot and his father, Auguste Walras, this is far from being the whole story. He chose the route that he did in part because of his natural inclination to develop what he thought of as an economic science and his fascination with the mathematical approach, but also because of the heritage of ideas of his many intellectual predecessors, such as Quesnay, Isnard, Descartes and J.S. Mill, to name but a few. The extent of their influence is open to discussion but its existence can hardly be denied.