LEON WALRAS AND THE NEO-CLASSICISM OF LAUSANNE
Leon Walras (1834-1910), a Frenchman who spent his professionally most productive years in Switzerland, approached the neo-classical problem along a path quite different from the one Marshall had chosen.
For Walras rigorous, formal elegance - rather than contact with the practical problems of real life - was the target appropriate for the aim of economists. His concern was with pure theory which he defined as ‘the theory of determination of prices under a hypothetical regime of perfectly free competition'.! He aspired to give economics a scientific status comparable to that enjoyed by the physical sciences and to distil its findings into the form of mathematical propositions. Walras was equally insistent that a sharp line of demarcation should be drawn between pure and applied economics. Though not himself indifferent to policy considerations, he vigorously maintained that the status of economics as pure science should never be compromised in the interests of bringing the work of the theorist closer to the problems of practical affairs. The contrast between the Walrasian and Marshallian intellectual styles could hardly have been more marked.2Walras's career was filled with disappointments. Thwarted in his original ambition to study engineering (ironically, because he failed to satisfy the admissions board of the Ecole Polytechnique of his competence in mathematics), he meandered for more than a decade - with only meagre success - as a journalist, aspiring novelist, railway clerk, and bank employee. Meanwhile, he directed much of his leisure to the study of economics, a pursuit in which he received little encouragement in his native country. Lacking the proper credentials, he was unable to break into the French academic establishment. In 1870 fortune at last smiled. He was then appointed to the newly created chair in economics in at the University of Lausanne.
While resident in Switzerland, he remained though he did not suppress a sense of irritation with French institutions.3The prime objective of Walras's intellectual programme was to produce an exhaustive account of the implications of a regime of perfect competition. Part of the value of this exercise, as he saw it, lay in the fact that many economists had been too readily persuaded of the merits of laissez-faire. ‘How could these economists', he asked, ‘prove that the results of free competition were beneficial and advantageous if they did not know just what these results were? And how could they know these results when they had neither framed definitions nor formulated relevant laws to prove their point?... the fact that economists have often extended the principle of free competition beyond the limits of its true applicability is proof positive that the principle has not been demonstrated.'4
For his purposes, perfect competition was likened to a situation in which buyers and sellers could be brought together in a massive auction 'in such a way that the terms of every exchange are openly announced and an opportunity is given to sellers to lower their prices and to buyers to raise their bids'.5 These conditions were admittedly divorced from reality. He defended the procedure by asking: 'What physicist would deliberately pick cloudy weather for astronomical observations instead of taking advantage of a cloudless night?'6 In his view the case for a procedure which began with abstract general cases and took up the qualifications later was too self-evident to require further comment.
The basic problem to be solved within this hypothetical regime of pure competition concerned the manner in which the prices of the various inputs and outputs were established. Marshall had addressed the same issue by invoking supply and demand curves in various types of markets as the basis for the determination of equilibrium prices. His procedure, however, contained an awkward ambiguity.
It will be recalled, for example, that his analysis of demand required the assumption that incomes were constant. Whether this condition was intended to refer to money income or real income was not entirely clear. In either case it could be objected - as Walras pointed out - that a reduction in any price (even when it could be represented as a movement from a higher to a lower point on the same demand curve) was unlikely to be accomplished without a change in someone's income. Barring the case in which the quantity sold increased by the same percentage as the price had been reduced, the income of sellers would necessarily alter. This, in turn, would imply a shift in the position of the original demand curve.Marshall's formulation was thus too loose to meet Walras's standards of analytical rigour. And it was also too 'partial'. Marshallian procedure called for the investigations of conditions in individual markets on terms which largely isolated them from wider influences. Walras, on the other hand, sought to trace out the manner in which an equilibrium solution could be reached in all markets simultaneously. His target was a statement of the process by means of which a 'general' equilibrium - one which took into account the inter-dependence of all economic activities - was established. A later commentator has described the Walrasian perspective on the economic system as one in which 'no blade of grass can move without altering the position of the stars'.
As a first step toward demonstrating the possibility of a general equilibrium solution,
Walras examined the case of the simplest economy imaginable. It possessed only two goods to be exchanged (identified as x and y). All persons were assumed to be buyers of one good or sellers of the other. On these assumptions, it could be argued that the supply of x and the demand for y (as well as vice versa) were interdependent because the market demand for y (or x) was derived from the incomes received by sellers of x (or y).
Consistent with neo-classical procedure, it was, of course, assumed that the terms on which sellers were prepared to exchange were regulated by the marginal utilities of x and y. Through competitive bidding an equilibrium price ratio would be established.The problem became more intricate, of course, when more than two goods were involved. In the three-commodity economy (with goods x, y and z), three price ratios could be established (x:y, x:z, and y:z). One of these ratios, however, would be redundant, adding no information that could not be derived from the other two. This example illustrated a larger principle: namely, that in a multi-good economy, the number of equilibrium price ratios required was always one less than the number of goods involved in exchange. Thus in an economy with n goods, (n-1) exchange ratios would have to be determined through competitive bidding. The redundant commodity could then be regarded as a standard - or a numeraire - in terms of which all other price ratios could be expressed. This standard commodity, whatever its identity, would possess all of the essential properties of money.
The Walrasian approach to the analysis of the competitive process had the considerable merit of lending itself neatly to presentation in the form of simultaneous equations susceptible to a determinate mathematical solution. This procedure also had an important recommendation in that it emphasized the interdependence of all prices within the economic system. At the same time, Walrasian general equilibrium dissolved the standard lines of demarcation between micro- and macro-theory. The activities of households, firms and industries could not be understood in isolation from one another or when detached from the economy as a whole.
This formal analysis of conditions required to produce an equilibrium was, of course, built on two important practical restrictions. The case of an underemployment of resources, for example, was obviously inadmissible. In fact, the whole argument rested on the assumption that full employment was the normal situation.
The general equilibrium solution could be reached only when it could be supposed that all income was spent; otherwise the total interdependence between supply and demand could not be asserted. Indeed Walras's approach can be interpreted as a logical extension of the tradition Say established when he wrote that 'goods constitute the demand for other goods'.Nor was Walras's system equipped to handle the case of increasing returns to scale. If such production conditions prevailed, a determinate set of equilibrium prices could not be reached. Walras placed too much of a premium on rigorous and tidy solutions to resort to the tactics Marshall had adopted - an appeal to the ‘special' and imperfect markets of the everyday business world - when confronted with this complication.
If these cases could not be handled within his hypothetical r6gime of pure competition
Walras's scheme could still throw some useful indirect light on practical issues. It could now be stated explicitly that laissez-faire would break down under conditions of increasing returns to scale. Alternative arrangements would then have to be devised. In his comments on this problem Walras provided few details beyond noting that the public services and the 'natural' monopolies could not conceivably be conducted under the rules of pure competition. He did insist, however, that additional considerations were pertinent to an assessment of the social results of competition. The outcome of the competitive process, he noted, depended on the initial distribution of income and property. For this reason it did not necessarily follow that the results produced were ideal, nor the only ones conceivable. Different distributional systems, both for income and property, were always possible. Perfect competition, though it might be a reasonably satisfactory allocative device in the existing order, could claim neither perfection nor immortality.
While recognizing the possibility of different modes of economic organization, Walras maintained that judgements on their merits were beyond the competence of economists as scientists. The economist could, of course, point to the existence of alternatives. But discussion of the options best calculated to serve the community's interest fell within the realm of art and was outside the domain of scientific discourse. As citizens, economists might still hold private views about the desirability of particular institutional arrangements. Walras personally was sympathetic to a regime of small agrarian freeholders, an institutional arrangement likely to approximate perfect competition about as closely as any system imaginable.
2.