General Equilibrium Analysis

A Century after Walras

Pascal Bridel

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781136719813
• Edition: 1
• Topic: Economics
• Subtopic: Economic History
• Index: Economics

2010 marks the hundredth anniversary of the death of Léon Walras, the brilliant originator and first formaliser of general equilibrium theory – one of the pillars of modern economic theory. In advancing much derided practical solutions Walras also displayed more concern for the problems of living in a second best world than is common in modern pure theories of the invisible hand, efficient market hypothesis, DSGE macroeconomics or the thinking of some contemporary free market admirers all based on general equilibrium theory.

This book brings contributions from the likes of Kenneth Arrow, Alan Kirman, Richard Posner, Amartya Sen and Robert Solow to share their thoughts and reflections on the theoretical heritage of Léon Walras. Some authors reminisce on the part they played in the development of modern general economics theory; others reflect on the crucial part played by general equilibrium in the development of macroeconomics, microeconomics, growth theory, welfare economics and the theory of justice; others still complain about the wrong path economic theory took under the influence of post 1945 developments in general equilibrium theory.

1 Walras: pioneer of illuminating complexity

William J. Baumol

Over the years, Léon Walras has acquired what may be regarded as more than his due share of both adulators and detractors. Indeed, among his most enthusiastic fans are those who have exhibited more than a slight tendency to downplay the contributions of other notable analysts—from Adam Smith to David Ricardo, as well as those who are part of the more recent Keynesian revolution. My purpose here is to argue that both of these evaluations are overly extreme and, moreover, generally have tended to misunderstand the accomplishments of Walras and those who followed in his directions.

The simplifiers and the complicators

To make my reasoning clear, it is first important to cover a bit of nomenclature. I think of the originators and expanders of general equilibrium theory as members of a group of economists that I designate ‘the complicators’. These include Walras, as well as a number of microeconomists—notably many who have devoted their efforts to game theoretic analysis. In contrast, those whose approaches have entailed elements of macroeconomic analysis—for instance, Ricardo and Keynes—I call ‘the simplifiers’.

Members of the latter group characteristically use approaches, such as the aggregation of disparate elements, that minimize the need to wrestle with the complexities of economic activity and its consequences. For example, they deal with economies that contain only four ‘factors of production’, land, labor, capital and entrepreneurship, treating each group as though its members were homogeneous. Of course, they are well aware that all of these factors are heterogeneous in nature, and sometimes, as in the case of Ricardian rent theory, their work even builds explicitly on quality differences within a particular factor—for instance, differences in the quality or location of pieces of land. Still, it remains true that such theories have made their progress by aggregation of the inputs and by treatment of the members of each of the resulting four groups as if they were identical.

In contrast, as noted, the Walrasian vision can be assigned to the former group, the complicators. Indeed, Walras drew our attention to some of the details in the workings of the markets that, though evidently significant, deliberately and legitimately had been assumed out of the picture by others.

There is, however, no good reason to deem either of these approaches to be inferior or to select one of them, a la Schumpeter, to be the only proper guide to our discipline. Indeed, within this discussion, Schumpeter’s great book—surely the most extensive and broadly informed volume on the history of economic ideas—is perhaps the most noteworthy example of what elicits my disagreement. We are compelled to treat Schumpeter’s History of Economic Analysis with respect and gratitude for its author’s careful and extensive labors. I, for one, always turn to it on the occasions when I compose a piece in the arena of doctrinal history. But although the volume is immensely informative, readers surely must note that it is more than a little opinionated and can hardly be considered dispassionate.

As Swedberg (1991) and others have noted, Schumpeter shows limited enthusiasm not only for Smith’s and Ricardo’s contributions, but also for the work underlying the Keynesian revolution, asserting that ‘there is really not one new idea in The Wealth of Nations and Ricardo’s work can best be characterized as a detour’ (Swedberg 1991: 63). In somewhat the same spirit, in a letter to Oscar Lange, Schumpeter summed up his view of Keynes’s General Theory of Employment, Interest and Money as ‘obviously bad workmanship’ (McGraw 2007: 275). In contrast, Schumpeter went to the other extreme in his assessment of Walras, remarking that ‘as far as pure theory is concerned, Walras is in my opinion the greatest of all economists’ (Schumpeter 1954: 827).

I contend that Schumpeter’s evaluation misinterprets what these writers have accomplished. The objectives of Smith, Ricardo, and Keynes, for instance, were very different from those of Walras and his successors in the arena of general equilibrium theory. In making this argument, it is not my goal to deprive Walras of the well deserved pedestal on which Schumpeter placed him, but rather, to assert that the other contributors, who received far less praise from Schumpeter, also have been outstanding contributors to our field.

I am confident that this hardly requires demonstration, and that my colleagues throughout the world already accept this conclusion. What may constitute some novelty in the remarks that follow, however, is my view about the nature of the basic distinction between the contributions of the two groups that I have dubbed the complicators (including Walras) and the simplifiers, as well as the goals that the members of each group pursue. I will turn to that subject presently, after a brief digression on Walras himself.

On Walras and his career

I am reasonably confident that William Jaffé has no close competitor in the thoroughness with which he has pursued the surviving evidence about Walras and his work. Letters, drafts, memoranda, and many other sources of insight are all grist for his mill. In uncovering, translating, and publishing these bits of relevant evidence, Jaffé evidently expended enormous effort. Moreover, his work was carried out with exquisite care and attention to detail—to a degree that may raise questions about his impartiality in these endeavours.

Indeed, Jaffé seems to consider that peril, when he takes pains to remind his audience, ‘Let there be no mistake: my devotion has been to the study of Walras and his works, not to the adulation of Walras and glorification of his writings’ (Walker 1983: 276). Jaffé perhaps seeks to bolster this (legitimate) claim of impartiality by remarking that Walras was ‘not very attractive as a person … was pompous, pedantic, cantankerous, quarrelsome, megalomaniacal and hypochondriacal’ (Walker 1983: 276). And he goes even further, devoting an entire article to A. N. Isnard (1749–1803) as ‘Progenitor of the Walrasian General Equilibrium Model’ (Walker 1983: 55–77).

These observations regarding Walras perhaps tell us more about Jaffé than Walras, but Jaffé’s analysis is more appropriate when he emphasizes Walras’s lack of mathematical training, famously illustrated by correspondence with his colleague at Lausanne, mathematician Hermann Amstein, to whom Walras appealed for help in solving what today would be considered a simple maximization problem with variable coefficients, in the theory of production. Amstein came up with a clear and straightforward answer, making use of Lagrange multipliers (very likely for the first time in any economics discussion), but it seems that, as Jaffé repeatedly emphasizes, Walras never understood this reply (Walker 1983: 83; see also Baumol and Goldfeld 1968: 309–12). Similarly, Jaffé is quite right to reiterate Walras’s oft noted misunderstanding of the requirements for existence and uniqueness of the solution to a system of simultaneous equations—a requirement that Walras believed to be satisfied when the number of equations equals the number of unknowns.

Perhaps most significant, however, is Jaffé’s attempt to find predecessors for the general equilibrium theory. Long ago, Jacob Viner, a careful student of the history of economic ideas, remarked to me that whenever some individual is hailed as the discoverer of a particular economic idea, we can be confident that not much time will elapse before an even earlier candidate is put forth as the true originator by some other scholar. Jaffé, too, cannot resist participation in this game. He offers us a number of candidates for paternity of the general equilibrium theory, including Turgot and Quesnay, with some hints of the idea said to be found in Petty, Boisguilbert, and Cantillon. But these works surely offer little more than crude hints of Walras’s theory, with little that can be regarded as sophisticated analysis of the implications for value theory. True, Quesnay’s Tableau Économique does focus on the interdependence of several major parts of the economy, notably that between agriculture and the handicrafts. But there is little in Quesnay’s work that can be interpreted as a systematic discussion of the formal relationships or of the ways in which the mathematical relationships interact and can be dealt with analytically.

But none of these thinkers is Jaffé’s leading candidate. Rather, as I hinted earlier, at the head of the queue is a little noted writer, Achille-Nicolas Isnard, whose name, we can be confident, is rarely even mentioned in the preponderance of university courses on the history of economic ideas. Although Jaffé and perhaps others¹ may disagree, it is my opinion that this oversight is reasonably well deserved. A reading of Isnard’s discussion of his model and its analysis shows it to be entirely primitive and, as such, surely no substantial threat to the primacy of Walras as the inventor of general equilibrium theory. It is true that Walras was never much of a mathematician, as already noted, but he clearly understood which variables are appropriately chosen for determination by simultaneous equations, how interdependence must enter the model, and how the general equilibrium analysis should be approached.

When we assess the influence of Walras in the adoption of mathematical methods in economic theory, matters are rather different. Here Walras was hardly the first to embrace such ideas. Indeed, his father, Auguste Walras, a relatively minor writer in the field, had already advocated such a move—though the elder Walras seems not to have acted on this idea. Moreover, Cournot already had produced his great masterwork (1838, English translation 1927) though, despite that author’s substantial reputation as a mathematician, his contribution to economics had gone largely unnoticed.² This is illustrated by correspondence between Walras and Cournot some four years before the death of the former (Jaffé 1965, Vol. I: 329n4). Walras, in search of a publisher, wrote to Cournot asking for an introduction to the latter’s publisher, Cournot replied, ‘A cette occasion, je dois vous confesser humblement que je suis loin d’être en bon odeur commerciale dans la maison Hachette [the publisher, of which]…[l]es chefs actuels sont peu d’humeur à se charger de livres qui attendent 35 ans un lecteur sérieux’³ (Jaffé 1965, vol. I: 375).

In concluding this section, it is not inappropriate to digress completely from my theme in order to take note of the perspicacity displayed by the University of Lausanne in its hiring of Walras in 1870 (and, similarly, in its appointment of Vilfredo Pareto as department chair in 1893). Both of these great men were near 40 years of age when they received their positions and, moreover, neither of them had published any serious work in economics at the time of their appointments. One can hardly imagine that any university today would take such a leap of faith.

On the value of simplification vs. complication

Let me turn, next, to my central contention here—that it makes little sense to rank either micro or macro analysis as superior to the other, just as it is hardly rational to make such a choice between the microscope and the telescope.

Macro analysis as well-designed simplification

Einstein is said to have asserted that ‘everything should be made as simple as possible, but not more so’. One can hardly dispute this judgment, nor are the benefits this precept offers to the reader readily questioned. Certainly, in the case of macroeconomics and its simplifications, the gains from carrying out Einstein’s prescription go well beyond enhancement of comfort for the reader, as I will argue presently.

Here it is essential to note that both Ricardo and Keynes, whom I have cited as prime examples of simplifiers, were not driven to their writings by idle curiosity (the motivation to which Veblen attributed academic research activity). Rather, they were led to reason and analyze in the manner they adopted by their desire to formulate economic policy. Ricardo, a successful businessman, surely had his eye focused on matters such as freedom of trade, rules of taxation, and the earnings of labor. His value theory does deal with the prices of individual commodities, but he turned toward a macro orientation in his trade model, which deals with entire industries, rather than with individual firms that import and export products. His comparative advantage model is clearly of this variety. Similarly, his growth model, which analyzes the longer term implications of diminishing returns to agriculture and Malthusian population theory, is also a macroeconomic model, with a focus on two economic sectors—the market for labor and that of agriculture. Ricardo used this model to advocate his free trade policies, which, he argued, could expand the quantity of land available to produce food for the British population, whose wages, measured in quantity of food, otherwise would have been driven to stagnation by the diminishing returns to agricultural labor on a fixed amount of land. In particular, Ricardo’s writing devoted to comparative advantage theory has never lost its attraction to economists, and there is much else among Ricardo’s work that we can appropriately consider macroeconomic in character, which is still of current interest. Without a talent for simplification, however, Ricardo would not have been able to attain these insights for government policy.

This is even more evident in the case of Keynesian economics. Indeed, the substantial aggregation of economic sectors in this theory is well recognized. Keynes’s theory, which divides expenditure into consumption, investment, and government outlays, focuses on two key productive inputs—labor and investment. And it is to the simplification of the theory, which derives from this aggregation and the resulting reduction in the number of variables that the analysis must consider, that we can attribute the formulation of Keynesian policy for combating unemployment, economic depressions, and inflation. These surely are among the prime objectives of Keynes’s analysis and, moreover, are among the main reasons that his work remains widely studied today.

From all of this, I conclude that, in many areas of economics, we are driven to simplification, if our work is to emerge as something usable, in practice. After all, one cannot conceive of a revised Keynesian analysis that looks only at individual industries or focuses strictly on individual firms and their decision-making processes. Keynes’s choice of focus was made with an eye on obtaining results that could be used to shape policy. Thus, he chose to concentrate on analysis of interest rates, rather than expectations for likely returns on investments, in his discussion of investment policy—though he believed that the latter exerts the more powerful influence on investment decisions. Interest rates, unlike expectations, are (arguably) more significant for policy design because they are so much more vulnerable to the influence of governmental actions.

Walras and the genius of illuminating complication

It is with little hesitation that I assign Walras the status of leader of the complicators. After all, general equilibrium theory, in retrospect, is the natural extension of the determination of market values in reality, and clearly, as I have argued, Walras seems to have no legitimate competitors as originator of the analysis. Although he was among the scarce and early readers of Cournot (1927) and even expressed some (rather guarded) appreciation of the latter’s writing in economics, Walras was evidently put off by the discussion of demand in Cournot’s Chapter IV, where the expression F(p) is used to indicate the quantity, D, demanded of a given article, as a function only of the price, p, of that commodity. He recognized the interdependence of the various parts of the economy, and it was clear to him, for example, that the demand for Commodity X is not dependent on the price of X, alone, ...

Table of contents

• Cover
• Title
• Copyright
• Contents
• 1. Walras: pioneer of illuminating complexity
• 2. Léon Walras and monetary economics
• 3. The normative origins of general equilibrium theory; or Walras’s attempts at reconciling economic efficiency with social justice
• 4. Walras, Keynes and the ‘Great Recession’
• 5. The stability of general equilibrium—what do we know and why is it important?
• 6. The computation of equilibria for the Walrasian model: a personal account
• 7. Walras, non clearing markets and imperfect competition
• 8. General equilibrium theory and public finance1
• 9. Macroeconomics and the uses of general equilibrium
• 10. Credit instruments and information in general equilibrium
• 11. Walras’s unfortunate legacy
• 12. On the modernity of Walras
• Index