I. TWO QUESTIONS RAISED BY PROFESSOR BLAUG

In the present paper, I propose answers to two questions about the evolution of the neoclassical theory of value and distribution, raised by a series of stimulating recent papers by the late Professor Mark Blaug (Reference Blaug, Curtis Eaton and Harris1997, Reference Blaug1998, Reference Blaug, Backhouse and Creedy1999b, Reference Blaug and Mäki2002a, Reference Blaug, Boehm, Gehrke, Kurz and Sturn2002b, Reference Blaug2003a, Reference Blaug, Samuels, Biddle and Davis2003b).^{Footnote 1} In these writings, he has accused modern economics of sterility and irrelevance,^{Footnote 2} and has traced the origin of this development to the Formalist Revolution undergone by economic theory in the 1950s and “marked, not just by a preference, but by an absolute preference for the form of an economic argument over its contents” (2003a, p. 145). I intend to concentrate on only one aspect of these rich papers, a message on which, it seems to me, Blaug particularly insists, and that is convenient to distinguish into two parts:

—first, a descriptive and evaluative part that argues that modern 'orthodox' economic theory deals with models based on unrealistic assumptions and therefore irrelevant for the understanding of actual economies, and that a basic reason is a turn taken by the (neoclassical) theory of value and distribution between the 1930s and the 1950s: the abandonment (epitomized by the Arrow–Debreu model of general equilibrium) of the notions of competition and equilibration as time-consuming processes;

—second, a cause-retracing part that suggests that the main reason why this turn won the favor of the profession was the rise of formalism, “which is not just the application of mathematical techniques to economics, but rather reveling in mathematical modeling as an end in itself” (2003a, p. 146), with too little attention to the economic content of the display of mathematical brilliance.

I happen to agree with Blaug's very negative assessment of modern general equilibrium theory,^{Footnote 3} but I find Blaug's historical reconstruction only partially correct. To anticipate: with the help of the insights of the late Pierangelo Garegnani (Reference Garegnani, Brown, Sato and Zarembka1976, Reference Garegnani1978, Reference Garegnani, Eatwell, Milgate and Newman1990, Reference Garegnani2012), I shall argue that the first part of Blaug's message is correct but grasps only a consequence of an analytical change in the formulation of the neoclassical theory of value and distribution that seems to have escaped Blaug: the adoption of a vectorial specification of the capital endowment, which entailed the reformulation of the notion of equilibrium as being very short-period, in place of the traditionally dominant notion of long-period general equilibrium, which had gone together, in all the founders of the neoclassical approach (with the sole exception of Léon Walras, who is less clear than the others on the issue), with the treatment of capital as a single factor (of variable 'form'), in spite of as complete a disaggregation of markets as in Walras. It was the shift to a Walrasian specification of the equilibrium's capital endowment as a given vector that, by depriving the equilibrium's data of persistence, had the consequences denounced by Blaug. The conception of capital as a single factor of variable 'form,' by giving the equilibrium the persistence necessary for the role of center of gravitation, had given the analyses of Alfred Marshall, John Bates Clark, Eugen von Böhm-Bawerk, or Knut Wicksell the plausibility that Blaug finds missing in Arrow–Debreu. This has implications for the second part of Blaug's message, too: once the root of the malaise is thus understood, one can find a more persuasive reason than formalism for the success of the Arrow–Debreu model (although, no doubt, formalism did have some influence): the growing realization of the untenability of the treatment of capital as a single factor. This, according to Garegnani, made it inevitable to turn to Walras’s treatment of the capital endowment (until then very unpopular) as the only way to maintain a supply-and-demand approach to value and distribution.

The reader will not find in the present paper an overall evaluation of the relevance of formalism in the evolution of economic theory after World War II. Certainly, I give formalism less responsibility than Blaug does for the development on which I concentrate, but this does not imply that the notion itself of a Formalist Revolution should be given up, especially if the term is given Benjamin Ward's original meaning, quoted by Blaug in (1999b, p. 257), that mathematics became “the natural medium for expressing [one's] professional ideas.” But my interest is not in assessing the legitimacy or possible meanings of the notion of a Formalist Revolution; it is, more narrowly, in the reasons for the 'wrong turn' taken from the 1930s to the 1950s by the neoclassical theory of value.

To get to the two questions that are my central concern, it is useful to expand on the first part of what I have described as Blaug's message. It seems to me that Blaug condemns the excessive importance given to mathematical elegance and to “rigor as understood in mathematics departments,” above all because it has helped expunge from equilibrium theory the study of “competition as a process,” in favour of an exclusive concentration on “competition as an end state,” with two strictly connected effects. It has prevented “consideration of all dimensions of competitive rivalry other than price, such as availability, quality of product, quality of delivery, quantity and quality of information about the product, etc.; in short, all aspects of non-price competition because those take place sequentially in real time” (1999b, p. 266), and it has also excluded all realistic study of the stability of equilibrium:

The disappearance of the “process-conception of equilibrium” is also central in Blaug's discontent with the game-theoretic notion of Nash equilibrium and with the models based on rational expectations (2002a, p. 42), both accused of the same disregard for the dynamical processes of actual choice and learning.

Blaug is particularly clear in his criticism of the paper “that marks the beginning of what has since become a cancerous growth in the very center of microeconomics” (2002a, p. 36), the 1954 article by Kenneth J. Arrow and Gérard Debreu on the existence of equilibrium, singled out as the most representative of the leading publications of the 1950s, because “It neatly exhibits the worst features of formalism” (2003a, p. 146). The article's existence proof, Blaug explains, required

The two negative aspects of the Arrow–Debreu approach to general equilibrium stressed here are, first, that it needs an unrealistic assumption of complete futures markets in contingent commodities; and, second, that it gives up any attempt to prove that the equilibrium is stable and concentrates exclusively on existence. A clarification is opportune on this second criticism, which may appear misplaced, since Arrow, a few years after the article with Debreu, wrote with Leo Hurwicz and H. D. Block two articles on the stability of equilibrium. However, Blaug rejects those studies because they are based on the fairy tale of the auctioneer and, therefore, are not dealing with real stability: “general equilibrium theory solved the stability-of-equilibrium question by ruling out disequilibrium trading” (2002a, p. 40). Neither should the reference to Walras mislead the reader: Blaug has in mind the Walras of the first three editions of the Eléments, where the tâtonnement consists of adjustments that “take place sequentially in real time,” involving the actual production and exchange of disequilibrium quantities; he considers the recourse to ‘bons’ of the later Walras as meaning that, with the fourth edition of the Eléments, Walras “simply gave up the effort to provide a convincing account of how real-world competitive markets achieve simultaneous multimarket equilibrium” (1997, p. 247) and shifted his focus from the stability problem to the existence question (2002a, p. 51n4).

When thus clarified as rejecting the modern tâtonnement in ‘logical time’ because only adjustments that “take place sequentially in real time” are acceptable, Blaug’s criticism on stability is applicable to the whole of modern general equilibrium theory and appears to be widely accepted. This raises the question of why modern general equilibrium theory expunges disequilibrium adjustments that “take place sequentially in real time.” This is the first question, of the two mentioned in the opening sentence of this article, to which the present paper intends to propose an answer. Basing myself on Garegnani's insights, I will argue that the answer is the vectorial endowment of capital goods, which also allows an explanation of why the Arrow–Debreu equilibrium, in order to be so interpretable as to apply to economies with capital goods, must assume complete futures markets (or perfect foresight); Blaug does not reach this answer because he is unclear about the role of capital as a single factor of variable ‘form’ in traditional neoclassical theory (section II). I will also argue that the same answer allows understanding of why the criticisms advanced by Blaug are a comparatively recent phenomenon, no analogous criticisms being historically moved against the different notion of (long-period) equilibrium that dominated the neoclassical approach from its birth to the Formalist Revolution, a notion shared by Walras, too (section III). And, I will argue that along this road, one reaches important insights on the second question implicitly posed by Blaug: what induced the profession to accept the specific notion of intertemporal equilibrium as the foundation of the neoclassical approach to value and distribution (section IV)? In the concluding section V, I will discuss the proposal to surmount the deficiencies of modern general equilibrium theory through a return to Marshall.

II. THE WALRAS–ARROW–DEBREU SPECIFICATION OF THE CAPITAL ENDOWMENT

I noted above that the assumption of no disequilibrium trading or production was also made by Walras in the fourth and fifth editions of the Eléments. One is then induced to ask: is there any analytical element common to Walras, and to Arrow–Debreu, that may explain the exclusion of disequilibrium trading and production from their analyses of stability? And might not the same element be also responsible for the other obvious absence of realism of the Arrow–Debreu model, the complete intertemporal markets assumption?

This common analytical element can indeed be found: it is the treatment of the equilibrium's endowment of capital goods as a given vector; in other words, the inclusion among the general equilibrium's data of a given endowment for each capital good, however short-lived. The lack of persistence of this group of data is what makes it impossible to admit time-consuming adjustments: these would involve actual productions that would alter the endowments of capital goods and, hence, would alter the equilibrium itself, rendering meaningless the question of the stability of the equilibrium corresponding to the initial data; for the same reason, the capacity of the equilibrium to indicate the behavior of real economies is undermined.^{Footnote 4}

What is missing in Blaug’s articles is a recognition of the fact that the rise to dominance of this readoption of Walras’s specification of the capital endowment was a novelty, relative to the treatment of the endowment of capital that had dominated the marginalist approach^{Footnote 5} until then. Apart from the exception constituted by Walras and the very restricted number of his close followers, before the Formalist Revolution, capital was treated like a single factor of variable ‘form.’ Thus, in J. B. Clark, Böhm-Bawerk, Wicksell, and John R. Hicks (up to 1932), the quantities of the several capital goods are explicitly left to be determined endogenously by the equilibrium, and the endowment of capital is a given single quantity (of exchange value) whose ‘form’—i.e., composition—is determined by the tendency toward a uniform rate of return on supply price, so equilibrium product prices are what Marshall called “long-period normal prices.” Accordingly, this notion of equilibrium can be called a “long-period general equilibrium,” which is no less disaggregated than the Arrow–Debreu equilibrium, as one can clearly see in Wicksell (Reference Wicksell1934), but nonetheless needs the given endowment of capital as a single quantity of variable 'form' in order to be determined because it treats the endowments of the several capital goods as endogenously determined variables.^{Footnote 6}

The difference this makes to the study of the stability of equilibrium is evident. When capital is conceived as a single factor whose 'quantity' is altered only by net accumulation, not by changes in its 'form,' then its endowment changes with a low speed comparable with the speed of change of the endowment of labor, and, therefore—in the same way as for labor—the change this endowment may undergo during the time-consuming disequilibrium adjustments of supplies and demands can be legitimately neglected. The speed of variation of the endowment of capital so conceived could indeed be argued to be of a lower order of magnitude than the speed of variation of the composition or ‘form’ of capital; this difference in relative speed rendered it legitimate to assume that the ‘form’ of capital was endogenously determined while treating its total endowment as given. The equilibrium could then be conceived to be as persistent and as compatible with time-consuming disequilibria as that of a non-capitalistic economy where the sole factors were labor and lands, whose endowments would be unaffected by disequilibrium adjustments. If, to the contrary, the data of equilibrium include a given endowment of each capital good, then stability can be studied only on the basis of processes that do not cause changes in those endowments, and, therefore, on the basis of absurd ultra-fast (instantaneous, in fact) adjustments with recontracting that exclude production and exchanges during the adjustments.^{Footnote 7}

Why the vectorial endowment of capital goods is responsible for the assumption of complete futures markets is also easily grasped. When the initial composition of capital is given, one can no longer assume, as is possible for long-period equilibria, that endogenous changes in equilibrium relative prices are slow enough as to make it legitimate to neglect them. The arbitrary, given, initial endowments of capital goods may be very far from the quantities that would induce firms not to wish to alter them, so they may be quickly changing with consequent relevant changes in relative prices. It becomes necessary, therefore, in determining the actions of agents at the time the equilibrium is established, to take into account the changes that they can expect relative prices to undergo. (In Walras, this need is not recognized because, as will be pointed out below, Walras thought he was determining a long-period equilibrium—i.e., persistent prices; this difference motivates the appellation ‘neo-Walrasian’ rather than simply ‘Walrasian’ for the modern general equilibrium notions that admit that equilibrium prices may be changing very quickly.) Then, either one assumes the simultaneous determination of equilibrium current and subsequent prices (intertemporal equilibria with complete futures markets or perfect foresight), or one introduces expectations of price changes and determines temporary equilibria with given expectation functions among the data. The first alternative was the first to be formalized because of the possibility to present it as a simple reinterpretation of commodites and prices as dated in the formal model of non-capitalistic production and exchange, a reinterpretation believed to be capable of making room for capital goods with no formal modification apart from the explicit consideration of intermediate goods. Attempts to formalize the second alternative started only at the end of the 1960s but were essentially abandoned after the difficulties encountered in the 1970s and 1980s.^{Footnote 8} So, nowadays, the exclusive representative of the 'rigorous' neoclassical theory of value and distribution is the intertemporal general equilibrium model.

The above considerations imply that it is difficult to agree with Blaug when he describes the shift undergone by “mainstream economics” as a concentration “entirely [on] static end-state equilibrium theorizing” (also cf. 1997, p. 242). This sentence implies that the notion of equilibrium did not change, but theorists concentrated exclusively on describing it, rather than attempting to prove its stability. It seems more correct to say that the conception of the equilibrium state as a center of gravitation, the tendential end result of time-consuming adjustments, was abandoned in favor of a different conception of equilibrium. An equilibrium describing the end-state result of competition must be an equilibrium resulting from time-consuming adjustments, and, therefore, having endogenously determined quantities of capital goods. What actually happened was a shift to a different, very-short-period notion of general equilibrium based on given amounts of the several capital goods and, hence, deprived of any persistence, an equilibrium that either is reached instantaneously or disappears, to which, therefore, the appellative “end-state” cannot be applied. This is not in denial of Blaug's distinction between competition “as an end-state,” by which he appears to mean firms individually facing a horizontal demand curve, and “as a process”; but the question remains as to why older neoclassical authors found no problem with admitting both, while “competition as a process” is not simply neglected but becomes impossible to admit in neo-Walrasian models: the recourse to the fairy tale of the auctioneer indicates a new need to avoid changes in the data of equilibrium during disequilibrium, clearly due to the given vector of capital endowments.^{Footnote 9}

But Blaug does not seem to recognize the presence in the marginalist tradition of a notion of long-period disaggregated general equilibrium, where capital goods are heterogeneous but their proportions are determined endogenously and their total endowment is given as a quantity of a single factor of variable 'form.' The only marginalist/neoclassical attempt to determine a disaggregated equilibrium simultaneously on all markets that he recognizes is the one of Walras and then of the neo-Walrasian models of Hicks's Value and Capital, Arrow–Debreu, and subsequent developments; this is what he means by “general equilibrium theory.” This forgets Wicksell (Reference Wicksell1934), whose model of general equilibrium is clear about the simultaneous presence of heterogeneous capital goods (whose endowments are endogenously determined) and of a given total quantity of (value) capital. It also forgets J. B. Clark, who is often misunderstood nowadays as having assumed an aggregate production function but, in fact, was talking about long-period multimarket equilibrium as much as Wicksell, and clearly indicated that capital goods were heterogeneous, and yet, the capital endowment of the economy was a quantity of a single factor that changed ‘form’ depending on the amount of labor with which it was combined.

And it also forgets Marshall, where that conception of capital is less explicit but no less present and indispensable. Marshall is amazingly slippery when it comes to specifying the data determining normal income distribution: in spite of his own declaration that the long-period general equilibrium—which he calls “the (static) stationary state”^{Footnote 10}—should be the starting point from which one can approach more concrete analyses, he never specifies its complete equations or, therefore, its data, and so he never makes explicit how to specify the capital endowment for the determination of income distribution in a situation in which all industries have been given time to reach long-period equilibrium and, therefore, the composition of capital is entirely endogenously determined. However, the conception of capital as a single value factor of variable ‘form’ emerges when investment choices are discussed, and is, in fact, very similar to J. B. Clark’s, in that technical choice is treated (e.g., in Principles, VI, I, 8, [1920] 1972, pp. 430–431) as if production functions with value capital as one of the factors were legitimate.^{Footnote 11} As confirmation of the presence in Marshall of the idea that concrete capital goods represent embodiments of acts of ‘waiting’ measured by the value of the savings invested in them, and that, therefore, the stock of physical capital goods represents a homogeneous amount of cumulated savings, one may note that even the recognition that durable capital goods, once built, earn quasi-rents, which may not correspond to their supply price, is evidently considered by Marshall as being of secondary relevance. It does not prevent him from speaking of the ‘total stock of capital’ of an economy as a single quantity, a (value) factor measurable independently of income distribution, increased by net savings, capable of reallocation among different uses, and functioning in the marginalist substitution mechanisms analogously to factors measurable in ‘technical’ units like labor or land. This is particularly evident when Marshall quotes Heinrich von Thünen approvingly and speaks unproblematically of “substitution of capital for labour,” and when, at last “considering the whole world, or even the whole of a large country as one market for capital,” he speaks of “the general fund of capital” and of “a rise in the rate of interest which will cause capital to withdraw itself partially from those uses in which its marginal utility is lowest. It is only slowly and gradually that the rise in the rate of interest will increase the total stock of capital” (Principles, VI, II, 3 and 4, [1920] 1972, pp. 433, 443–444). In these expressions, the change in the composition of capital associated with an increase of “the total stock of capital,” a change that will generally include the disappearance of many types of capital goods and the appearance of new ones, does not prevent the description of the effect of net savings as a change of the endowment of a single factor capital, an endowment described as capable of ‘withdrawing’ from some uses and moving to other uses, much like labor. The conception of the capital endowment is, therefore, the same as the one more clearly enunciated in J. B. Clark, although Marshall tries to avoid making it explicit.^{Footnote 12} The short-period framework of his analysis of what determines the rate of interest—that is, the attention to the fact that in any short period, the durable capital goods of firms are mostly given and earn quasi-rents, and the rate of interest is, therefore, determined in the savings-investment market by equilibrium between supply and demand for the flow of ‘free’ capital—only brings out more clearly what is implicit anyway in the traditional marginalist approach: that the demand for capital can concretely manifest itself only through a succession of demands for savings.^{Footnote 13}

It must anyway be stressed that in his short-period analyses involving production, Marshall takes only the amounts of durable capital goods as given, so the short-period equilibria he determines are still persistent enough to be conceived as centers of gravitation of time-consuming adjustment processes. John Maynard Keynes follows him in this respect (Petri Reference Petri2004, Appendix 2A1). The difference is radical from modern General Equilibrium (GE) models where the endowments of all capital goods are given, even the ones of extremely short duration, and even the initial inventories of consumption goods.

III. THE LONG-PERIOD METHOD, AND WALRAS

My second question requires, then, essentially an answer to why the Walras–Arrow–Debreu treatment of the capital endowment as a given vector eventually came to be preferred by marginalist/neoclassical economists over the originally dominant treatment of capital as a single factor of endogenously determined ‘form,’ in spite of the elements of unreality of the resulting notion of equilibrium. (I say eventually because the vectorial specification of the capital endowment was already in Walras but, up to at least Hicks’s Value and Capital, it remained clearly minoritarian—Blaug agrees [1997, p. 253; 1999b, p. 263]—so one must also understand the reason for this fact.)

In one article, Blaug suggests an influence of Bourbakism, the project of recasting the whole of mathematics as deductions from axioms (2003, pp. 148, 150). But this can perhaps explain Debreu’s style, not the model—the proposal of a reinterpretation of the atemporal, non-capitalistic general equilibrium of production and exchange as an intertemporal complete-futures-markets equilibrium—or the success of that model in a profession surely not significantly touched by those tendencies in pure mathematics.

In another article, after explicitly posing the question of why the Formalist Revolution happened, Blaug suggests a sociological explanation:

But, considerations of this type contribute to explaining why mathematical competence became increasingly important among economists; they can hardly explain the shift to very-short-period notions of general equilibrium. The long-period framework offered abundant difficult questions open to formalization and further study; it suffices to think of Wicksell’s attempts to deal with fixed capital. Love for formalization by itself does not dictate the direction in which to formalize. And since, as Blaug admits, “When Arrow and Debreu employed game theory and the Nash equilibrium to prove existence of general equilibrium in the 1950s, the Formalist Revolution was still in its early stages” (2003a, pp. 149–150), it is hard to believe that, at the time, economic theorists were already so deformed by formalism as to be ready to accept nearly anything as long as it was mathematically elegant.^{Footnote 14}

A more promising direction in which to find an answer is again suggested by Garegnani (Reference Garegnani, Brown, Sato and Zarembka1976, Reference Garegnani2012), who has argued that (i), at least until the 1930s, adherence to the traditional long-period method was the normal way to do economic theory, and neither was Walras an exception; and that (ii), unease with the notion of capital as a single value factor was an important determinant of the subsequent shift to neo-Walrasian notions of equilibrium, with proof from Hicks. The remainder of the present section adds something on the first argument; the next section, on the second.

The meaning and universal acceptance of the long-period method can be illustrated by stressing that Walras, too, intended to determine a long-period equilibrium, a thesis still not widely accepted. Marshall, Dennis H. Robertson, Wicksell, or J. B. Clark took it for granted—as did Adam Smith, David Ricardo, or Karl Marx—that it is not only uninteresting but also impossible to describe fully the forces determining each production decision, or the details of the moment-by-moment behavior of market prices. However, they shared with the classical authors the belief that it was possible to explain and predict the average of each price or quantity, because the actual path of a price or quantity would tend to gravitate around and toward definite values, or “centers of gravitation,” independent of the details of the gravitational process itself. The existence of this gravitation made the prediction of each single transaction unnecessary (and uninteresting). Changes of this “center of gravitation,” caused by changes in the data determining it, could then be used to explain and predict the trend of the actual path of the variable under consideration, a trend determined by the tendency to gravitate toward the new (or the shifting) center of gravitation. The differences between the classical and the marginalist theories of distribution and outputs entailed that the centers of gravitation were determined differently in the two approaches, and could be qualified as ‘equilibria’ only in the marginalist approach; but the distinction between market and normal prices, the latter being associated with a uniform rate of return on supply price and being the centers of gravitation of the former, is found in both approaches. So, the role traditionally assigned to equilibria by marginalist authors was the very concrete and relevant one of determining the average and the trend of the observed prices and quantities of economies admitted to be continually in disequilibrium. The long-period or normal nature of the equilibrium prices is revealed by the uniform rate of return on supply price, and by the persistence attributed to these prices, revealed by the absence of any consideration of price changes in their determination. Walras is no different in this respect. The role of equilibrium as a center of gravitation, to which the economy tends through time-consuming adjustments, is, for example, crystal clear in this passage, present from the first to the last edition of the Eléments:

Now, if the processes causing the economy to gravitate toward equilibrium “at best ... are slow,” then it is impossible to include a given quantity of each capital good among the data determining the equilibrium, because the time-consuming disequilibrium processes can and will quickly alter these quantities, which must, therefore, be conceived as determined by, rather than determining, the “center of gravitation.” As a consequence, the positions qualifying as centers of gravitation in a general equilibrium analysis must be such that the relative amounts of the several capital goods in existence have themselves reached an equilibrium and are, therefore, endogenously determined by the equilibrium itself. The force responsible for the adjustment will be the same as in the classical authors: the “mobility of capitals” in the search for the highest rate of return; i.e., the tendency of investments to be directed to the prevalent purchase of the capital goods offering the prospect of a higher rate of return—the same process also responsible for the tendency of rates of return on supply price toward uniformity.

Here, too, Walras is no different; he, too, writes that in equilibrium, this process must have completed its operation:

Consistently with this quotation, in his complete general equilibrium equations,^{Footnote 15} Walras assumes the equality between cost of production and “selling price” (his term for “demand price,” the present value of the future rentals to be earned by the capital good). He assumes a uniform rate of return on supply price (URRSP) for all capital goods, and he treats the prices he is determining as very persistent. For example, he determines the purchase price of land by dividing the rental of land by the rate of interest, the capitalization formula for perpetual revenues, implying that equilibrium prices and equilibrium interest rate could be treated as if unchanging for very long periods. These are the distinctive marks of long-period analysis. The above quotation furthermore admits that it is changes in the relative endowments of the several capital goods that bring about the equality between ‘selling price’ and cost of production. Again, this is fully traditional.^{Footnote 16}

The long-period nature of Walras’s notion of equilibrium, evident also in other aspects of his analysis (e.g., the constant-returns-to-scale production functions with no fixed-factors/variable-factors distinction), confirms that the traditional method of long-period positions was universally accepted at the time. Then, it is not surprising that Walras’s treatment of the capital endowment remained minoritarian: the other founders of the marginalist approach were clear on the need to leave the composition of capital to be determined endogenously. But then why was the situation reversed some decades later?

My answer in the next section to such a broad question, without aspiring to be a full historical reconstruction (even a large book would probably be insufficient), will argue for the plausibility of Garegnani’s interpretative line by stressing elements missing in Blaug’s historical picture. The main one is the admission by several important authors in the 1930s of difficulties with the conception of the several capital goods as embodiments of a single factor 'capital' of variable 'form.’ The importance of this fact is underlined by the following observation: without the recognition of those difficulties, it is unclear why there should have been a movement away from that conception of capital, which played a fundamental role in the plausibility of the supply-and-demand approach. This role can be made evident by noting how that conception avoided criticisms such as Blaug’s: the persistence of the data of equilibrium, achieved by treating capital as a single factor and leaving its composition to be determined endogenously, allowed a discussion of stability based on time-consuming disequilibrium. It also allowed neglect of the slow changes that normal prices may be undergoing, and thus it avoided the need to consider price changes in the determination of the equilibrium position. Furthermore, the variable ‘form’ of capital avoided a third difficulty of modern general equilibria, stressed by Garegnani (1990, p. 57) but not by Blaug: the insufficient substitutability among factors when the kinds and quantities of capital goods are given. Little wonder, then, that no Blaug-like complaints were raised against marginalist value theory in its early versions.

IV. WHY THE DOMINANCE OF LONG-PERIOD NOTIONS OF EQUILIBRIUM WAS SUBVERTED

It is well known by now that the proposal of a shift to a vectorial endowment of capital goods and to notions of intertemporal or temporary equilibrium, first advanced at the end of the 1920s by Erik Lindahl and Friedrich August von Hayek, reached the generality of economists only some years later, with Hayek's controversy with Frank H. Knight and above all with Hicks's Value and Capital. I can be brief because the issue has been ably discussed already (Garegnani Reference Garegnani, Brown, Sato and Zarembka1976; Murray Milgate Reference Milgate1979, and 1982, pp. 125–142; Heinz D. Kurz and Neri Salvadori 1995, pp. 455–460; Christian Gehrke Reference Gehrke2003; Paolo Trabucchi 2011). No doubt, one cause of the shift was Wicksell, who, after abandoning Böhm-Bawerk’s ‘average period of production’ and the connected conception of the amount of capital as a ‘subsistence fund,’ grew uneasy with the need for an endowment of 'capital' measured as an amount of value; indeed, in the Lectures, he wrote: “But it would clearly be meaningless—if not altogether inconceivable—to maintain that the amount of capital is already fixed before equilibrium between production and consumption has been achieved. Whether expressed in terms of one or the other, a change in the relative exchange value of two commodities would give rise to a change in the value of capital” (Wicksell Reference Wicksell1934, p. 202), admitting a few lines later that this implied an “indeterminateness” of the endowment of capital.^{Footnote 17} In all likelihood, it is by reflecting on these lines that his pupil Erik Lindahl came to the conclusion that the notion of a ‘quantity of capital’ was indefensible because it was indeterminable independently of relative prices (Lindahl [1939] 1970, pp. 316–317; actually written in 1929). Hayek developed a similar rejection of value capital in about the same period, and vigorously criticized the conception of capital as a single factor, a ‘fund,’ in a series of articles culminating in “The Mythology of Capital” (Hayek Reference Hayek1936).^{Footnote 18} Both Lindahl and Hayek turned to the specification of the capital endowment as a given vector, but, being familiar with long-period equilibria and the treatment in them of capital as of endogenously determined 'form,' differently from Walras, they realized that the vectorial capital endowment prevented the determination of a long-period equilibrium, and developed the notions of intertemporal and of temporary equilibrium, consciously very-short-period notions. Around 1935, Hicks, too, became unhappy with capital as a 'fund,' under the impact of Gerald Shove's harsh objections to his uncritical use of that notion in The Theory of Wages, and, under the influence of Hayek and perhaps even more of Lindahl (whose papers were published in English in 1939, but Hicks could read them in preview because the translator was his wife Ursula), he, too, turned to temporary equilibria.

Unease with value capital is, therefore, clearly behind the shift by Lindahl, Hayek, and Hicks to a Walrasian specification of the capital endowment. This unease certainly does not disappear in the following two decades. Several elements suggest that, while the belief in the right to treat capital as a single factor in applications remained dominant (it suffices to think of the literature on international trade and on growth theory), in pure theory, confusions and uncertainties were strong and capital as a single value factor was not defended, leaving a void that had to be filled somehow if the supply-and-demand approach to value and distribution was to remain the accepted one.

Thus, Friedrich A. Lutz writes in 1956: “the subsistence fund, in the sense of a given value magnitude, cannot be taken as a datum but is itself one of the unknowns, so that the system of these writers [Lutz is referring to Böhm-Bawerk, Wicksell, and other ‘Austrian’ authors] lacked one equation for determining the equilibrium” (Lutz Reference Lutz1967, p. 69). It would have been more precise to say that the equation imposing the equality of the demand for value capital with its endowment was illegitimate, but the important thing is the rejection of the value capital endowment. Lutz, like Hayek, opts for the treatment of each capital good as a separate factor with its given endowment.

Also interesting is Robert E. Kuenne’s Reference Kuenne1963 ambitious treatise on general equilibrium, in which an extensive knowledge of the history of neoclassical equilibrium and capital theory does not spare the author several misunderstandings. Kuenne argues that the basic question raised by capital goods—why these are able to earn a positive rate of interest—requires the study of stationary states; but he formulates the stationary state as a secular one, where net savings are zero because consumers so decide (e.g., Kuenne Reference Kuenne1963, p. 235). And yet, evidently persuaded that the sole way to specify a general equilibrium system was, like in Walras, by taking as given the endowments of the several capital goods, he formulates this stationary equilibrium as including as data the amounts of capital goods in the endowment of each consumer, and reconciles this with stationariness by assuming that these amounts have already adapted to a stationary state (1963, p. 221), without noticing that then he should have treated them as variables to be determined endogenously, and should have checked that the theory was able to determine them. This trick of taking as given but assumed to have already adapted what, in fact, are endogenous variables he applies to Walras, too, whose model he considers only interpretable as a stationary one (1963, pp. 227–228). In this way, having assumed that Walras's given endowments of capital goods are the ones appropriate to a stationary state, he does not notice the formal inconsistency finally admitted even by Walras.^{Footnote 19} Nowhere does he recognize the presence in Clark, Böhm-Bawerk, or Wicksell of a notion of long-period (not secularly stationary) equilibrium based on a given amount of capital conceived as a single factor of variable 'form,' but he clearly indicates that he would not accept such a conception of capital, by writing of Clark's “mystical eternal fund of capital” (1963, p. 239), and by reporting Hayek's dismissal of the Austrian approach and Knight's need “to escape a circularity in the definition of the interest rate as a return on a cost-of-production value of capital stock which includes interest” (1963, pp. 249–250n62). He discusses at length Arrow and Debreu but considers it only a generalization of Abraham Wald’s model (more on this below), never mentioning the possibility of interpreting their model as intertemporal.

Kuenne is proof of the influence of Hicks's Value and Capital. As stressed by Garegnani (Reference Garegnani2012), Hicks had misrepresented the long-period static equilibrium of Marshall as a secular stationary state, which he could then accuse of being too far removed from actual economies to be of any use for explanation and prediction, and needing, therefore, replacement with the method of temporary equilibria. In this way, Hicks obscured the role of the given capital endowment of variable ‘form’ in the marginalist approach, a role that Hicks himself had recognized in earlier analyses, but that now disappeared, because in a secular stationary equilibrium the quantity of capital is endogenously determined. Even more importantly, in this way, Hicks obscured the notion central to the theory of value from its first systematic elaboration by Adam Smith—the notion of normal or long-period position—leaving room only for very-short-period, neo-Walrasian equilibria, or secular equilibria (or steady states), and thus helping the profession to lose sight of the fact that the speed with which the composition of capital tends toward a uniform rate of return is of a higher order of magnitude than the speed of the changes induced by accumulation and population growth, which makes it legitimate to neglect the latter changes when determining normal prices. The effect can be seen in Kuenne, who lacks the notion of long-period position (as different from a secular stationary state), as well as clarity on the presence and role of a given endowment of value capital in earlier marginalist economists.

Actually, in the years after Value and Capital, there appears to have been a strikingly quick loss of familiarity with the long-period method implicit in earlier neoclassical analyses: the ‘Patinkin controversy’ in monetary theory (1948 to 1960), which involved dozens of economists, lasted so long because the contributors were unable to reconstruct the logic of the traditional ‘neoclassical dichotomy,’ owing to their reasoning in terms of very-short-period equilibria where the initial money endowment of each agent is given. This made them unable to understand that the dichotomy had been meant to apply to long-period equilibria where the distribution of the total money endowment among agents was endogenously determined. (For space reasons, I must refer to Petri [2004, p. Appendix 5A1, pp. 166–186] for further details.)

Another aspect of the period is the nearly universal limitation of the presentation of formalized general equilibrium theory to the model of exchange and production without 'capitalization' (i.e., without production of capital goods, which makes the model applicable only to economies where the factors are only labor and land). The example had been set by Vilfredo Pareto, who, in the Manuel ([1909] 1963), drops Walras’s 'capitalization' equations, limiting the presentation of the system of general equilibrium equations to the cases of pure exchange and of non-capitalistic production, as if that could be sufficient to understand the determination of prices and quantities in a capitalistic economy. Hans Neisser, Frederik Zeuthen, Heinrich von Stackelberg, Kurt Schlesinger, and Abraham Wald, who, between 1932 and 1936, discuss the existence of solutions to the general equilibrium equations, also limit themselves to the non-capitalistic model, and Wald, for example, admits that the model does not deal with capital and interest.^{Footnote 20} As shown by E. Roy Weintraub and Thomas Gayer (2001), between the end of the 1940s and the end of the 1950s, the main textbooks in value theory used in graduate courses in the US (Sidney Weintraub, George J. Stigler, James M. Henderson and Richard E. Quandt) presented only the non-capitalistic general equilibrium model, without discussing whether and how that model could accommodate capital goods.^{Footnote 21}

One can conclude that, by the 1950s, no one dared, in formalized general equilibrium theory, to include among the data of equilibrium a given scalar quantity of capital—necessarily a quantity of exchange value—but no generally accepted alternative had emerged.

Given such a background, it is doubtful that the 1954 article by Arrow and Debreu can be considered an upward jump in formalism in the sense of neglect of the plausibility of the economic assumptions implicit in the mathematical formalization: it was about the same problem and the same model as Wald’s. The suggestion, only briefly hinted at in the article, that the model could make room for capital goods by being reinterpreted as intertemporal was already in Hicks.^{Footnote 22}

As Kuenne shows, the proposal of such a reinterpretation (reiterated by Tjalling Koopmans in 1957 and by Debreu in 1959) did not meet immediate general acceptance. So the question arises—on which, I have argued, Blaug does not offer convincing insights—as to what caused this intertemporal reinterpretation of the non-capitalistic model to become more and more widely accepted afterwards as the new foundation of value theory. The answer, along Garegnani’s interpretative line, starts from what Lindahl, Hayek, and Hicks show: that, with the growing realization of difficulties with the conception of the capital goods as transient crystallizations of a single capital quantity, the treatment of each capital good as a distinct factor came to be seen as the only way to remain within a factor-supply-and-demand approach to income distribution, and obliged the shifting to very-short-period notions of equilibrium, of which one version was the intertemporal equilibrium. Then, the next question is why acceptance of this shift has nowadays taken the form of intertemporal equilibria rather than the temporary equilibria favored by both Lindahl and Hicks. Here, the answer lies in the subsequent difficulties encountered by the formalization and existence of temporary equilibria without correct foresight. This does not exclude some influence of formalism: no doubt, some role in the popularity gained by the Arrow–Debreu intertemporal model must be attributed to its being simply a reinterpretation without formal modifications of the model to which, in the situation of great uncertainty in the 1940s and 1950s about how to include capital in the theory of value and distribution, the formalized versions of that theory had essentially reduced themselves: the non-capitalistic model of general equilibrium. The influence of formalism emerges in the underestimation of the evident difficulties of the reinterpretation.^{Footnote 23} But this influence could act only on the favourable terrain prepared by the crisis of traditional neoclassical capital theory.

There is another consideration supporting a limited role of formalism in these developments. The shift to neo-Walrasian equilibria in Hayek, Lindahl, and Hicks was not accompanied by changes in the view of how market economies work: in these authors, one finds the same certainty as in Clark, Marshall, or Wicksell that decreases of the rate of interest cause switches to production methods that require capital goods of greater value per unit of labor, and therefore raise the flow demand for savings, thus ensuring stability of the savings-investment market; and that if real wages decrease, the demand for labor will rise, if not immediately (Hicks admitted that in the very short period, labor employment could not significantly increase, for lack of substitutability; compare Hicks 1980–81, p. 146), then through changes in the physical composition of capital over a succession of periods. The traditional marginalist factor substitution mechanisms were still believed to be fully operative, although possibly over a sequence of temporary equilibria (or of periods of an intertemporal equilibrium): the traditional conception of capital was only apparently abandoned; it no longer appeared in the specification of production functions or of the economy’s capital endowment, but traditionally operating capital-labor substitution was still implicitly present in the assumed decreasing labor-demand function and decreasing investment function, notions never questioned in spite of the absence of general proofs of their validity now that capital as a single value factor was declared to have been rejected. Thus, borrowing a term from Garegnani (2000, p. 443), the shift to very-short-period equilibria was essentially a cosmetic operation; the abandonment of the value capital endowment did not mean the abandonment of the traditional conception of substitution between labor and value capital (savings), with the result of the old adjustments operating now over a sequence of very-short-period equilibria. That the old conception of capital had been only apparently abandoned emerges in Hayek's declaration in a 1945 interview, quoted by Blaug, that “Böhm-Bawerk was fundamentally right” (1999b, p. 261); it emerges even more clearly in Hicks, who reaffirms in 1963 his faith in the possibility of conceiving capital as a single quantity in some physical sense (Hicks 1932, p. 345). Evidently, the belief in the existence of the tendencies postulated by the marginalist approach had, by the 1930s, so deeply permeated the profession that those tendencies were considered almost an immediate evidence, rather than the result of a complex deductive chain undermined by the problems of the conception of capital as a single value factor. This, on the one hand, helps to explain why no alternative to the supply-and-demand approach was explored; on the other hand, it must have favored the acceptance of the new notions of equilibrium without much worry about the problem of reconciling them with a reality characterized by time-consuming adjustments, since those notions maintained the old results: full employment, distribution determined by marginal products, investment determined by savings, and a decreasing demand curve for labor.

The same consideration helps one to make sense of the co-existence, in the 1950s and early 1960s, of the acapitalistic general equilibrium model in textbooks, of the intertemporal model in specialist articles, and of the traditional treatment of capital as a single value factor in applications. Let us remember Robert M. Solow: when replying to the famous 1953–54 article in which Joan Robinson started the Cambridge controversy by asking in what units capital is measured, Solow admitted problems with the notion of ‘quantity of capital’ and argued that they could be surmounted through intertemporal equilibrium theory:

(Thus, in order not to abandon the neoclassical 'vision,' evidently considered indubitable, Solow was ready to accept even “something foolish”!) But, in about the same period, he proposed the one-good-growth model and even based econometric applications on it.

The subsequent neoclassical reaction to 'reswitching' would appear to confirm this assessment. The Cambridge controversy in capital theory of the 1950s and 1960s “rendered finally untenable the notion of capital as a single factor at the level of pure theory and opened the way to dominance for a treatment of capital on Walrasian lines, with the associated necessary reformulations of the concepts of equilibrium” (Garegnani Reference Garegnani2012, p. 1425), a view confirmed by neoclassical author Christopher Dougherty: “Clark['s] ... theory of the nature of capital ... encouraged the formulation of such ‘laws’ as the existence of an inverse relationship between the rate of interest and the capital-intensity of efficient production techniques ... dramatically in the mid-1960s it was shown that it was easy to construct counterexamples.... Since then the general equilibrium model has been the undisputed core of neoclassical capital theory” (Dougherty Reference Dougherty1980, p. 3).^{Footnote 24} Indeed, in the early 1970s, the texts suggested to graduate students on advanced value theory were the textbook by Edmond Malinvaud (Reference Malinvaud1969) and the treatise by Kenneth Arrow and Frank H. Hahn (1971), where the way to deal with capital was neo-Walrasian intertemporal and temporary equilibria. But in mainstream macroeconomics, in growth theory and elsewhere, the use of one-good models, where capital was a single factor homogeneous with output (a thin disguise for a value measurement of capital), did not stop. It would seem that the adjective “rigorous,” often used by the neoclassical side in the Cambridge controversy to distinguish disaggregated neo-Walrasian general equilibrium theory from aggregative models, paradoxically served to allow the treatment of capital as a single factor in applied ‘non-rigorous’ analyses, evidently owing to the belief that ‘rigorous’ disaggregated theory would anyway confirm the qualitative conclusions of analyses based on capital as the single factor, and the remaining issue was only one of quantitative imprecision of the applied analyses. But then, it would seem, it was not mainly formalism but rather, above all, a persisting belief in the correctness of the traditional marginalist/neoclassical 'vision' (labor demand being a decreasing function of the real wage, investment tending to equal savings because of the equilibrating role of the rate of interest, etc.) that permitted the acceptance of intertemporal equilibria as sufficiently approximating the actual behavior of market economies obviously lacking complete futures markets or perfect foresight.^{Footnote 25} It was not realized that that ‘vision’ had been born on the basis of the belief in a well-behaved substitution between labor and capital conceived as a single factor, a belief now shown to be deprived of foundations, and certainly not given new bases by a neo-Walrasian theory of general equilibrium unable to tell anything on economies not continually in equilibrium.

V. BACK TO MARSHALL?

In the same spirit as Blaug, who clearly viewed his analysis of the Formalist Revolution as contributing to understanding how to improve economic theory, I conclude by pointing out some implications of the above historical reconstruction for modern economic theory.

The main implication concerns the question of how to surmount the sterility of modern general equilibrium theory and make room for time-consuming adjustment processes and for the more realistic conception of competition that Blaug rightly considered essential to an understanding of concrete economies.

Blaug himself has indicated the way, in the continuation of the passage quoted in section I, where he accuses modern general equilibrium theory of preventing “consideration of ... all aspects of non-price competition because those take place sequentially in real time.” The passage continues: “This is precisely what competition meant to Smith, Ricardo and Marx and, even after Cournot, this is what it meant to Marshall” (1999b, p. 266).

The suggestion to return to the way of studying market economies of Smith, Ricardo, Marx, and Marshall requires us to understand what allowed them to admit a realistic conception of competition. What these authors had in common was a method based on the distinction between market prices and quantities, and normal prices and quantities, toward which market prices and quantities gravitate: a distinction that permits the consideration of phenomena taking place “sequentially in real time.” My reconstruction implies that that distinction was abandoned in neoclassical ‘rigorous’ theory, not because of intrinsic deficiencies of the traditional method of normal or long-period positions, but because of the difficulties the neoclassical approach encountered in fitting capital goods into its supply-and-demand determination of income distribution. The distinction need not be abandoned if a different theory of distribution can be found that does not suffer from the neoclassical difficulties with determining normal prices and quantities.

On this issue, Marshall presents a problem. We cannot go back to notions of ‘centers of gravitation’ of market prices and quantities, while retaining the marginalist, or supply-and-demand, approach to value and distribution. The present paper has attempted to clarify that what prompted the shift to sterile neo-Walrasian general equilibrium theory was precisely the decision not to abandon the supply-and-demand approach to income distribution in the face of its inability to determine equilibria compatible with the role of centers of gravitation. The root of the problem is the supply-and-demand approach to distribution itself, which is not able satisfactorily to treat capital in all its versions.

Thus, Blaug’s ‘back to Marshall’ appeal (1999a, p. 230; 1999b, p. 267; 2009, p. 241) can be accepted only insofar as it means ‘back to analyses that admit time-consuming adjustments’; but, on issues such as what determines income distribution or the level of employment, Marshall was a neoclassical theorist, as shown in section II, and his analyses, insofar as they rely on the neoclassical approach, cannot be resumed.^{Footnote 26}

Luckily, as Blaug himself reminds us, there remain Smith, Ricardo, and Marx. Their approach to wage determination does not suffer from the neoclassical inconsistencies, is compatible with realistic descriptions of industrial pricing and competition as a process, allows the determination of normal competitive relative prices once the labor theory of value is replaced with Sraffa-like equations,^{Footnote 27} and can be fruitfully combined with a Keynesianism freed of neoclassical elements for the explanation of aggregate demand, employment, and growth. Books such as The End of the Golden Age, by Stephen A. Marglin and Juliet B. Schor (1990), or Capitalism since 1945, by Philip Armstrong, Andrew Glyn, and John Harrison (1991), or the textbook by Samuel Bowles, Richard Edwards, and Frank Roosevelt (2005), appreciated by Blaug himself (2009, p. 237), bear testimony to the fruitfulness of the resulting analyses.