Archive for the 'Michel De Vroey' Category

The Walras-Marshall Divide in Neoclassical Theory, Part II

In my previous post, which itself followed up an earlier post “General Equilibrium, Partial Equilibrium and Costs,” I laid out the serious difficulties with neoclassical theory in either its Walrasian or Marshallian versions: its exclusive focus on equilibrium states with no plausible explanation of any economic process that leads from disequilibrium to equilibrium.

The Walrasian approach treats general equilibrium as the primary equilibrium concept, because no equilibrium solution in a single market can be isolated from the equilibrium solutions for all other markets. Marshall understood that no single market could be in isolated equilibrium independent of all other markets, but the practical difficulty of framing an analysis of the simultaneous equilibration of all markets made focusing on general equilibrium unappealing to Marshall, who wanted economic analysis to be relevant to the concerns of the public, i.e., policy makers and men of affairs whom he regarded as his primary audience.

Nevertheless, in doing partial-equilibrium analysis, Marshall conceded that it had to be embedded within a general-equilibrium context, so he was careful to specify the ceteris-paribus conditions under which partial-equilibrium analysis could be undertaken. In particular, any market under analysis had to be sufficiently small, or the disturbance to which that market was subject had to be sufficiently small, for the repercussions of the disturbance in that market to have only minimal effect on other markets, or, if substantial, those effects had to concentrated on a specific market (e.g., the market for a substitute, or complementary, good).

By focusing on equilibrium in a single market, Marshall believed he was making the analysis of equilibrium more tractable than the Walrasian alternative of focusing on the analysis of simultaneous equilibrium in all markets. Walras chose to make his approach to general equilibrium, if not tractable, at least intuitive by appealing to the fiction of tatonnement conducted by an imaginary auctioneer adjusting prices in all markets in response to any inconsistencies in the plans of transactors preventing them from executing their plans at the announced prices.

But it eventually became clear, to Walras and to others, that tatonnement could not be considered a realistic representation of actual market behavior, because the tatonnement fiction disallows trading at disequilibrium prices by pausing all transactions while a complete set of equilibrium prices for all desired transactions is sought by a process of trial and error. Not only is all economic activity and the passage of time suspended during the tatonnement process, there is not even a price-adjustment algorithm that can be relied on to find a complete set of equilibrium prices in a finite number of iterations.

Despite its seeming realism, the Marshallian approach, piecemeal market-by-market equilibration of each distinct market, is no more tenable theoretically than tatonnement, the partial-equilibrium method being premised on a ceteris-paribus assumption in which all prices and all other endogenous variables determined in markets other than the one under analysis are held constant. That assumption can be maintained only on the condition that all markets are in equilibrium. So the implicit assumption of partial-equilibrium analysis is no less theoretically extreme than Walras’s tatonnement fiction.

In my previous post, I quoted Michel De Vroey’s dismissal of Keynes’s rationale for the existence of involuntary unemployment, a violation in De Vroey’s estimation, of Marshallian partial-equilibrium premises. Let me quote De Vroey again.

When the strict Marshallian viewpoint is adopted, everything is simple: it is assumed that the aggregate supply price function incorporates wages at their market-clearing magnitude. Instead, when taking Keynes’s line, it must be assumed that the wage rate that firms consider when constructing their supply price function is a “false” (i.e., non-market-clearing) wage. Now, if we want to keep firms’ perfect foresight assumption (and, let me repeat, we need to lest we fall into a theoretical wilderness), it must be concluded that firms’ incorporation of a false wage into their supply function follows from their correct expectation that this is indeed what will happen in the labor market. That is, firms’ managers are aware that in this market something impairs market clearing. No other explanation than the wage floor assumption is available as long as one remains in the canonical Marshallian framework. Therefore, all Keynes’s claims to the contrary notwithstanding, it is difficult to escape the conclusion that his effective demand reasoning is based on the fixed-wage hypothesis. The reason for unemployment lies in the labor market, and no fuss should be made about effective demand being [the reason rather] than the other way around.

A History of Macroeconomics from Keynes to Lucas and Beyond, pp. 22-23

My interpretation of De Vroey’s argument is that the strict Marshallian viewpoint requires that firms correctly anticipate the wages that they will have to pay in making their hiring and production decisions, while presumably also correctly anticipating the future demand for their products. I am unable to make sense of this argument unless it means that firms — and why should firm owners or managers be the only agents endowed with perfect or correct foresight? – correctly foresee the prices of the products that they sell and of the inputs that they purchase or hire. In other words, the strict Marshallian viewpoint invoked by De Vroey assumes that each transactor foresees, without the intervention of a timeless tatonnement process guided by a fictional auctioneer, the equilibrium price vector. In other words, when the strict Marshallian viewpoint is adopted, everything is simple; every transactor is a Walrasian auctioneer.

My interpretation of Keynes – and perhaps I’m just reading my own criticism of partial-equilibrium analysis into Keynes – is that he understood that the aggregate labor market can’t be analyzed in a partial-equilibrium setting, because Marshall’s ceteris-paribus proviso can’t be maintained for a market that accounts for roughly half the earnings of the economy. When conditions change in the labor market, everything else also changes. So the equilibrium conditions of the labor market must be governed by aggregate equilibrium conditions that can’t be captured in, or accounted for by, a Marshallian partial-equilibrium framework. Because something other than supply and demand in the labor market determines the equilibrium, what happens in the labor market can’t, by itself, restore an equilibrium.

That, I think, was Keynes’s intuition. But while identifying a serious defect in the Marshallian viewpoint, that intuition did not provide an adequate theory of adjustment. But the inadequacy of Keynes’s critique doesn’t rehabilitate the Marshallian viewpoint, certainly not in the form in which De Vroey represents it.

But there’s a deeper problem with the Marshallian viewpoint than just the interdependence of all markets. Although Marshall accepted marginal-utility theory in principle and used it to explain consumer demand, he tried to limit its application to demand while retaining the classical theory of the cost of production as a coordinate factor explaining the relative prices of goods and services. Marginal utility determines demand while cost determines supply, so that the interaction of supply and demand (cost and utility) jointly determine price just as the two blades of a scissor jointly cut a piece of cloth or paper.

This view of the role of cost could be maintained only in the context of the typical Marshallian partial-equilibrium exercise in which all prices — including input prices — except the price of a single output are held fixed at their general-equilibrium values. But the equilibrium prices of inputs are not determined independently of the values of the outputs they produce, so their equilibrium market values are derived exclusively from the value of whatever outputs they produce.

This was a point that Marshall, desiring to minimize the extent to which the Marginal Revolution overturned the classical theory of value, either failed to grasp, or obscured: that both prices and costs are simultaneously determined. By focusing on partial-equilibrium analysis, in which input prices are treated as exogenous variables rather than, as in general-equilibrium analysis, endogenously determined variables, Marshall was able to argue as if the classical theory that the cost incurred to produce something determines its value or its market price, had not been overturned.

The absolute dependence of input prices on the value of the outputs that they are being used to produce was grasped more clearly by Carl Menger than by Walras and certainly more clearly than by Marshall. What’s more, unlike either Walras or Marshall, Menger explicitly recognized the time lapse between the purchasing and hiring of inputs by a firm and the sale of the final output, inputs having been purchased or hired in expectation of the future sale of the output. But expected future sales are at prices anticipated, but not known, in advance, making the valuation of inputs equally conjectural and forcing producers to make commitments without knowing either their costs or their revenues before undertaking those commitments.

It is precisely this contingent relationship between the expectation of future sales at unknown, but anticipated, prices and the valuations that firms attach to the inputs they purchase or hire that provides an alternative to the problematic Marshallian and Walrasian accounts of how equilibrium market prices are actually reached.

The critical role of expected future prices in determining equilibrium prices was missing from both the Marshallian and the Walrasian theories of price determination. In the Walrasian theory, price determination was attributed to a fictional tatonnement process that Walras originally thought might serve as a kind of oversimplified and idealized version of actual market behavior. But Walras seems eventually to have recognized and acknowledged how far removed from reality his tatonnement invention actually was.

The seemingly more realistic Marshallian account of price determination avoided the unrealism of the Walrasian auctioneer, but only by attributing equally, if not more, unrealistic powers of foreknowledge to the transactors than Walras had attributed to his auctioneer. Only Menger, who realistically avoided attributing extraordinary knowledge either to transactors or to an imaginary auctioneer, instead attributing to transactors only an imperfect and fallible ability to anticipate future prices, provided a realistic account, or at least a conceptual approach toward a realistic account, of how prices are actually formed.

In a future post, I will try spell out in greater detail my version of a Mengerian account of price formation and how this account might tell us about the process by which a set of equilibrium prices might be realized.

The Walras-Marshall Divide in Neoclassical Theory, Part I

This year, 2021, puts us squarely in the midst of the sesquicentennial period of the great marginal revolution in economics that began with the almost simultaneous appearance in 1871 of Menger’s Grundsatze der Volkwirtschaft and Jevons’s Theory of Political Economy followed in 1874 by Walras’s Elements d’Economie Politique Pure. Jevons left few students behind to continue his work, so his influence pales in comparison with that of his younger contemporary Alfred Marshall who, working along similar lines, published his Principles of Economics in 1890. It was Marshall’s version of marginal utility theory that defined for more than a generation what became known as neoclassical theory in the Anglophone world. Menger’s work, via his disciples, Bohm-Bawerk and Wieser, was actually the most influential work on marginal-utility theory for at least 50 years, the work of Walras and his successor, Vilfredo Pareto, being too mathematical, even for professional economists, to become influential before the 1930s.

But after it was restated in a form not only more accessible, but more coherent and more sophisticated by J. R. Hicks in his immensely influential treatise Value and Capital, Walras’s work became the standard for rigorous formal economic analysis. Although the Walrasian paradigm became the standard for formal theoretical work, the Marshallian paradigm remained influential for applied microeconomic theory and empirical research, especially in fields like industrial organization, labor economics and international trade. Neoclassical economics, the corpus of economic mainstream economic theory that grew out of the marginal revolution was therefore built almost entirely on the works of Marshall and Walras, the influence of Menger, like that of Jevons, having been largely, but not entirely, assimilated into the main body of neoclassical theory.

The subsequent development of monetary theory and macroeconomics, especially after the Keynesian Revolution swept the economics profession, was also influenced by both Marshall and Walras. And the question whether Keynes belonged to the Marshallian tradition in which he was trained, or became, either consciously or unconsciously, a Walrasian has been an ongoing dispute among historians of macroeconomics since the late 1940s.

The first attempt to merge Keynes into the Walrasian paradigm led to the first neoclassical synthesis, which gained a brief ascendancy in the 1960s and early 1970s before being eclipsed by the New Classical rational expectations macroeconomics of Lucas and Sargent that led to a transformation of macroeconomics.

With that in mind, I’ve been reading Michel De Vroey’s excellent History of Macroeconomics from Keynes to Lucas and Beyond. An important feature of De Vroey’s book is its classification of macrotheories as either Marshallian or Walrasian in structure and orientation. I believe that the Walras vs. Marshall distinction is important, but I would frame that distinction differently from how De Vroey does. To be sure, De Vroey identifies some key differences between the Marshallian and Walrasian schemas, but I question whether he focuses on the differences between Marshall and Walras that really matter. And I also believe that he fails to address adequately the important problem that both Marhsall and Walras failed to address, namely their inability adequately describe a market mechanism that actually does, or even might, lead an economy toward an equilibrium position.

One reason for De Vroey’s misplaced emphasis is that he focuses on the different stories told by Walras and Marshall to explain how equilibrium — either for the entire system (Walras) or for a single market (Marshall) – is achieved. The story that Walras famously told was the tatonnement stratagem conceived by Walras to provide an account of how market forces, left undisturbed, would automatically bring an economy to a state of rest (general equilibrium). But Walras eventually realized that tatonnement could never be realistic for an economy with both exchange and production. The point of tatonnement is to prevent trading at disequilibium prices, but assuming that production is suspended during tatonnement is untenable, because production cannot be interrupted until the search for the equilibrium price vector is successfully completed.

Nevertheless, De Vroey treats tatonnement, despite its hopeless unrealism, as sine qua non for any model to be classified as Walrasian. In chapter 19 (“The History of Macroeconomics through the lens of the Marshall-Walras Divide”), DeVroey provides a comprehensive list of differences between the Marshallian and Walrasian modeling approaches which makes tatonnement a key distinction between the two approaches. I will discuss the three that seem most important.

1 Price formation: Walras assumes all exchange occurs at equilibrium prices found through tatonnement conducted by a deus-ex-machina auctioneer. All agents are therefore price takers even in “markets” in which, absent the auctioneer, market power could be exercised. Marshall assumes that prices are determined in the course of interaction of suppliers and demanders in distinct markets, so that the mix of price-taking and price-setting agents depends on the characteristics of those distinct markets.

This dichotomy between the Walrasian and Marshallian accounts of how prices are determined sheds light on the motivation that led Marshall and Walras to adopt their differing modeling approaches, but there is an important distinction between a model and the intuition that motivates or rationalizes the model. The model stands on its own whatever the intuition motivating the model. The motivation behind the model can inform how the model is assessed, but the substance of the model and its implications remain in tact even if the intuition behind the model is rejected.

2 Market equilibrium: Walras assumes that no market is in equilibrium unless general equilibrium obtains. Marshall assumes partial equililbrium is reached separately in each market. General equilibrium is achieved when all markets are in partial equilibrium. The Walrasian approach is top-down, the Marshallian bottom-up.

3 Realism: Marshall is more realistic than Walras in depicting individual markets in which transactors themselves engage in the price-setting process, assessing market conditions, and gaining information about supply-and-demand conditions; Walras assumes that all agents are passive price takers merely calculating their optimal, but provisional, plans to buy and sell at any price vector announced by the auctioneer who then processes those plans to determine whether the plans are mutually consistent or whether a new price vector must be tried. But whatever the gain in realism, it comes at a cost, because, except in obvious cases of complementarity or close substitutability between products or services, the Marshallian paradigm ignores the less obvious, but not necessarily negligible, interactions between markets. Those interactions render the Marshallian ceteris-paribus proviso for partial-equilibrium analysis logically dubious, except under the most stringent assumptions.

The absence of an auctioneer from Marshall’s schema leads De Vroey to infer that market participants in that schema must be endowed with knowledge of market demand-and-supply conditions. I claim no expertise as a Marshallian scholar, but I find it hard to accept that, given his emphasis on realism, Marshall would have attributed perfect knowledge to market participants. The implausibility of the Walrasian assumptions is thus matched, in De Vroey’s view, by different, but scarcely less implausible, Marshallian assumptions.

De Vroey proceeds to argue that Keynes himself was squarely on the Marshallian, not the Walrasian, side of the divide. Here’s how, focusing on the IS-LM model, he puts it:

As far as the representation of the economy is concerned, the economy that the IS-LM model analyzes is composed of markets that function separately, each of them being an autonomous locus of equilibrium. Turning to trade technology, no auctioneer is supposedly present. As for the information assumption, it is true that economists using the IS-LM model scarcely evoke the possibility that it might rest on the assumption that agents are omniscient. But then nobody seems to have raised the issue of how equilibrium is reached in this model. Once raised, I see no other explanation than assuming agents’ ability to reconstruct the equilibrium values of the economy, that is, their being omniscient. On all these scores, the IS-LM model is Marshallian.

A History of Macroeconomics from Keynes to Lucas and Beyond, p. 350

De Vroey’s dichotomy between the Walrasian and Marshallian modeling approaches leads him to make needlessly sharp distinctions between them. The basic IS-LM model determines the quantity of money, consumption, saving and investment, income and the rate of interest rate. Presumably, by autonomous locus of equilibrium,” De Vroey means that the adjustment of some variable determined in one of the IS-LM markets adjusts in response to disequilibrium in that market alone, but even so, the markets are not isolated from each other as they are in Marshallian partial-equilibrium analysis. The equilibrium values of the variables in the IS-LM model are simultaneously determined in all markets, so the autonomy of each market does not preclude simultaneous determination. Nor does the equilibrium of the model depend, as De Vroey seems to suggest, on the existence of an auctioneer; the role of the auctioneer is merely to provide a story (however implausible) about how the equilibrium is, or might be, reached.

Elsewhere De Vroey faults Keynes for characterizing cyclical unemployment as involuntary, because that characterization is incompatible with a Marshallian analysis of the labor market. Without endorsing Keynes’s reasoning, I cannot accept De Vroey’s argument against Keynes, because the argument is based explicitly on the assumption of perfect foresight. Describing the difference between a strict Marshallian approach and that taken by Keynes, De Vroey writes as follows:

When the strict Marshallian viewpoint is adopted, everything is simple: it is assumed that the aggregate supply price function incorporates wages at their market-clearing magnitude. Instead, when taking Keynes’s line, it must be assumed that the wage rate that firms consider when constructing their supply price function is a “false” (i.e., non-market-clearing) wage. Now, if we want to keep firms’ perfect foresight assumption (and, let me repeat, we need to lest we fall into a theoretical wilderness), it must be concluded that firms’ incorporation of a false wage into their supply function follows from their correct expectation that this is indeed what will happen in the labor market. That is, firms’ managers are aware that in this market something impairs market clearing. No other explanation than the wage floor assumption is available as long as one remains in the canonical Marshallian framework. Therefore, all Keynes’s claims to the contrary notwithstanding, it is difficult to escape the conclusion that his effective demand reasoning is based on the fixed-wage hypothesis. The reason for unemployment lies in the labor market, and no fuss should be made about effective demand being [the reason rather] than the other way around.

Id. pp. 22-23

De Vroey seems to be saying that if firms anticipate an equilibrium outcome, the equilibrium outcome will be realized. This is not an argument; it is question-begging, question-begging which De Vroey justifies by warning that the alternative to question-begging is to “fall into a theoretical wilderness.” Thus, Keynes’s argument for involuntary unemployment is rejected based on the argument that the in the only foreseeable outcome under the assumption of perfect information, unemployment cannot be involuntary.

Because neither the Walrasian nor the Marshallian modeling approach gives a plausible account of how an equilibrium is reached, De Vroey’s insistence that either implausible story is somehow essential to the corresponding modeling approach is misplaced, each approach committing the fallacy of misplaced concreteness in focusing on an equilibrium solution that cannot plausibly be realized. For De Vroey instead to argue that, because the Marshallian approach cannot otherwise explain how equilibrium is realized, the agents must be omniscient is akin to the advice of one Senator during the Vietnam war for President Nixon to declare victory and then withdraw all American troops.

I will have more to say about the Walras-Marshall divide and how to surmount the difficulties with both in a future post (or posts).


About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey’s unduly neglected contributions to the attention of a wider audience.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner

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