Walras’ law in the context of pre-analytic visions: a note

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Walras’ law is central to the formation of economic theory. For mainstream economics, it is a device for testing rigorousness and consistency of model-building; for heterodox economists, the refutation of Walras’ law is key to understanding Keynes’ revolutionary contribution to a new economic paradigm. The purpose of this short research note is to elaborate on the possibility of a refutation of Walras’ law and to inquire into its preconditions. It will be argued that this can only be achieved on the basis of an alternative pre-analytic vision of a genuine monetary economy as forshadowed by John Maynard Keynes.

Posted for comments on 5 Aug 2016, 3:19 pm.

Comments (6)

  • Thomas Palley says:

    This paper addresses an important theoretical issue; it is well written; and describes the issue and the prior literature in a clear informative way.

    Section 4 (p.7-9) is the critical section with the new argument. Unfortunately, I do not think the argument is sufficiently clear. The argument needs to be supplemented with a mathematical model showing how it leads to a violation of Walras’ law. That should be very easy to do if the argument is correct.

    • Arne Heise says:

      Dear Tom Palley,

      thank you very much for your positive – as I take it – feedback. When I wrote the paper, I felt uncertain about whether I should supplement my argument with some maths. As I always argue that maths is just another language but no better argument, I felt, at the end, that I could go along without applying maths. However, if you – and the editors of ET – believe it necessary to make the point mathematically in order to get attention, I would be very willing to (try to) do so – it should be easy as I believe the argument to be correct.

  • Bruce Littleboy, University of Queensland, Australia says:

    It’s a long time since I was reasonably on top of this area (I turned my PhD into On Interpreting Keynes, Routledge, 1990), but I offer some comments — beyond suggesting that you take a look at my book!

    It’s worth noting the possibility that there are multiple Walrasian equilibria, if Keynes’s 1939 EJ adjustment to the meaning of involuntary unemployment is considered. If real wages are procyclical (e.g., if industry concentration rises during slumps and the profit-share rises), then it’s possible that the lower real wage in the slump equals the marginal disutility of labour (and labour is on its supply curve) and this clears the labour market at a lower price and quantity of labour than would occur if aggregate demand were higher. And if firms harvest higher profits in the form of inventory of wage-goods (presumably to export), then the contracted flow supply of domestic output clears too. There arguably would be Walrasian as well as effective-demand equilibrium. Weird, but of symbolic interest, I propose.

    I still think that fundamentalists sometimes read some of the meaning and significance out of Clower and Leijonhufvud and are inclined to complain of faults that are not really there. This is what a significant part of my book is about.

    Clower and Leijonhufvud carefully distinguish Say’s Identity, Say’s Equality and Walras’ Law, and I’m not sure that Palley does.

    And I think you perhaps should read more Clower-Leijonhufvud and not unduly press them into their 1960s moulds. Their views evolved, and they even drifted apart as the years passed.

    An aside/detail: I think it makes more sense to say that earning income induces household consumption than it does to say that a firm’s realised revenues determine its next round of production. This is because firms indeed produce in the expectation of sales; realised revenue is not the same as expected revenue except in short-run equilibrium. (But with Keynes’s instantaneous multiplier, short-run equilibrium instantly arises, I note.) The fundamentalists make a fair point that if the firms have ready access to finance then their sales expectations trump what sales are currently realised. Of course, if their financier looks to realised sales, Davidson’s assertions about the independent roles of expectations and finance are compromised.

    Victoria Chick Aust Econ Papers June 1978 also wrestles with Clower’s math. I vaguely recall that Colin Rogers wrote on this, by the way. Clower’s math has been a loose end for quite a while: if it’s faulty, can it be repaired?

    My regards, Bruce

    • Arne Heise says:

      Dear Bruce,
      thank you very much for your comments which, I believe, are entirely understandable from the perspective of a connaisseur of Clower’s and Leijonhufvud’s work. However, I am not sure wheather they really touch the gist of what I wanted to adress: the need for an ontological shift (from an intertemporal exchange economy to an economy based on nominal obligations) in order to rigorously refute Walras’ law – which, by the way, I do not simply take as a mere accountancy truism but as the statement of active forces leading the economy back to equilibrium unless there are rigidities or peculiar assumptions (such as the rejection of gross substitution). In this sense, probably, I shall distinguish somewhere – according to ‘Say’s identity’, ‘Say’s equation’ and ‘Say’s law’ as provided in the 1952 Becker/Baumol paper – between Walras’ identity, Walras’ equation and Walras’ law.

      Your suggestion that Clower and Leijonhufvud should better and less critically be treated particularly by the fundamentalist faction of the Post Keynesians and their intellectual evolution should better be reflected, would definitely be worthwhile to be considered if one intends to focus on their contribution to heterodox economics in general. However, that is not the focus of my research note.

      I am also not sure why the possibilty of multiple Walrasian equilibria should be emphazised. The focus of the paper is not on the uniqueness of Walrasian equilibrium (as stated in foodnote 10) but its existence.

      Finally, I am in complete agreement with you “that it makes more sense to say that earning income induces household consumption than it does to say that a firm’s realised revenues determine its next round of production”. Hopefully, nowhere in my paper I stated otherwise – at least, I could not find it.

      To summarise, I will take your comments to look more closely at your book and define more precisely what is meant by ‘Walras’ law’.

      Thanks again, best


  • Colin Rogers says:

    In his paper Arne Heise argues that Walras’s Law is central to the formulation of general equilibrium theory, particularly for testing its ‘rigorousness’ and consistency. He also states that it is the link between the microeconomics of exchange and the macroeconomics of general equilibrium.

    The economics of Keynes in the General Theory (GT), on the other hand is inconsistent with Walras’s Law. He intends to examine the possibility of a rigorous refutation of Walras’s Law and argues that this can best be done from the perspective of Keynes’s concept of a monetary entrepreneur economy.

    This characterisation of the issues is a rather confusing amalgam of statements that are vaguely correct with those that are completely wrong.

    For a start, with what is wrong, Walras’s Law is not central to the formulation of Walrasian GE theory but a trivial implication of the model based on the re-contracting or time-0 auction. It is the latter that is the cause of all conceptual problems for Walrasian GE theory.

    Walras’s Law follows by construction under the time-0 auction because the exchange value of what is offered (supplied) is always equal to the exchange value of what is demanded across all endowments. From the perspective of monetary theory this is a fatal conceptual flaw because it means there is no need for money or credit in Walrasian GE theory.

    The recontracting or time-0 auction is the source of all the conceptual problems because it reduces the Walrasian GE theory to a model of perfect barter not actual barter that is subject to all the well-known inefficiencies.

    This problem was first noticed by Hahn (1965). In plain English, Hahn demonstrated that there was no role for money in a Walrasian GE system. Although this has been known for some time now, e.g., Rogers (1989) or Laidler (1990) it has not been taken on board and the consequences have been documented in Rogers (2006, 2011, 2013).

    What we can now conclude with some confidence is that Walrasian GE theory has nothing to tell us about monetary theory. On that score Keynes’s was surely correct when he wrote to Hick’s that Walrasian GE theory was little better than nonsense, Rubin (2014).

    Consequently, it is plain wrong to believe that Walrasian GE theory provides a test for the rigor and consistency’of economic theory. If anything, the opposite is true. Walrasian GE theory is based on conceptual error and leads only to confusion when applied to monetary theory.

    Furthermore, it is also clear that Walrasian GE, or Walra’s Law, does not provide the link between microeconomics and macroeconomics. The ‘microeconomic foundations’ debate was nonsense because Walrasian GE theory cannot provide the foundation for any macroeconomics, even on its own terms, Kirman (1989).

    Finally, what is vaguely right is Heise’s conclusion that Keynes’s monetary theory requires the rejection of Walrasian GE theory. This is well known. But the properties of Keynes’s monetary analysis are not needed to refute Walras’s Law. Walras’s Law is simply a property of the incoherent Walrasian approach to general equilibrium.

    To sum up. I think the discussion by Heise is wrong in parts, vague and misleading in others and likely to obscure rather than clarify the relationship between Walrasian GE theory and Keynes’s monetary analysis. The references are also rather dated.


    Hahn, F. H. 1965. ‘On some problems of proving the existence of equilibrium in a monetary economy’, in (F. H. Hahn and F. P. R. Brechling, eds.), The Theory of Interest Rates, pp. 126-135, London: Macmillan.
    Kirman. A. 1989. ‘The intrinsic limits to economic theory: The emperor has no clothes’, Economic Journal, 99 (supplement); 117-36.

    Laidler, D. 1990. Taking Money Seriously, New York: Phillip Allen.

    Rogers, C. 1989. Money Interest and Capital: A Study in the Foundations of Monetary Theory, Cambridge: Cambridge University Press.

    Rogers, C. 2006. “Doing without money: a critical assessment of Woodford’s analysis”, Cambridge Journal of Economics, vol. 30(2) (March): 293-306.

    Rogers, C. 2011. “The failure of Woodford’s model of the channel system at the cashless limit”, Journal of Money Credit and Banking, 43(2-3): 535-563.

    Rogers, C. 2013. “The Scientific Illusion of New Keynesian Monetary Theory”, The Oxford Handbook of Post-Keynesian Economics, edited by G. C. Harcourt and P. Kriesler, Volume 1, chapter 8.

    Rubin, G. 2014. Oskar Lange or how IS-LM came to be interpreted as a Walrasian model, HAL Archives.

    • Arne Heise says:

      Dear Colin,

      thank you very much for your critical comments. As they are harsh, I expected strong and substantial arguments. Unfortunately, that appears not to be so:

      You claim the characterisation of the issues to be “a rather confusing amalgam of statements that are vaguely correct with those that are completely wrong” – well, hard stuff. As you happen not to explain what exactly confused you, I cannot really help by rendering things less confusing. I hoped the structure of my research note to be concise enough to follow the arguments.

      You argue that I am completely wrong in believing Walras’ law to be central to the formulation of Walras’ GE but it is instead merely a trivial implication of the model based on re-contracting. Actually, I do believe that Walras’ law – understood here as a mere accountancy truism (and what I should probably rather call ‘Walras equality’) – is a trivial implication of Walrasian GE analysis. Although I nowhere claim that Walras’ law is central to the formulation of Walras’ GE, I do believe that Walras’ law- epitomizing an equilibrium process in an exchange economy – plays a central role in the ontological vision of mainstream GE economics.

      You seem to believe that Walras’ law only holds in a pure barter economy which I tried to show (with reference to others such as Tom Palley) is erroneous. It is not the use of money to facilitate intertemporal exchange that makes up for a genuine monetary economy, but the basic constituent of nominal obligations (and, as a basis to that, private property) which renders money as the most liquid asset of the economy so important. I dwelt on that point in part 4 of the research note and I am aware that you may not share this ontological dimension with me. As a pluralist, however, I can easily live with such theoretical differences but I do not think it is fair to rate my arguments as just ‘vaguely right’ simply because I do not follow your approach.

      Moreover, you consider it planly wrong that Walras’ GE provides a test for rigour and consistency of economic theory. Although I nowhere made such a statement but rather focused on Walras’ law as such a ‘plausibilty check’, I am entirely on your side: The plausibilty claim, that you rightly reject, is not mine but the claim of maisntream Walrasian economists. Having read the passage of my paper, where the claim is mentioned, again and again, I cannot understand that you (or potentially more carefull readers) might misunderstand it.

      Finally, I am aware about your – rather pecualiar, as I would call it in line with Peter Kriesler’s review of your 1989 book – position that partial analysis is better suited for macroeconomics than general analysis. Although I do not share this methodical position, my probably misleading synonymous use of partial and micro on the one hand and general and macro on the other hand should be revised and altered to stating that Walras’ law links partial microeconomics of goods exchange and the macroeconomics of general equilibrium analysis.

      To sum up, I would suggest that what you believe to be ‘plain wrong’ may rather be completely misunderstood (by you) and what you believe to be ‘vaguely right’ is probably completely right if one is willing to take a different ontological perspective than you do. Of course, one must not do that but, at least, pluralists should be open-minded enough to allow others to do that.

      All the best