Steedman’s ‘critique’ of the isoquant

Ian Steedman from Manchester Metropolitan University was in Graz this week. Yesterday he gave a paper in our research seminar. I couldn’t find the paper he presented online, but he published a shorter version of it here.

Prof. Steedman is a well-known figure in Sraffian economics, a school of economic thought initiated by Piero Sraffa’s 1960 book on production theory. (Sraffians are also known as Neo-Ricardians for reasons that need not concern us here.) The primary research agenda of Sraffians is to show that the simple neoclassical models which dominate modern textbooks are fundamentally flawed. Steedman’s presentation is a fairly typical specimen of that research program. I have long been looking for an excuse to write about Sraffians. Here it is.

The paper deals with the capital-labor isoquant in the consumer good sector in the context of simple multi-sector production models. Steedman shows that “simple models of production […] can give rise to ‘capital-labor isoquants’ in the consumer good sector that are utterly unlike those so often presented in the textbooks […].” They can slope up, bend backwards, run in circles, or else behave in almost any imaginable way. He concludes: “There really is no excuse for blithely assuming that [the isoquant is downward sloping and convex to the origin].”

What should we make of such an argument?

First, the negative slope of isoquants in neoclassical models is not an assumption, it’s a result. Take any production function F(K,L) that monotonically increases in K and L. Holding output constant K falls as you increase L and vice versa. There is no logical flaw in this theorem. Neither is there a flaw in another theorem: If F(K,L) is concave in K and L, the isoquant is convex to the origin.

Why, then, does Steedman get those weird-looking isoquants? The answer is pretty simple: What he calls isoquants has nothing to do with the homonymous curves in our beloved textbooks. They are quite different beasts.

A textbook isoquant is a purely technical relationship between physical inputs. It shows how producers can trade off one physical input against another. It’s a technical constraint in the firm’s cost minimization problem. A Steedman ‘isoquant’ is a relationship between the market value of capital goods (what Steedman calls K) and the quantity of labor (what he calls β) employed in a given sector. It shows how K varies with β as the relative cost of those inputs change. It’s an outcome of the firm’s cost minimization problem.

The strategy followed by Steedman’s paper is, as I said in the beginning, typical of the general strategy of Sraffian economics: Write down a model that is completely different from textbook models. Introduce a variable whose label is known from textbooks (‘capital’, ‘isoquant’, etc.). Show that the variable does not behave in your model as it does in the textbook model. Claim that this proves the textbook model is utterly wrong.

Imagine a schoolboy who calculates 1+2=3. Then Prof. Steedman comes along saying: “My dear boy, your 1 is really a 2, and 2+2=4!” At first, the schoolboy will be confused. Maybe he will stop adding 1+2 for a while. But eventually he will ignore Prof. Steedman’s lecture, realizing that there is no point arguing whether a 1 is really a 2 or not.


8 thoughts on “Steedman’s ‘critique’ of the isoquant

  1. I am pleased that Herr Gödl has taken the trouble to comment on my recent Graz seminar paper. And I am happy to assure him that I have only ever been interested in criticism of theory that begins from the assumptions adopted by those who advocate the theory. More specifically, in the present case, my starting point is the famous paper by Paul Samuelson in the Review of Economic Studies 1962. (It may be recalled that the very purpose of Samuelson’s contribution was explicitly to rationalize the familiar Y = F(K,L) relationship. Needless to say, this production function can equally well be represented as an isoquant. Thus the argument of my paper was entirely in the spirit of Samuelson’s seminal contribution, albeit switching attention to one particular industry.)

    I supposed constant returns to scale, strong competition, uniform pricing and infinitely many methods of production – hardly unfamiliar assumptions to the textbook economist! Starting from these assumptions and, of course, choice of technique based on cost minimization, I showed that the (unintended) consequence could be that the consumer good industry capital-labour isoquant might take very unconventional forms. This is simply a logical consequence of the familiar asssumptions entertained.

    How could one avoid such a finding, while still making these assumptions? By assuming in addition that for every single technique alpha.b = a.beta. Without this assumption one simply cannot consistently make all the standard assumptions referred to AND assert that the consumer good capital-labour isoquant must necessarily be downward sloping and convex from above.

    What economist would wish either to be internally inconsistent or to be dependent on the amazingly strong “equal proportions” assumption?

    Unfortunately, despite the good work of Samuelson, Garegnani and many others the typical macroeconomic book today still begins from Y = F(K,L). May Herr Gödl contribute to eliminating this highly regrettable practice!

    Graz, 20/06/I4 Ian Steedman

    • Prof. Steedman, I am very grateful indeed for your reply. It has long been my hope to enter into an open and constructive discussion with Sraffians, because I think it could be mutually beneficial. May I hope that this is the beginning of one?

      Let me reply to what I think is the key question you are raising: “What economist would wish either to be internally inconsistent or to be dependent on the amazingly strong “equal proportions” assumption?”

      I believe this is a false trade-off. The issue you are raising in the paper, insofar as it is an issue at all, is not about internal consistency. There would be a problem of internal consistency if the textbook model would claim that the market value of heterogeneous capital goods is always and everywhere a declining and convex function of labor when output is held fixed. But the textbook makes no such claim. It imagines an economy with a single good which can either be consumed or invested into the capital stock (‘corn’ as Prof. Kurz is fond of calling it). The downward sloping and convex K-L-isoquant follows logically as I explained above.

      Now you may say that such an economy never existed outside of econ textbooks so it can never be of any use in analyzing real-world economies. Yet NO model economy, neoclassical or Sraffian, ever existed in the real world. And the question whether a model is useful for understanding the real world is NOT one of logical consistency. That is an empirical question: How well do the predictions of those models compare against observed facts?

      An effective critique of neoclassical models would be to show that alternative models, like the Wicksellian model you discuss in your paper, or the 1960 Sraffa model, would perform better in predicting those real-world phenomena which neoclassical models are designed to predict. Show me a Sraffian model that does a better job of predicting the long-run patterns in economic growth than the Solow model (or versions thereof) and I will surrender.

      Until that happens I feel perfectly entitled to stick to my aggregate production functions and my downward sloping isoquants.

  2. Dear Herr Gödl, I agree, of course, that any strictly one-commodity model must have the normally assumed properties. I agree also that questions of prediction are significant matters.

    I think it important, nevertheless, to be absolutely clear that the very starting point of Samuelson’s 1962 paper was that he took it for granted (quite rightly) that the Clark-Ramsey-one-good-parable is only of interest to the serious economist if it can be shown to mimic the many capital goods world in which we live. But of course the agreed conlusion has been that it does not so mimic that world without the peculiar equal proportions assumption. Incidentally, the implicit “prediction” that proportions are equal is empirically false. (C.f. Samuelson’s Kyklos response to Friedman on methodology, what Samuelson called the F-twist.)

    Again, Samuelson QJE 1966 took it for granted that we cannot be seriously interested in one commodity models. He stated that the Sraffians were correct and that a scholar must not expect to live an easy life. As Samuelson knew fifty years ago, economic theory cannot responsibly be simplified down to F(K,L).

    I think that is all that needs to be said.

    • I am glad we agree that internal consistency is not really the issue here. The issue is whether the macroeconomic F(K,L) function can be rigorously derived from a more complex and arguably more realistic microeconomic model with heterogeneous capital goods. It is, if you will, an issue of micro-foundation. Apparently Samuelson in 1962 thought this possible under not too stringent conditions. This turned out to be wishful thinking. Fine. But does the lack of micro-foundations in itself mean we should throw away F(K,L)? I think few economists would take such a radically micro-fundamentalist position.

      Kepler’s Laws of planetary motion are incompatible with Special Relativity. What astronomer would conclude from this fact alone that Kepler’s Laws should never be used? I guess “serious astronomers” can accept that Kepler’s Laws are not exactly true and yet rely on them (within limits) for predicting the motions of planets around the sun. By analogy, “serious economists” can accept that a one-good model is not a literal description of reality (duh!) and yet rely on it (within limits) for, say, predicting the growth patterns of real economies.

  3. To be quite clear, what we must agree on, is that internal consistency, whilst not sufficient, is necessary (because from inconsistent assumptions one can derive logically any proposition whatsoever).

    Does Herr Gödl imply that economists like J.B. Clark, K. Wicksell, F.A. Hayek and P.A. Samuelson were foolish, wasting their time by asking whether F(K,L) mimics the many capital goods world? Surely not.

    Physicists do care about prediction (and they seem to do admirably well in this regard). And they do, of course, care about internal consistency. They become anxious when not achieving it. Prediction in economics appears to be a vastly more difficult thing. Is the predictive success of economists using any approach to be greatly admired? Again, surely not.

    Major mainstream economists have been greatly concerned both about internal consistency and about microfoundations. Is Herr Gödl in any position to brush such people aside?

    That would definitely seem to be all that need be said.

    • Prof. Kurz, thank you for your intervention. I agree (who wouldn’t?) that theories must be logically consistent. The issue is whether Prof. Steedman’s paper challenges the logical consistency of the neoclassical F(K,L) models. I think it doesn’t. It merely shows that multi-sector models with heterogeneous capital goods behave differently from one-sector models with homogeneous capital.

      So we have two broad classes of models: one-sector neoclassical models and n-sector Sraffian ones. Both are internally consistent. Which is the better class? I think there is no way to decide that question other than looking at how well each fits the available economic data.

      That’s all I wanted to say.

  4. Time and again in the past century economists looked for salvation by comparing their science to natural sciences of different kinds, one of them being physics. I think it is neither the time nor the place to repeat these discussions and the singling out of the may differences from a methodological point of view – hence I also do not intend to give a reply to Max Gödl but to reveal dead end of a discussion dealing with his kinds of arguments. The interested reader is referred to, for example, the book “More Heat than Light” from Philip Mirowski and countless articles on this topic. Just to give a hint and some keywords which are related to this topic: (1) It is a question of the subjct matter. Never compare nomologic systems like those studied by Newtonian physics with a good record concerning predictability, with reflexive autpoietic systems like economic systems. For the latter, predictability is questionable in terms and impossible by the standards set by physics. Looking at the transition from physical to meteorological to biological to social systems makes the difference obvious; but sometimes this gradual transition from simple to complex systems covers the fundamental difference from a methodological point of view. (2) This last point indirectly includes an advice for all those who want to evaluate economic theories by comparing their methodological approach to physical theories. It is legitimate to enter a methodological discussion in this vein, but never – and I mean NEVER – try this if your knowledge on physics does not exceed high school level. To take the example of Mr. Gödl: Special relativity is a generalization of Newtonian mechanics as well as quantum mechanics. Each theory is logically consistent (since axiomatic formulations of physical theories are state-of-the-art at least since Isaac Newton). They are logically incommensurable since they use different concepts, but due to the Correspondence Principle of Niels Bohr they can be related to each other since they look at the same system (there is only one nature) but at different scales. Conclusion: As I said this comment cannot be exhausticve onthis issue, thousands of pages were written about it. It is also true that no final answer can be given on how to evaluate economic theories. But the defense of Max Gödl by pointing at physics is outdated, however, now I know that it is still alive in the heads of (professional) economists. Hence I do not want to pass sentence on Mr. Gödl’s arguments but this Blog entry ought to raise red flags to those who are responsible for the economics curricula to include more lectures and seminars on Economic Methodology, about Philosophy of Economics and especially about the History of Economic Thoughts (HET).

    • Andi, thanks for the lecture in physics. It is clear that economic models are far worse than physics in terms of empirical success. But from my high school knowledge of natural science I thought that physicists were in the business of building logically consistent models from a set of simplifying assumptions (treat the falling car as a point particle in a perfect vacuum…) and then testing their conclusions against real-world data. This has been an extremely successful enterprise. I don’t see why social sciences should not try to use the same approach in their (much more complex) fields too. I think mainstream economists have done exactly that, and did make a good deal of progress since the days of J.B. Clark, K. Wicksell and F.A. Hayek.

      But that’s sort of beside the point. My point was that Steedman’s critique is not about internal consistency of the one-good model. It is about the micro-foundations of the one-good model. We agree on that. Prof. Kurz and Prof. Steedman seem to think that you should never use a model if you cannot micro-found it with a heterogeneous capital goods model. My position is that micro-foundations are interesting, but only relevant if they improve the predictive success of a model. It is not clear to me that the 1962 Samuelson model, or the 1960 Sraffa model better fit the relevant economic time series than the simpler neoclassical models.

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