Wednesday, January 01, 2025


I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Thursday, August 06, 2020

Nicholas Georgescu-Roegen On Mathematical Methods In Economic Science

I have long been convinced that many mainstream economists, however they performed under hazing, do not understand mathematics.

"T. C. Koopmans, perhaps the greatest defender of the use of the mathematical tool in economics, countered the criticism of the exaggeration of mathematical symbolism by claiming that the critics have not come forward with specific complaints. The occasion was a symposium held in 1954 around a protest by David Novick. But, by an irony of fate, some twenty years later one of the most incriminating corpora delicti of empty mathematization got into print with the direct help of none other than Koopmans. R. J. Aumann had already published in Econometrica an article dealing with the problem of a market in which there are as many traders as the real numbers, that is, as many as all the points on a continuous line. In 1972, Koopmans presented to the National Academy of Sciences a paper by Donald Brown and Abraham Robinson for publication in its official periodical. The authors assumed that there are more traders even than the elements of the continuum. Now, since the authors of both these papers and Koopmans are well versed in mathematics, they must have known the result proved long ago by George Cantor, namely, that even an infinite space can accomodate at most a denumerable infinity of three-dimensional objects (as the traders must necessarily be)." -- Nicholas Georgescu-Roegen (1979) Methods in Economic Science. Journal of Economic Issues, XIII (2): 317-328.

I do not intend to get a Twitter account. Yesterday(?) some economist illustrated what they learn by tweeting a screenshot of a couple of pages from Mas-Colell, Whinston, and Green..

Tuesday, August 04, 2020

Gautam Mathur Introduces Edward Nell To Piero Sraffa

I have been exploring Sraffa's correspondence after the publication of his book. Here is a letter dated June 18, 1962, from Mathur to Sraffa (D3/12/111: 298):

Dear Mr. Sraffa,

In Nuffield there is a senior research student Edmund Nell who is attached to the faculty of Literae Humaniores[?] and is researching into the significance of concepts in economics. He is highly interested in the type of analysis you have proposed, and has been trying to work his way through it. In Oxford there is no other person whom I have met or heard of who has made a more detailed study of your book.

He would very much like to meet you, to discuss some of his problems, and would be writing to you direct regarding it. In the meantime, he has asked me to introduce him to you. This letter is meant to perform that function, though imperfectly.

I shall be in Cambridge on 25th, 26th, 27th, and would like to see you sometime. I shall ring you up on arrival. I am leaving England on the 30th June.

With regards,

Yours sincerely

Gautam Mathur

Nell's 14 July 1962 letter (D3/12/111: 299-302) is the longest I have found in the archives so far:

Dear Mr. Sraffa,

I believe Gautam Mathur wrote to you about me recently. I had rather hoped that I might be able to see you in Cambridge before you left for the summer, but I'm afraid I just left it too late. Anyway, I don't know if I really have anything to say that would be of much interest to you (and perhaps I'm a little afraid I'm on the wrong track completely.) I was greatly impressed and excited by Production of Commodities, when it was brought to my attention last year by Luigi Pasinetti. Subsequently I have tried to use it in my own work, which is an attempt to criticise (what I take to be) the neo-classical theory of general equilibrium in production and exchange, which I think to be nonsense. (Roughly speaking, I cannot see either what utility functions and production functions are supposed to be predicated of, or how in general preference orderings and production possibilities could be defined independently of each other. Nor do I see what the neo-classical theorists mean when they talk of a (homogeneous) commodity. Indeed, it seems to me that the implications of the notion of an artefact are quite inconsistent with the neo-classical doctrine of "substitution" on both sides of the market.)

Perhaps I should give some background information. I came to Oxford from Princeton, where I studied Politics, as a Rhodes Scholar. I read PPE at Magdalen, received a First, and was elected to Nuffield, where I have been for the past three years. I am now working on a D.Phil. thesis which might be call something like, "Agent and Object in the Theory of Production and Exchange".

Let me sketch briefly the problem that worries me, what I take to be the solution of it, and the way I propose to support this solution.

The general question that troubles me is this: I do not see at all clearly what is meant when one uses a mathematical formula to represent social behavior. Are the actual, historical acts of particular persons supposed to be represented? Or is what is represented supposed to be the relations of various roles in institutions? Many further questions present themselves: How are the value-ranges of the variables defined? Are all the concepts that regulate role-behavior such as to "have number"? Is the relation of a particular act to the general concept of the action of which it is an instance the same as the relation of a value to the variable of which it is a value. And so on. These rather general worries take a much more particular and concrete form, however, when one comes to consider the neo-classical theory of general equilibrium. For example, one wants to know how the value-range of the variable standing for the quantity of some good demanded by an "individual" can be defined independently: a) of the quantity of any and all goods he supplies - whatever does he use the good for? And if what he uses it for is not fixed, then on what grounds does he "prefer" the good to others? To want something is to want it for something. b) of the quantities of other goods that he consumes. Goods are the goods they are because they have certain technological properties, which imply that they must be used in certain (relatively) fixed proportions with other goods; light bulbs require sockets, lampshades lamps.

Even more worrying, however, is the idea that the set of variable demands for each commodity by each individual can be defined independently of the set of variable supplies of each commodity by each firm. For instance it would seem that to make plausible the idea of substituting one good for another in demand, one must require that each good be carefully and minutely distinguished from each other good. But the more sharply we define a good, the more we specify its technological qualities, and therefore the more we determine both the kinds of things and the relative proportions of things that go into its make-up; hence the more plausible we make the idea of substitution in demand, the less plausible we make this same idea in supply. More generally, however, to say that a certain amount of any artefact exists, has been produced, is to imply that someone has been the producer of it; hence has acted in a role, has certain abilities, and has used up something in order to produce the artefact. Any production implies some consumption, and the qualities of the thing produced tell us what kinds of things have been consumed.

A further worry arises over the notion of "price". Even very elementary reflection suggests that exchange must take place between many holders of many different goods, and there seems no reason to assume at the outset that the price of a good can be adequately represented by a scalar variable1.

Finally, even supposing that these problems about the definitions of the value-ranges of the variables could be overcome, there remains the question of just what it is that has been represented: Have we represented here the behavior of actual persons, so that conclusions drawn from the theory could be used for prediction? Or have we represented the structure of institutions, so that conclusions drawn from the theory would serve to make explicit the way people ought to behave - and what the results of their doing of their duty must be? Even if the mathematical representation is valid, there remains the questions of exactly what has been represented, and what the representation can be used for.

These considerations may be summed up in four problems:

a) to discover and classify all the kinds of statements there are about agents acting upon, with, by, through, etc. to produce objects; that is, to analyze the agent-verb-object relation.

b) to see what differences there are in the way various forms of agent-verb-object are demonstrated; and also to see if any of these differ in the way they are demonstrated from the way propositions of the form φa and aRb are demonstrated. That is, what difference does the notion of "agency" make?

c) to see if statements of the agent-verb-object form are formally similar to (hence representable by) mathematical statements; and to see what are the conditions for this to be possible.

d) to see what limitations there are upon the use of a formal representation of statements of the agent-verb-object kind; in particular to see if these can be used for prediction. (My argument tentatively is that prediction and mathematical calculation are incompatible for purely logical reasons.)

So far I have just tried to give a very rough sketch of the problems that bother me and the general position I take on them. I don’t want to prolong this letter, so I won’t try to summarize my work on these four questions. Instead, I should like to mention briefly how I have drawn on Production of Commodities in my work, and indicate a problem that has arisen out of this.

Very shortly, I have tried to classify social actions according to the implications respectively about the agent and about the object(s) of a statement containing as verb the concept of the action. It seems that on the basis of such a study of verbs the concept of the action. It seems that on the basis of such a study of verbs one can make some general classification of institutions, and for each class, one can state the general form of the institutions in it, showing the logical relations of the elements of these institutions. The classes of institutions that stand out as particularly interesting I call "productions" and "performances". These involve, respectively, verbs of making and breaking, and verbs appropriate to what Austin has called "performative utterances". Now the connection with Production of Commodities comes in this way: a set of "productions" will do very nicely as an interpretation of the model there, but it seems more difficult to fit in performances (commands, orders, directives, advice, undertakings, making contracts, judging, passing sentence, etc.) since such roles do not produce any definite quantifiable product which can be shown both as output and as input. Yet a society is inconceivable without these institutions. How are these to be treated? They differ from non-basics in the fact that they are essential.

A second problem arises in that the "plus" sign is used to represent the relations of various commodities to each other in each industry. This seems harmless enough, but a verbal description would contain such prepositions as "on", "with", "by", "in", "through", "to", etc., each of which expresses quite a different relation. So long as neither substitution nor growth is contemplated, and the only point of the mathematical representation is to compute the ratios of exchange required for the possibility of reproduction, no harm seems done. I wonder about switches in methods of production, though.

I'm afraid this letter is very disorganized, and probably not at all clear. On the other hand, my purpose in writing it has been not so much to say something clearly, as to convey a general approach - to communicate an attitude rather than to make a statement. In short, I am writing in the hope that something I've said here may arouse your interest in one or more of my various muddles, and that we might correspond further.

Yours sincerely,

Edward J. Nell

1 That is, a variable whose value-range is a set of cardinal or ordinal numbers. To assume this is to assume away the possibility that a price of a good might change so as to be different but neither greater nor less. But this is exactly what would happen necessarily to at least the price of one good, if one carried out "substitution" of one good for another in an industry, in the system of equations in Section II of Production of Commodities - i.e assuming total proportions constant - hence that somewhere else the reverse substitution takes places. (But it is also the case if just one good is just increased in total amount.)

Sraffa wrote his response on 18 August 1962 (D3/12/111: 303):

Dear Mr. Nell

Thank you for your letter of 14 July which has reached me with delay as I have been moving about.

I greatly sympathise with your critical attitude to the neoclassical theory of equilibrium in production and exchange. On the other hand I have only partly understood what you say on particular points. This is probably due to your assumption that I am familiar with the language and technique of philosophy, which I am not.

I should very much like to discuss some of your criticisms, if we could meet sometime. My movements will be rather unpredictable next year, which will be a sabbatical for me. I am however likely to be in Cambridge during the latter part of September and in October, and if at that time you can get in touch by writing at Trinity perhaps we can arrange to a meeting.

Yours sincerely

P. S.

I have not included strikethroughs, handwritten emendations, and such-like above.

Saturday, August 01, 2020

Jonathan Nitzan On The Factual And Logical Invalidity Of Neoclassical Economics

Neoclassical Political Economy

You may have seen the above overly polite video.

I have not done this in a while, even before the pandemic. I used to, when I visited an academic bookstore or a college library, skim through textbooks, concentrating on introductory or intermediate microeconomics. Economics is in an extraordinary state, where the textbooks are full of nonsense that has been known to be logically invalid for half a century.

Here is an example. David D. Friedman (Milton's son) has made the 1990 or second edition of his Price Theory: An Intermediate Text available online. And it contains this manure:

This conclusion is useful for seeing how various changes affect the distribution of income. Suppose the number of carpenters suddenly increases, due to the immigration of thousands of new carpenters from Mexico. Both before and after the change, carpenters receive their marginal revenue product. Both before and after, they receive a wage equal to the marginal value of the last hour of leisure they give up.

But the wage after the migration is lower than the wage before. Since the supply of carpenters is higher than before, the equilibrium wage is lower. At that lower wage more carpenters are hired and their marginal product is therefore lower. With lower wages, the existing carpenters work fewer hours (assuming a normally shaped supply curve for their labor) and, when they are working fewer hours, have more leisure and value the marginal hour of leisure less. Some carpenters--those with particularly good alternative occupations--find that, at the lower wage, they are better off doing something else. The marginal cost to the worker of working an additional hour falls, either because the marginal hour is worked by one of the old carpenters who is now working fewer hours or because the marginal carpenter is now one of the new immigrants. -- David D. Friedman Chapter 14

Is Friedman a liar or a fool?

Saturday, July 25, 2020

Why Do Mainstream Economists Not Make More Out Of The CCC?

Marx is mostly right.

That is the conclusion one should draw from capital theory. But honestly understanding how we are fed, clothed, and housed under capitalism is not what academic economics is about.

Ownership of property in, say, the United States results in the generation of income. This income takes the form of interest on debt, dividends, capital gains, rent, and so on. Many of those who are among the most wealthy often have returns to property ownership as their only source of income.

Overall, laborers work within a given environment to recreate the capital goods used up in production and to produce more. The source of the returns to property ownership comes from paying workers less than what they produce, over and above the constantly reproduced capital. The owners of capital direct and control the workers and the environment in which they work, in hierarchical structures, so as to attempt to ensure the surplus is as large as possible.

Marx provides a vocabulary to talk about the above qualitative outline, to understand the formal and real subsumption of labor.

Marx provides many details to investigate and modify. I do not think the law of the tendency of the rate of profits to fall (TRPF) can be deduced from the remainder of his system. But just like a simple labor theory of value, it seems to work surprisingly well empirically. When one tries to make sense about the stagflation of the 1970s and the transition from the post war golden age to the neoliberal era, trends in the rate of profits seem quite important.

How important is the question of labor values versus prices of production in any quantitative analysis built on this basis? One can say a lot while confining one's attention to employment multipliers and prices of production. The non-applicability and incoherence of the theory of supply and demand is a major point of the Cambridge Capital Controversy. Supply and demand functions no longer should appear in any long run theory, in any investigation of persistent trends in capitalist economies.

And, of course, Leontief figured out how to organize data for empirical and quantitative investigations along these lines. One can construct Leontief input output tables from the make and use tables that are kept for the national income and product accounts (NIPAs). I would also like price indices for each industry at the level of the available NIPAs. There are many details and conventions that one should understand in working with such data, which I think I get muddled over when I've gone into details.

And much room exists for qualitative and historical work. One could draw on institutional economics in examining capital as power.

You can start to see scholars developing economics in this direction in the 1970s and early 1980s. I think of Donald Harris' Capital Accumulation and Income Distribution, Stephen Marglin's Growth, Distribution and Prices, Michio Morishima's Marx's Economics: A Dual Theory of Value and Growth, Luigi Pasinetti's Lectures on the Theory of Production, John Roemer's Analytical Foundations of Marxian Economic Theory, or Peter Skott's Conflict and Effective Demand in Economic Growth.

But most of the economists at the supposed best schools were uninterested or too craven to accept work along these lines as valid research programs. So much of academic economics is special pleading in bad faith for their paymasters among the plutocracy, as comes out in the news every once in a while. (Disclaimer: I own stock in Amazon and Apple.)

Friday, July 17, 2020

Marx's Theory Of Value Is Consistent With And More General Than Marginalist Economics

1.0 Introduction

One inspiration for this post is stumbling across this abstract

2.0 Marx

Start with labor coefficients and a Leontief input/output matrix, in physical terms. You can construct this from make and use tables for your country, given price indices by sectors.

For any existing capitalist economy, I expect that matrix to characterize a more than viable economy. After all the capital goods used up in producing the final demand in, say, a year are reproduced, some commodities will remain for consuming and investing.

As with any other matrix, a set of n Eigenvalues and corresponding Eigenvectors can be found for that matrix. And, if I recall correctly, the maximum Eigenvalue has an associated Eigenvector in which all elements are non-negative. The components for Sraffa's basic commodities are all strictly positive. And they are in the proportions of Sraffa's standard commodity. If wages are zero (the worker's live on air) and the final demand is all invested, the final demand will be in proprortions of Sraffa's standard economy and the economy will expand at a rate of growth related to this eigenvalue. One can read von Neumann (1945) as describing this model of uniform growth.

So given the technique in use in a capitalist economy, a composite commodity of average capital composition is picked out. Georg von Charasoff called this composite commodity 'Urkapital' which, I guess, is translated as "original capital". In some sense, this urkapital is a commodity of average organic composition of capital. This numeraire is picked out by the technique in use. In the production of this numeraire:

  • The rate of profits, as calculated in the system of embodied labor values, is identically equal to the rate of profits, as calculated in the system of prices of production.
  • Gross output, as evaluated at embodied labor values, is equal to gross outputs, as evaluated at prices of production.
  • Net output, as evaluated at embodied labor values, is equal to net output, as evaluated at prices of production.
  • The division of net output between workers and capitalist makes no difference to the above invariants.

So Volumes 1 and 3 of Marx's Capital are consistent.

3.0 Marginalist Economics

If one is ill-informed and malicious these days, one could insist that Sraffa's model is a special case of a neoclassical model of intertemporal equilibrium. Consumers maximize utility, and managers of firms maximize profits. Initial endowments just happen to be so that the economy expands along a steady state growth path.

4.0 Conclusions

But, of course, utility-maximization is nonsense, especially inter-temporally. Furthermore, the von Neumann ray has saddle-point instability. As Joan Robinson showed with her models of metallic ages, one need not assume that the workforce is fully employed in the long-run.

The model that has no need of restrictive assumptions is the more general.

Thursday, July 16, 2020

Where Can I Read Correspondence Between Robinson And Sraffa?

I have been looking at Sraffa's archives. Scott Carter was responsible for putting them online, as I understand it. Anyways, I know some contents has been published. What should I read for transcripts of letters between Robinson and Sraffa? Maybe something by Marcuzzo?

Anyways, here is a 18 June 1960 letter from Robinson to Sraffa (D3/12/111: 340-341)

All the work that I have been doing the last 10 years has been very much influenced by you – both our conservations in old days and by your Preface. When I went off my head I thought that the idea I had seen in a blinding flash was yours, because it came to me in terms of Ricardo’s corn economy, but it was connected with TIME and it so appears is very much akin to your point of view (though one it seems to fit perfectly well.) Since, quite apart from your worldly success, I have a lot of fun. I have a very deep feeling of gratitude to you. The fact that you reject it doesn’t affect the case at all.