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The capital controversy

from Lars Syll

As every mainstream textbook on growth theory, most mainstream economists choose to turn a blind eye to the concept of capital and the Cambridge controversy over it and pretend it’s much fuss about nothing. But they are wrong!


The production function has been a powerful instrument of miseducation. The student of economic theory is taught to write Q = f(L, K) where L is a quantity of labor, K a quantity of capital and Q a rate of output of commodities. He is instructed to assume all workers alike, and to measure L in man-hours of labor; he is told something about the index-number problem in choosing a unit of output; and then he is hurried on to the next question, in the hope that he will forget to ask in what units K is measured. Before he ever does ask, he has become a professor, and so sloppy habits of thought are handed on from one generation to the next.

Joan Robinson

As Edwin Burmeister admitted already twenty years ago:

It is important, for the record, to recognize that key participants in the debate openly admitted their mistakes. Samuelson’s seventh edition of Economics was purged of errors. Levhari and Samuelson published a paper which began, ‘We wish to make it clear for the record that the nonreswitching theorem associated with us is definitely false’ … Leland Yeager and I jointly published a note acknowledging his earlier error and attempting to resolve the conflict between our theoretical perspectives … However, the damage had been done, and Cambridge, UK, ‘declared victory’: Levhari was wrong, Samuelson was wrong, Solow was wrong, MIT was wrong and therefore neoclassical economics was wrong. As a result there are some groups of economists who have abandoned neoclassical economics for their own refinements of classical economics. In the United States, on the other hand, mainstream economics goes on as if the controversy had never occurred. Macroeconomics textbooks discuss ‘capital’ as if it were a well-defined concept — which it is not, except in a very special one-capital-good world (or under other unrealistically restrictive conditions). The problems of heterogeneous capital goods have also been ignored in the ‘rational expectations revolution’ and in virtually all econometric work.

Edwin Burmeister

  1. September 3, 2020 at 1:02 am

    Labor capital expressed by a young person with focused energy competes with banker’s capital propped up by military empire. Is that a difference ignored by capitalist economics?

  2. September 3, 2020 at 10:25 am

    Thank you for this, Lars. It is the first time I have been able to see what the Capital Controversies were about. It takes me straight back to what the typed logic of Algol68 was all about. In the equation Q = f(L,K), L and K are not just variables but variably typed variables only capable of being “equalled” when referring to something specific. The near-equivalent American language ‘C’ (propped up by “military empire”) retained the variability of what was being referred to, but hived off the reference dimension of the variable as a separate ‘pointer’ type, referring to the computer location (“the owner”) rather than the value of the variable, so that the “capital value” appears to be that of its owners.

    C.f. my https://rwer.wordpress.com/2020/08/22/mmt-debunking-the-deficit-myth/#comments on August 24, 2020 at 5:06 pm.

    Somewhere recently I’ve seen a comment to the effect that the nineteenth century economists, though keen on numbers, were weak on logic.

  3. A.J. Sutter
    September 3, 2020 at 4:36 pm

    What makes the modern teaching about production functions especially egregious is all the improvisation about the units in which each of the variables is measured (or more accurately: improvisation about the dimensions of the variables). It’s clear that most textbook authors haven’t read the original paper, “A Theory of Production” (1928). C&D sidestepped the issue of dimensions altogether by indexing each quantity to its value in 1899; so for them, the variables in the function are all dimensionless. Using dimensionless quantities is also necessary in order to give some meaning to the exponents α and 1-α as empirical quantities, because otherwise no two functions could be dimensionally comparable to each other.

    Of course, C&D did aggregate heterogeneous sorts of capital, and did the same with labor, which were key issues in the Capital Controversy. But the way modern pedagogy mucks up the dimensions issue is truly an own-goal.

    • September 5, 2020 at 1:46 pm

      In “the original [Cobb – Douglas] paper, “A Theory of Production” (1928). C&D sidestepped the issue of dimensions altogether by indexing each quantity to its value in 1899”. Interesting.

      Following this up, I found “The theory of the production function depicts the relation between physical outputs of a production process and physical inputs, i.e. factors of production. The practical application of production functions is obtained by valuing the physical outputs and inputs by their prices”.

      Surely that makes the argument circular: valuing the inputs by their price and the price of outputs by the price value of their inputs? So yes: “key issues in the Capital Controversy”.

      • A.J. Sutter
        September 5, 2020 at 3:32 pm

        @davetaylor1 Thanks for your comment. To be clear, though: you are quoting from Wikipedia, not from Cobb & Douglas.

        In fact, in the original paper, the labor factor was based on the number of people employed (made dimensionless by normalizing to the base year amount), not on labor costs. Also, even though prices were considered in determining the amount of capital, the authors do discuss some problems with that approach (e.g., at p.146 in the paper).

  4. Yoshinori Shiozawa
    September 5, 2020 at 3:44 am

    Cambridge controversy did not produced a new foundation. Cambridge, Massachusetts, intentionally ignored and forgot the internal logical inconsistency in its capital theory. Cambridge, England, often remembers the history but could have present no alternative theory. Post Keynesian economics comprises this internal contradiction. And yet, the majority of PK economists pretend that no foundation is necessary.

    • Craig
      September 5, 2020 at 8:14 am

      Cost accounting is the essence of the micro-economy and money is basically accounting because it adheres to the debit-credit accounting convention. Retail sale is presently the single integrative point between micro and macro-economics because retail sale is both the terminal ending point of the economy (where production leaves the economy and becomes consumption) and also the aggregative cost and price point for every item or service in any economy.

      These truths and realities are the infrastructure within which the entirety of the economy operates and is inextricably embedded in, and they also expose private for profit finance as totally parasitic and de-stabilizing.

      Economics has been analyzed every which way from the middle while missing these basic points. Steve Keen has belatedly realized the importance of double entry bookkeeping as he uses his debit-credit Godley tables to follow flows of money and debt in the economy but still does not recognize that a single policy (the 50% discount/rebate at retail sale) utilizes all of the above realities to accomplish beneficial paradigm changing effects for all economic agents.

      Life and economics are as obscure, unworkable and ethically challenged as they are (unnecessarily) complicated, and as enlightening and enjoyable as the directly observed deep simplicities of science and wisdom.

      • A.J. Sutter
        September 5, 2020 at 8:50 am

        @Craig At the risk of wandering far afield from the original post: Retail sale *would be* an integrative point between micro and macro — but for a tenet of micro theory. Namely, that prices are orderings.

        What matters in micro theory is that
        p(ice cream cone) ≺ p(iPad) ≺ p(BMW),
        where ‘p(x)’ means ‘the price of x’. That is, the ordering of the prices matters, but the absolute prices of those commodities don’t matter. The problem is that GDP is, per the most common method of computation, the sum of the retail prices of final goods within a certain spatiotemporal interval. Retail prices are absolute prices.

        Either absolute prices matter, or they don’t. So there is a conceptual disconnect exactly at the “integrative point” between the micro and macro points of view.

      • September 5, 2020 at 1:18 pm

        Craig seems to be suggesting that micro-economics is that subset of economics which concerns only buyers and sellers, leaving macro-economics as the theory of how to provision everybody.

        A J is right in saying the ordering of prices matters to individuals (i.e. at the micro level), but what is inconsistent about GDP seems to be its summing them as if they were at the macro level, not that absolute (actual) prices of particular goods do not matter (even when signalling the environmental cost of or lack of need for the particular goods).

        I beg to differ. Goods available should be priced to reflect their environmental cost, with everyone left free to buy them if they need them by using an interest-free local credit card and helping regenerate the goods used by doing necessary work. GDP would then account for everybody, short-falls or gains in particular resources could be estimated and prices and net incomes rationed accordingly. A separate prize system could encourage development of resource-use efficiency and quality.

      • Craig
        September 6, 2020 at 12:42 am

        For the individual and for the enterprise retail price and the ability to both set it and pay it is everything. To macro theorists, especially those who count for profit financial costs/prices as a legitimate part of GDP, they aren’t.

        As I said in my prior post macro-economics although it can bring occasional insight (mainly in a round about fashion that brings such insights back to the basic realities of micro-economics like cost, the terminal and aggregative nature of retail price and accounting conventions like equal debits/credits summing to zero) it mainly became an obscuratant fall back position for finance to avoid confronting the de-stabilizing effects of its monopolistic paradigm of Debt Only. Here is a link to Michael Hudson’s blog today that enumerates the history and numerous ways that we have devolved toward feudalism since doing away with the “clean slates” (partial and palliative) solution that nations in the near east used in the second millennium BC. We have to smarter than the ancients and not as dumb as we’ve become since in dealing with the problematic paradigm of Debt Only.

        The 50% discount/rebate policies and other policies and regulations of Wisdomics-Gracenomics are the outline for the paradigm change required.

      • Craig
        September 6, 2020 at 12:48 am
  5. Yoshinori Shiozawa
    September 5, 2020 at 2:54 pm

    Any microfoundations must comprise price theory, production theory (not necessarily production function), how transactions (product versus money) are made, how they are connected with each other, and the time pattern of these interactions. See our book Microfounations of Evolutionary Economics.

  6. A.J. Sutter
    September 5, 2020 at 3:57 pm

    @davetaylor1 [01:18] Again, a bit distant from the original post, but: You mention “Goods available should be priced to reflect their environmental cost, with everyone left free to buy them if they need them by using an interest-free local credit card and helping regenerate the goods used by doing necessary work.” But how would this actually work?

    Say I’m a manufacturer of some plastic gizmo. Issue #1, who is going to calculate the environmental cost of the gizmo, and is this even something that can be known? E.g., we didn’t know until recently that microplastics enter the guts of marine animals. How could we possibly calculate the value of that impact? And what about accounting for other effects not yet discovered, just as that one had not been until a couple of years ago?

    Suppose we calculate anyway, and come up with an $X markup per unit. Issue #2: My customer pays that to me — but what happens with that revenue? It goes into my pocket, unless there is some mechanism to make sure that the $X is actually applied to cure the various ills that are reflected in the markup. Serving as a “signal” doesn’t do anything to actually cure the problems caused by the manufacture; at best, it can only limit future damage if it reduces demand for my gizmo enough that I make fewer of them. But the damage done by making each gizmo I sold can’t be undone unless someone is going to remediate it.

    Morevover, even one cheap item can cause many different types of damage: pollution and emissions during manufacture, microplastics and marine or soil damage after its useful life, etc. So Issue #3: Who is going to administer the divvying up of the $X to help clean up the very heterogeneous sorts of environmental problems occasioned by my making the gizmo?

    Finally, I was a little unclear about the free local credit card and the aspect of “help[ing] to regenerate the goods used by doing necessary work.” Suppose I manufacture my plastic gizmo in Shanghai and sell it in Chicago. What locality does the credit card relate to? And suppose my customer is a health care provider, a professional musician, or any of any number of other professions: how are they supposed to get the time and knowledge to remediate the environmental damage done during the manufacture, useful life and afterlife of the gizmo they bought? Or did I misunderstand this part? (I guess Issues #4 etc. are raised within this paragraph.)

  7. September 7, 2020 at 5:18 am

    A.J., thank you! How nice to have someone questioning what I mean rather than ignoring or rubbishing what I have been trying to say! On your earlier comments about the Cobb-Douglas paper, points taken. Not being an academic, I have not been able to read the original paper myself, my mathematical mind and background in engineering and applying the new dynamic computer logic making me pick up on differences like that between industrial (already semi-aggregated) pricing and the logically necessary particular pricing.

    How would my own proposals actually work, then? Let me first point out what I am aiming at in practice (their applying to everyone, enabling human and environmental issues to be addressed), and their Copernican nature (changing not so much what we do but how we interpret its direction of motion, so that, understood as a Kantian cause, money and doesn’t start and end up accumulating in banks).

    Apologies if you are not familiar with the philosophy: Kant’s arguing against Adam Smith’s mentor David Hume that causality (like money here and in Modern Monetary Theory) may not physically exist but is basically [just] a concept that is needed to make sense of what we see. We see banks giving us credit and our becoming indebted by spending it. Or more narrowly: those of us who have earned – or won, or been given – the credit in our bank account, reducing that by spending it. But in principle, given a credit limit, anything we can buy with a debit card we can buy with a credit card. All that changes is the order of repayment. Instead of working to eat, we can eat first and pay later. In fact, as we all start off as children unable to work, this is what we actually do.

    Dealing with the environmental cost of gismos, then. First, the employer does not have to pay his employees. They are able to buy all they need on credit, and all he needs to do is credit them for having worked for him. To gain employees he needs to offer work worth doing and good working conditions. Indeed to continue making his gismos he can work for himself and order new materials on credit; likewise anyone taking on the jobs of transporting or marketing them. So far, then the price has just had to cover the cost of materials: environmental costs and wages in the form of a proportional supply of credit.

    You now quite rightly want to know about recouping the cost of pollution via its plastic waste. The cost is that a lot of people are going to have to work to resolve the problem: work worth doing which can be done on credit provided nature and their fellow men can continue to more than sufficiently supply these worker’s needs. We have done that by means of mass production, but that has led to the epidemic of plastic waste, so that the epidemiological part of the solution is localisation: using more efficient new techniques to produce to locally for local consumption and recycling. Related to the capital controversy, this is about organising local machinery and practical education rather than just supplying credit: for example, going back to local dairies supplying milk and fresh fruit juice in re-usable glass bottles.

    Fellow workers include researchers discovering the problems, governments advising us of work worth doing to resolve them, bankers keeping accounts showing what has actually been done, etc. In other words, in the long run there will be some things we will need to get back to doing ourselves, locally, but others will still require mass production, work sharing, commuting and transportation. Right now we will not need fictitious money to finance this work: just generosity in giving each other due credit for what we do for others and need to do for ourselves. And as far as pricing the gismos are concerned, that means an indicative overhead cost for the proportion of the total workforce committing annually to clearing up the mess. If this was too low this year because we hadn’t discovered and/or tackled the problem, then the problem will have got worse and we will need to up the remedial overhead (hence price) in the next year.

    So your issue #2: what happens to the revenue? It is paid into the bank, where the accountant writes off that much of the buyer’s debt and credits the salesman for doing his job. Our personal residual debts can be written off if they are reasonable and unused credit accumulated, since the credit is notional. I totally agree about remediating the damage done by supplying the gismo.

    Issue #3: The local banks are accounting for who is doing what job, so computers can do any aggregation and dividing up necessary.

    Issue #4 etc. As against the present profit-seeking and borrowing at interest of fictitious bank money, all the professional work you mention is done not on the bank’s credit but our own, which can be accounted for and advised on locally, the banker himself being “paid” with credit. Government comes into this as advising on or constitutionally defining what should be produced locally, regionally and internationally, so banks need to account separately for our personal balances of trade outside our locality. This is equivalent to having multi-level rather than $/£/Euro type currencies. Philosophically, the key word is ‘subsidiarity’.

    In view of the length of this, I can only hope you find it helpful!

  8. Yoshinori Shiozawa
    September 7, 2020 at 2:43 pm

    Please read the last paragraph of my Reply on September 7, 2020 at 1:53 pm to Asad Zaman’s article Post-Keynesian Response. There is no need to argue about aggregate production functions (including Cobb-Douglas one). The notion of “(aggregate) production function” is wrong. There is no other solution than to abolish the notion itself.

    The solution is simple, but to reconstruct a new relevant theory is not easy, because it needs to reconstruct the theoretical core from the very beginning of economics. As I have mentioned in my previous post in this page on September 5, 2020 at 2:54 pm, it must contain “price theory, production theory (not production function), how transactions (product versus money) are made, how they are connected with each other, and the time pattern of these interactions.

    Macroeconomics often ignore all these details and pretends to be able to tell the movements of macroeconomic variables. But it is almost always false except for macroeconomic identities (or national accounting identities), because basic movements occur in the microeconomic levels. If we do not understand this movement, we cannot understand macroeconomic movement. Post Keynesians who think they do not need microfoundations are wrong, but they do not understand this simple truth.

  9. Gerald Holtham
    September 7, 2020 at 3:06 pm

    There are all sorts of things wrong with aggregate production functions. One is that the dependent variable is value added, which is not the same as retail sales or gross output. This assumes that the production of economic “value” through the application of labour and something called capital can be analysed ignoring the scale of material inputs, like raw materials and energy and ignores by-products like pollution. This detaches economic activity from the physical world and distracts attention from environmental constraints.
    The Cambridge attack was on the use of the concept of capital to claim that “it” had a marginal product that determined the rate of profit in equilibrium. The attack was well founded. Aggregation issues alone mean the marginal product is not well defined for the whole economy. Anyway not all investments are successful so you can’t expect to be in an equilibrium where everything is working out smoothly.
    We can define capital pragmatically as the sum total of expenditures in the past x years on goods and software that are used in producing something else. We then have a practical definition and it is clear enough what we mean. It is not unreasonable to suppose that the average productivity of an hour of labour in an economy might have a positive association with capital as so defined. A man with a bulldozer can shift more earth in an hour than a man with a spade. However, If you try to find that association empirically (as I have for many countries) you find it is very loose. It depends on which sectors saw the expenditure. An association that may hold in a particular business gets very muddy at the level of the whole economy. In the real world there are also mistakes – people may pay too much or too little for capital goods relative to their productive and profit-generating potential; you can get under and over-investment. The aggregate production function is therefore not only theoretically unfounded it is of limited use in practice in predicting economic output and growth.

  10. Ken Zimmerman
    September 24, 2020 at 12:54 pm

    I want to look at production in terms of political economy as explained by an anthropologist.

    One consequence of capitalist arrangements of production is that it is a considerably more productive ‘economic system’ than all previous styles of production. It facilitates an unprecedented accumulation of capital and concentration and centralization of the ‘means of production.’ Huge corporations arise. Large financial entities and stock markets emerge. Technical progress takes place at an extraordinary rate never known in human history. The division of labor becomes international and scientific technology is applied directly to the processes of production. There is a massive socialization and internationalization of the arrangements of production. Capital is systematically exported to and subordinates other less-capital-focused economies. Global economy emerges.

    Yet the actual facilities and resources for producing goods continue to be privately owned. It appears that this fundamental contradiction of the capitalist system leads to crises of overproduction (often made worse by financial players) which ultimately results in its transformation. Socialism’s part in all this is moving to achieve a fundamental harmonization of these contradictions. The facilities and resources for producing goods are removed from private to public ownership. The relationships of production are thereby made congruent with the relationships in the communities (of various forms) in which production is situated. An economist might conclude that economic efficiency (as defined in the closed framework of the modern mainstream economics discipline) is sacrificed to preserve societal sustainability. This is certainly the conclusion of an anthropologist.

    The first point to note here is that this is a theory of value, a theory of money and a theory of ‘realization’. The theory of the export of capital is also a theory of the economic basis of imperialism, which is an integral part of the political economy outlook. In keeping with its focus, a distinction is made between the sphere in which value arises and the sphere in which it is exchanged, realized, and distributed. In political economy, value is created only in the process of production, never in the process of exchange.

    The second point is the source of value. It is human labor that is the chief force of production and the source of value in the economic sense. This is regarded as a given for all economic systems. A basic distinction is made at this point between two differing senses of value, ‘use value’ and ‘community value’. Use value has to do with the physical properties of a product to which people attach a use, in one way or another. Value in the second sense has to do with the importance attached to goods and services and is socially assigned. This is so whether production is for self-consumption or for exchange. Once the division of labor and market relations emerge, value in this second, social sense is necessarily expressed in ‘exchange value.’ In a capitalist economy exchange value is roughly approximated in price. Likewise, money is a measure and a store of this value. Distribution and exchange are the spheres where value is realized but not where it is generated. Demand and supply cause fluctuations in exchange value but are not themselves its source. For instance, they may cause fluctuations in the value of currencies, but the source of the relative value of currencies is necessarily the relative productivity of the economies to which these currencies belong, more or less captured over a long period of time in balance of payment transactions. The source of exchange value and thus of value in this economic sense is the quantity of socially necessary labor time expended on its production.

    The third point to note is that the production of value, crucial though it is, is only one part of the economic process. This value still must be ‘realized.’ After being produced, the products that now embody value must be consumed. In a subsistence agricultural economy some of the crop must be stored for future use. Food or other goods may have to be exchanged for tools and other craft items. This can become a somewhat complicated process. Severe inequalities may arise, especially in gender relations, even though fully developed classes have not yet arisen. As the work of the French Marxist anthropologists (e.g., Maurice Bloch, Maurice Godelier) has shown, seniors often exploit juniors. As the work of Josephides (Josephides, L. 1985. The production of inequality: gender and exchange among the Kewa) demonstrates, men badly exploit women.

    In a capitalist economy the process of realization is considerably more complex.
    Almost every single product and service is bought and sold on the market,
    including human labor power. This is a complex process of exchange given that some goods are for direct consumption, some are for consumption in the process of production and that there is a continuous (although cyclical) expansion of the process of production. Today one is dealing with a global market, in particular a global stock and currency market.

    Once the facilities and resources for producing goods achieve this high level of socialization, the social value embodied in goods and services can only be expressed through this process of exchange, with realization now taking place on an international scale. Given the global scale of the production process, a global process of exchange becomes inescapable. The social significance that goods and services have today is internationally evaluated and no longer the ‘decision’ of the economy of a single nation or region. Global market exchange then becomes the only feasible way for the globally-embodied value in products to find expression. Markets, although fluctuating, distorted, manipulated and subject to periodic crises in the short term, over the long term provide the economy with a social verdict. Limited and incomplete as it may be. Within the limits of the class relations of capitalism, markets are a social mechanism for measuring the value consumers accord to a particular good or service relative to others and for the distribution of surplus value across the economy.

    Furthermore, under capitalism, the socially necessary labor time embodied in goods and services takes the form of their cash value. Value embodied physically or in a specific service must be converted into its money equivalent. From this outcome wages must be paid; raw materials, utilities and other supplies must be bought; rent and interest must be paid; provision must be made for depreciation; wholesaling, retailing, advertising, marketing and other producer services must be paid; capital must be accumulated and the next round of production moved forward by reinvestment in the production process. The process of the realization and distribution of value, especially of surplus value, among all these parties and among the different branches of the economy, becomes extraordinarily complex. Making it not only error prone but a target for criminals who use its complexity to hide their larceny and fraud. These, like the owners of the facilities and resources for producing goods are mostly private citizens rather than government officials. Though with the current events and emerging cultural changes in the federal government, this distinction is becoming blurred. Often quite noticeably so.

    Is this a more complete and/or useful description of capitalist production than that rehearsed by Joan Robinson?

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