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The Cambridge Controversy – a fundamental refutation of orthodox economic theory – Part 2

This is Part 2 in a two part series that deals with the importance of the = Cambridge capital controversy – which saw economists associated with Cambridge University in England and MIT in Cambridge, Massachusetts argue about the validity of neoclassical distribution theory. Most recently, in response to a New York Times article about Joan Robinson, one of the key protagonists in that controversy, Paul Krugman declared the Controversy “a huge intellectual muddle” which was really unimportant in the scheme of things. That just revealed his ignorance and/or his part in an on-going denial that the basis of the framework he operates in is deeply flawed and has no scientific legitimacy. In this Part, we get down to the complexity (as best I can without becoming too technical) of the debates. The import though is clear – orthodox economics, which is still taught on a daily basis in our universities and which people like Krugman use to make money by writing textbooks about is based on a series of myths that cannot be sustained, both logically, in terms of their own internal consistency, and, in relation to saying anything about the real world we live in.

The earlier installment:

1. The Cambridge Controversy – a fundamental refutation of orthodox economic theory – Part 1 (April 27, 2021).

The beginnings of the dispute

In the 1950s, growth theory was all the rage.

By the mid-1940s, economists, who followed in the steps of Keynes (that is, emphasising the importance of fluctuations in effective demand in explaining economic cycles), such as – Roy Harrod and Evsey Domar – had developed a dynamic representation of the General Theory (Harrod, 1939 and Domar, 1946).

This means that while Keynes and co were largely concerned with explaining the economic cycle and departures from full employment, the growth theorists were interested in how effective demand interacted with the supply-side developments (productive capacity accumulation, etc) over time.

They wanted to work out why economies grew and their work also fed into the emergence of development economics as a sub-discipline in its own right.

I won’t delve into these models here but in the development of our textbook, we considered their contributions in some detail.

Please read my blog post – Growth and Inequality – Part 4 (February 7, 2014) and related blogs cited there, for more discussion on this point.

For our purposes here, it is sufficient to say that the emphasis on the demand (expenditure) side didn’t sit well with some neoclassical economists at the time, who concentrated on the supply-side of the economy.

They came out of the tradition that denied that aggregate demand fluctuations create situations where unemployment could persist.

For them, Say’s Law (and later Walras’ Law) meant that if consumption expenditure fell, for example, the increased saving would be taken up by business investment and total spending would not suffer.

Of course, they had difficulty explaining how the productive capital that was used to produce consumption goods and services could instantly morph into capacity capable of producing capital goods (meaning).

We will come back to that.

But, they particularly were unhappy with the conclusion by Keynes and others that a monetary capitalist economy is prone to prolonged departures from full employment and stable growth rates, as a result of demand fluctuations (driven by variations in business investment).

So the dispute began over whether the spending fluctuations could influence the growth trajectory of the economy.

The neoclassical economists considered that temporary cycles driven by demand could not dominate the supply-side factors like population growth, technical progress or resource discoveries over the long-run.

For them, there was a given (exogenous) growth trajectory defined by these supply-side variables that was independent to fluctuations in aggregate spending.

They defined an aggregate production function which said that output, in any period, was a function of labour and capital resources, with a given state of technological development known in each period.

To make their analysis tractable (as the use of mathematics became more in vogue) they had to make particular assumptions about the specification of the production function.

For it had to generate results that were consistent with their central organising framework that included marginal productivity theory, which we discussed in Part 1.

So adopting the idea that we could define the economy as one big production process then total output (Q) is defined as a function of the factors of production, labour inputs (L) and capital inputs (K), for a given technological state (A).

And as we add more of each factor of production to the production process, the marginal contribution declines (this is the so-called “law of diminishing returns”).

Technological improvements mean that for given L and K, total Q rises.

Now we encounter the first problem.

What does K actually mean at the economy-wide level.

In her classic 1953-54 article – The Production Function and the Theory of Capital, Joan Robinson wrote (p.81):

… 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.

(Reference: Robinson, J. (1953–54) ‘The Production Function and the Theory of Capital’, Review of Economic Studies, 21(2), 81–106).

It was this article that triggered the two decade-long debate between the Keynesians (Cambridge, UK) and the Neoclassicals at MIT (Cambridge, US).

Let’s see what that all means.

The Cambridge Controversies – The meaning of capital

In economics, the term ‘capital’ can represent different things, which goes to the heart of the Cambridge dispute.

On the one hand, it can be amount of money that an entrepreneur has in hand.

Alternatively, it can be a stock of productive capacity, embodied in physical objects like machines, equipment, plant etc that allow firms to produce goods and services.

If we are talking about money capital then the units of measurement are currency units (dollars, for example).

But if we are talking about physical capital then the situation gets tricky.

Neoclassical economists, like Paul Krugman, assumed that we could express the heterogeneity of physical in single unit terms – that is, in monetary terms. – to derive an aggregate amount of K.

So, a nation, has $1 billion worth of productive capital.

What is the problem?

Well to add up all the different physical forms that capital can take requires we value the capital using their prices.

So we might have a car worth $1,000, a printer worth $300, and something else worth $2,000 and we can sum them to get an aggregate expression worth $2,300, which overcomes the heterogeneity of the different pieces of capital.

That satisfied the neoclassical economists.

But it was flawed.

Italian economist, Piero Sraffa produced a magnificent book in 1960 – Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory (published by Cambridge University Press), which showed that the neoclassical solution was flawed.

Why?

Because he was able to show that this financial aggregate was dependent on the rate of profit.

So why is that a problem?

Well, the production function said that this physical blob of capital generated output and a marginal product (a physical amount of output) could be defined as the incremental outcome forthcoming by adding one extra unit of this physical blob while all other factors of production were held constant.

The marginal product is, conceptually, a physical entity – an amount of output.

And neoclassical distribution theory – which was developed to explain the distribution of income between labour and capital – asserted that firms would add capital to the production process up to the point where the rate of return (profit) on the capital unit was equal to the marginal product (valued in terms of the price of goods and services).

A firm would be maximising profits at that point, the logic of which could then be extended to all firms.

The point is that in neoclassical (mainstream) theory, if we know the production function (technology, relative factor inputs) then we can determine the rate of profit and the real wage by finding the marginal contribution of each productive factor (L and K), assuming that firms behave in competitive markets and there is no unemployment.

That is the theory.

So the marginal product of capital determines the rate of profit, which as I explained in Part 1, was a theoretical construction designed to make capitalism look fair in the face of criticisms coming from the Marxists.

Capital gets back what it put in to production as labour does. That is the message of marginal productivity theory.

All is fair and reasonable.

For Marx, the real wage was determined before profits were realised and the task of the capitalist was to minimise the value going to workers and maximise the surplus value.

The neoclassical economists, departed from this tradition and considered all factor returns were simultaneously determined by the relative scarcity of each factor and their relative productivity (contribution).

Now note that the real return on capital (the rate of profit) is equal to the rate of interest in a competitive economy. Firms with money to invest would at the margin be indifferent between investing in machinery to earn a rate of profit or leaving their money where it was to earn interest, if the two were equal.

The question then is how do we evaluate the capital stock in monetary terms in order to aggregate all the different capital items?

We have to value it to derive a marginal product (in value terms).

Capital valuation methods invariably rely on computing the present value of the future output stream that the capital produces.

This measure recognises that time is important, which then immediately involves a rate of interest.

Why?

See Part 1 – the interest rate is the reward for foregoing consumption now for consumption tomorrow, given that consumption now is preferable.

So we have the problem of circularity: neoclassical economists claim that the marginal product of capital determines the rate of profit (rate of interest) but to compute the stock of capital (and its marginal product) in value terms we need the rate of profit (rate of interest).

The point is that the value of capital in the economy depends on the rate of interest.

That circularity means that the marginal product cannot determine the rate of profit and so neoclassical (mainstream) distribution theory fails.

They simply cannot explain the distribution of income at the aggregate level and we are left to search for a more adequate explanation of the existence of profit, one, that is not based on a moral view that capitalism is fair.

Marx remains viable in other words.

Reswitching and capital-reversal

The other significant error in mainstream capital and distribution theory that the Cambridge Capital Controversy exposed was the so-called reswitching and capital-reversing phenomena.

This is a very difficult topic and I will only touch the surface.

Neoclassical production and distribution theory was built on three parables (in the words of Paul Samuelson who prosecuted the MIT case).

In his classic 1962 statement of this theory, he wrote:

1. The rate of profit (interest) equals the marginal product of capital.

2. As a result of diminishing returns, adding more capital (with labour fixed) reduces its marginal product and pushes down the rate of return. At university, the lecturer used to explain this to us (as students) as imagining more and more brooms are added to sweep the floor!

3. The income split between labour and capital is determined by the combination of factor of production scarcity and the marginal product of each.

Taken together and recognising that the price of labour (in real terms) is the real wage and the price of capital is the rate of profit, if the relative price ratio changes, then firms will adjust the relative quantities of L and K they use to produce a given level of output.

In the short-run, with capital assumed fixed, if the real wage falls relative to the rate of profit, then firms will use more labour and the labour intensity of production will rise and the marginal product of capital will rise.

Samuelson said that:
There is always a trade off between the wage and profit level: in the absence of innovation both cannot go up …

(Reference: Samuelson, P.A. (1962) ‘Parable and Realism in Capital Theory: The Surrogate Production Function’, Review of Economic Studies, June,
293), 193–206).

According to this theory, there is a one-way relationship between the capital intensity chosen by firms and the relative price ratio (wages to rate of profit).

Through substitution of capital for labour, firms will increase the capital intensity as the real wage rises relative to the rate of profit and that substitution is unidirectional.

What does that mean?

It means that one would never be able to find a capital intensity production process at high and low interest rates with a labour intensive process at some interest rates in between.

If that was ever possible, then the whole theory, defined by Samuelson’s parables, collapses.

That is what the reswitching debate was about.

It was shown by Sraffa that such switches in technology can occur depending on interest rate movements.

Capital reversal referred to the possibility that more labour intensive technique would be the cost-minimising choice at low interest rates, defying the theory that capital scarcity drove up the rate of interest.

I won’t go into why those events can occur but they are related to interest rate compounding and different time periods necessary to produce a certain set of goods.

However, it was clear that such behaviour might be observed in production systems.

As a result, the Cambridge Capital Controversies of the 1960s demolished the foundations of marginal productivity theory and its application to income distribution.

In 1966, Paul Samuelson conceded defeat in his Quarterly Journal of Economics article – A Summing Up

He wrote (p.568):

The phenomenon of switching back at a very low interest rate to a set of techniques that had seemed viable only at a very high interest rate involves more than esoteric difficulties. It shows that the simple tale told by Jevons, Böhm-Bawerk, Wicksell and other neoclassical writers — alleging that, as the interest rate falls in consequence of abstention from present consumption in favor of future, technology must become in some sense more ’roundabout,’ more ‘mechanized’ and ‘more productive’ — cannot be universally valid.

“Cannot be universally valid” means the theory he was defending was incorrect and at that point all mainstream economists should have realised they cannot explain profits or wages in a monetary economy.

Samuelson went on to conclude (p.583):

If all this causes headaches for those nostalgic for the old time parables of neoclassical writing, we must remind ourselves that scholars are not born to live an easy existence. We must respect, and appraise, the facts of life.

Essentially, the debate proved that you cannot explain the distribution of income (as the marginal productivity intended) by appealing to contributions to production (conceptually captured by ‘marginal products’).

In the style of the debate, the famous Italian economist Luigi Pasinetti said in his 1969 article – Switches of Technique and the ‘Rate of Return’ in Capital Theory – published in the Economic Journal, that (pages 522-3):

Very far from embodying the relevant features of the general case, and from being a simplified way of expressing it, the one-commodity infinite-techniques construction is … revealed to be an entirely isolated case. As such, it can have no theoretical or practical relevance whatever. At the same time the whole traditional idea that lower and lower rates of profit are the natural and necessary consequence of further and further additions to “capital” is revealed to be false.

In other words, mainstream marginal productivity theory was internally inconsistent and without application.

You might wonder why it still appears in all the mainstream textbooks.

The answer is that the orthodox economists just ignored the outcomes of the Cambridge debates and proceeded as if nothing happened.

Because the debates were rather esoteric and very mathematical, they didn’t attract public attention and so the results were confined to the academy.

Even so-called progressives like Thomas Picketty in his magnus opus – Capital in the Twenty-First Century – falls foul of these errors in capital theory.

While casting aside the insights of Karl Marx on surplus value, Picketty conceptualised ‘capital’ in the same aggregated way that the 1950s and 1960s mainstream neoclassical economists did – thus violating the capital value question entirely.

His own scant representation of the Cambridge Controversies was a disgrace – he missed the point entirely.

See the Op Ed by James Galbraith in Dissent Magazine – Kapital for the Twenty-First Century? (Spring 2014) – for a better discussion of the flaws in Picketty’s work.

Conclusion

Far from being just an “intellectual muddle” a la Krugman, the conclusions drawn from the Controversy were far-reaching and devastating for mainstream economics.

Of course he would want to cast these implications aside (assuming he even understood them).

Because they cast a big black cloud over his own career’s work.

In addition to rejecting outright the claims by mainstream economists that wages reflect the marginal product of labour and the rate of profit reflects the marginal product of capital, which means large swathes of the undergraduate economics curricula is plain wrong, the Cambridge conclusions had wider implications.

What our conclusion leads to is a recognition that the existence of profit (as unpaid labour) and its realisation relates in significant ways to the power relations in our societies and the mediation or otherwise of the capital-labour conflict by government regulation and legislation.

Investment behaviour by firms is important because it determines the technologies in use (and conditions costs) but the ability of capital and their representatives in the workplace to suppress real wages and/or get governments to introduce legislation that stifles wages growth is an important source of profits.

There is no way that a proposition that each factor of production is rewarded according to its marginal contribution to income generation can be justified in logic or evidence.

The conclusions also help us understand the process of development.

As James Galbraith wrote “richer countries … [did not get] … that way by using ‘more’ capital.”

He went on:

… these countries became rich … by learning, by improving technique, by installing infrastructure, with education, and … by implementing thoroughgoing regulation and social insurance … There is no reason to think that financial capitalization bears any close relationship to economic development.

So no one that really understood this literature would conclude that the conclusions were just “an intellectual muddle”.

That is enough for today!

(c) Copyright 2021 William Mitchell. All Rights Reserved.

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    This Post Has 21 Comments
    1. Thank you for these two posts. At this point I am confident that I understand any of this at least as well as the next guy. Just don’t put it on the quiz please. Well maybe I would not want to explain to Krugman why he is wrong. I guess I won’t ever have to worry about telling Samuelson he was wrong.

      Maybe I should summarize part 2 , having summarized part 1 successfully apparently.

      So there is this thing economists call ‘capital’. It is basically everything other than the labor and the raw materials that you use when producing some kind of product. It has some kind of value in the production process and economists spent a lot of time trying to quantify that value. And more time trying to figure out how this ‘capital stuff’ relates to growth. And apparently, someone was paying for them to spend a whole lot of time thinking about this or maybe they were just very bored people who had nothing better to do. Well anyways, it turns out they didn’t come up with much of anything useful but they had a big argument about it anyway. And then they named it the ‘Cambridge Capital Controversy’ because it was a catchy name and they really needed to justify spending all that time thinking about capital. Which they never ever bothered to define very well because they knew that if they did then their whole gig would be open to all kinds of criticism.

      And then the good guys and Joan Robinson did better in that big argument than the misguided neoclassicalish pre-neoliberal types. But that didn’t matter because those who lost the intellectual argument were more aligned with the defacto powers and here we are today.

      Um, I guess that was not a summary but more a story rather loosely based on my understanding of the post.

    2. ‘So we have the problem of circularity: neoclassical economists claim that the marginal product of capital determines the rate of profit (rate of interest) but to compute the stock of capital (and its marginal product) in value terms we need the rate of profit (rate of interest).’

      I’m not getting where the circularity come in. If one assumes the rate of profit to be exogenous then market forces (mainly the tendency towards profit equalization in different industries) would guide the price of consumer goods and the price of capital goods so that in equilibrium the value of the marginal product of the capital good as a proportion of the price of the capital good would equal the rate of profit. If this applied for each individual capital good then it would also apply to capital goods in aggregate. A change in the rate of profit would lead to price adjustment to reestablish the correct ratios between capital and consumer goods.

    3. So put my previous dopey story aside. The most important things about this post are at the end and they draw from conclusions about this ‘debate’. Although I would argue most of these things are apparently true just looking at them and that we didn’t really need such a debate to understand that which we can readily see.

      Power. If you can’t see that there is a difference in power between the employer and the employee you are blind. If you don’t think the employer exploits that difference to their own advantage well you need to get out more. Has nothing to do with return on capital as a factor of production. I don’t know if that is the surplus value that Marx talks about or just part of it.

      “There is no way that a proposition that each factor of production is rewarded according to its marginal contribution to income generation can be justified in logic or evidence.” Yes.

    4. “I’m not getting where the circularity comes in.”

      The circularity is when the neoclassicals, in their attempt to justify a financial rate of return (profits), say that it is proportional to the value of the capital goods invested. But the value of the capital goods can only be determined by a financial rate of interest (profits)!

      That the rate of profit is exogenous and that price adjustment reestablishes correct ratios between capital and consumer goods are both false assumptions.

    5. Dear Professor Mitchell

      Another great and educative post. I had been waiting for your views on the CCC for a long time. But the wait was well worth it. Thanks for it.

      As I’ve just came to the discussion, I would like to ask a question from your previous post. The so-called Marginal Revolution had two stages. In the first phase the protagonists were Menger, Walras and Jevons. In the second we had John Bates Clark, Alfred Marshall (Keynes’ mentor at Cambridge-UK), Philip Wicksteed and others.

      Who actually came up with the idea of marginal productivity? I ask because I checked Jevons’ The Theory of Political Economy (5th edition) and he never used neither the word nor the concept.

    6. Which you look at and then think.

      Okay how does all of the dynamics change with the introduction of a Job Guarantee and a competition and monopolies authority that has some teeth. Some real power to hold them to account ?

      It works brilliantly but rather than say that, our critics just use the inflation scare story to hide the fact they have had everything wrong for years. Start talking about basic incomes that addresses none of it.

    7. Joan Robinson,

      “The exposition both of general equilibrium and of long-run accumulation seems generally to be conducted by drawing a two-dimensional diagram on a black-board and then introducing historical events into it. A change cannot be depicted on the plane surface or the blackboard. Changes occur in time, and as soon as a point moves off the blackboard into the third dimension of time, it is no longer bound by the relationships shown in the diagram.

      Samuelson knows that a functional relationship is timeless and makes no reference to history or to the direction of change … However, Professor Samuelson continues to use his construction to describe a process or accumulation that raises wages, alters technology, and changes a stock or inputs made, say, or wood into one made of iron and then into copper …

      To Kornai. Harcourt, and myself, this methodology is unacceptable, but Professor Samuelson assures us that it is quite all right.

      In a properly specified stationary state, there is no distinction between any one day and any other. On a properly specified growth path, such as a von Neumann ray, exhibiting a particular pace of expansion of employment and of a specified stock of means of production, there is no movement forward and upward or backward and downward, except the movement of the reader’s eye along the curve.

      Unfortunately, the great majority of models in the textbooks are not properly specified. Take, for instance, the familiar Marshallian cross of supply and demand curves showing an equilibrium point in the middle. At a price above the equilibrium level, offer exceeds demand, and below, demand exceeds offer.

      Now we are told, if price at any moment is not at the equilibrium level, it will tend toward it. This means that historical events are introduced into a timeless picture. As Professor Samuelson kindly explained to me, ‘When a mathematician says “y rises as x falls”, he is implying nothing about temporal sequences or anything different from “When x is low, y is high”.’

      To move implies a temporal sequence. To fill in the story of a movement towards equilibrium, a complicated dynamic process must be specified and to specify a process that will actually reach equilibrium is by no means a simple matter.

      I really cannot allow him to get away with that. “

    8. Thank you, Professor Mitchell. I thought so, but I wanted to check with someone really knowledgeable about the matter.

      I’ve seen people wrongly associate Menger, Jevons and/or Walras with the marginal productivity.

    9. My 2 cents worth.
      It is flatly for these to things to be true at the same time.
      1] The value of the finished good is determined by the market, where the owner of the finished good tries to set the price as high as possible to get the most money for it. Supply and demand. This decision is made after the finished good is created.
      2] The value of a finished good is determined as it is made by totaling the value of the labor to make it and some portion of the capital used to make it.
      Therefore, labor can only be fairly paid if there is a system to pay them more as the price of what they make increases. Maybe with a generous profit sharing system.

    10. “So we might have a car worth $1,000, a printer worth $300, and something else worth $2,000 and we can sum them to get an aggregate expression worth $2,300”

      Is there a summing up error here? Or were you just borrowing Krugman’s calculator?

    11. mr. jal

      Thanks for the reply.

      Looking at it slightly differently:

      – Its tautological true to say that the value of a capital good is derived from the $ value of its rent and the prevailing rate of interest

      – it seems reasonable to assume that business will hire capital until the $ value of the additions units of output added fall below the $ value of the rent.

      – The rate of interest therefore determines both the marginal productivity of capital and (tautologically) the value of capital with no circularity

      (market process or a smart CB determine the rate of interest that leads to the right balance between capital and consumer goods that allows full employment

    12. Have to admit I don’t quite get it all….but I do get the basic reality all around us that workers don’t get paid what is fair for their contribution to the production process. And that the owners of the means of production get far in excess. I also get that a macroeconomy is not some self-regulating natural order but is a set of social institutions and power relations that we construct and can also change. We can reshape distribution of what we produce if we choose to.

    13. Rob,

      but the rate of interest isn’t fixed, so it must be estimated, and estimating it based on whatever margin you want (or is realized) from production means investors always invest exactly the appropriate amount of money, thus proving the total rational agent theory.
      As far as I get it.

    14. Like others admit, a lot of this more technical economic stuff goes over my head as a layperson. But I think we all can get at least the gist of what Bill is laying out. My takeaways are twofold: (1) Bill’s reference to “a theoretical construction designed to make capitalism look fair in the face of criticisms coming from the Marxists” as a pretty good summation of mainstream economics in toto; and (2) cs’s observation that “a macroeconomy is not some self-regulating natural order but is a set of social institutions and power relations that we construct and can also change.” These takeaways lead me to ponder the difference between quantum mechanics theory and orthodox economic theory. In the former, if you do the math correctly, then experiments invariably prove the truth of the equations. In the latter, there is no such correspondence, which indicates that a macroeconomy is precisely what cs says it is.

    15. Kalecki’s theory of distribution:
      – ex ante (desired profit): the size of the markup (over the ULC)
      – ex post (realized profit): Kalecki’s profit equation.

      What else do we need?:)

    16. Joan Robinson that remarkable lady and brilliant economist did not win the Nobel prize in economics! She developed the theory of Imperfect Competition (independently with Edward Chamberlain) and help demolish the neoclassical growth theory and income distribution. Is it surprising?

    17. Really!!-‘As James Galbraith wrote “richer countries … [did not get] … that way by using ‘more’ capital.”

      He went on:

      … these countries became rich … by learning, by improving technique, by installing infrastructure, with education, and … by implementing thoroughgoing regulation and social insurance … There is no reason to think that financial capitalization bears any close relationship to economic development.’

      So acquiring resources by expansion of empire and utilising military might had insignificant bearing on becoming richer!

    18. This was a bit of a trip down memory lane for me. I was lucky enough to come across Sraffa’s ‘Production of commodities’ in 1974. But I also read a book then called ‘The Reconstruction of Political Economy’ by Jan Kregel, which explained the whole issue very well and introduced me to a more Wynne Godley approach to economics. Robinson wrote the preface to Kregel’s book. Kregel is still active in economics but has expressed reservations about MMT which I struggled to understand.

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