u/Accomplished-Cake131

'Neoclassical' economists accepted, in the third quarter of last century, that the theories they teach and apply have no rigorous foundation. They are illogical and incoherent. Why does that not matter? This presents a puzzle.

>"The basic principle of factor substitution cannot be generalized to study market economies with heterogeneous capital goods. Indeed the results known as reswitching and capital reversing showed that factor demand functions will not necessarily be inversely related to their respective rates of remuneration. The reason behind those results ultimately lies in the fact that the capital endowment is specified in value terms among the data of equilibrium in neoclassical theory. But this implied, as was ultimately admitted (e.g., Samuelson 1966), that the theory cannot robustly determine long-period equilibrium prices and distributive variables, and therefore provide a robust supply and demand framework to study real market economies. After more than fifty years since the first exchanges in those debates, one might ask: what happened in the discipline after that historical period in which even some of the most authoritative neoclassical scholars admitted that their theory was at stake?" -- Andres Lazzarini (2015) [Bold added]

Many have surveyed or responded to the Cambridge Capital Controversy. Here are some surveys and responses:

• Mark Blaug. 1974. The Cambridge Revolution: Success or Failure?. London: Institute of Economic Affairs. (I stumbled upon this negative review in the History of Political Economy.)
• Jack Birner. 2002. Cambridge Controversies in Capital Theory: A Methodological Analysis. Routledge.
• Christopher Bliss. 1975. Capital Theory and the Distribution of Income. Elsevier North-Holland.
• Edwin Burmeister. 1982. Capital Theory and Dynamics. Cambridge University Press.
• Avi J. Cohen and G. C. Harcourt. 2003. Whatever happened to the Cambridge capital theory controversies. Journal of Economic Perspectives 17(1): 199-214.
• Avinash Dixit. 1977. The accumulation of capital theory. Oxford Economic Papers 29(1): 1-29.
• Roger W. Garrison. 2006. Reflections on reswitching and roundaboutness. In Money and Markets: Essays in Honor of Leland B. Yeager (ed. by Roger Koppl). Routledge.
• Daniel Hausman. 1981. Capital, Prices and Profits. Columbia University Press.
• Andrés Lazzarini. 2011. Revisiting the Cambridge Capital Theory Controversies: A Historical and Analytical Study. Pavia University Press..
• G. C. Harcourt. 1969. Some Cambridge controversies in the theory of capital. Journal of Economic Literature 7(2): 369-405.
• G. C. Harcourt. 1972, 2022. Some Cambridge Controversies in the Theory of Capital. Cambridge University Press.
• Joseph E. Stiglitz. 1974. The Cambridge-Cambridge controversy in the theory of capital: a view from New Haven. Journal of Political Economy 82(4): 893-903.
• Leland B. Yeager. 1979. Capital paradoxes and the concept of waiting. In Time, Uncertainty, and Disequilibrium: Exploration of Austrian Themes (ed. by M. J. Rizzo). Lexington Books.

Harcourt (1972) is my favorite of these surveys - an utterly conventional view. I do not specify which you might find online not behind a paywall. I disagree with much in many of these surveys and responses. But those who have never been exposed to the CCC will learn something from any of them.

Well-known contributions to philosophy in Europe and America in the twentieth century are often divided into analytical and continental philosophy. Analytical philosophers often state their arguments with formal reasoning and notation, while concentrating on narrow points. How do you know that you have not always used 'green' to mean grue? Continental philosophers provide a more intuitive reasoning and focus on larger issues such as culture. Gender is performative. I take no issue to those who argue that the division is not well-defined. I lean more towards the analytical side.

Sometimes, when I read postmodernists - another ill-defined term - I can follow, but I do not retain much. I sometimes quote some, like Slavoj Zizek, for amusement.

Here I want to focus on Theodor Adorno and his 1951 book Minima Moralia: Reflections from Damaged Life. I could not make much out of his book, Negative Dialetics. I have yet to read The Dialetic of Enlightenment.

As I poorly recall, Minima Moralia has a narrative arc, although it takes some work to perceive it. I was surprised at passages that presume an understanding of technical terms in Marx's political economy. I note a few here.

Here Adorno rejects some concepts of a post-capitalist society because they continue commodity fetishism:

>"Sur l'Eau. He who asks what is the goal of an emancipated society is given answers such as the fulfillment of human possibilities or the richness of life. Just as the inevitable question is illegitimate, so the repellent assurance of the answer is inevitable, calling to mind the social-democratic ideal of the personality expounded by heavily-bearded Naturalists of the ''nineties, who were out to have a good time. There is tenderness only in the coarsest demand: that no-one shall go hungry any more. Every other seeks to apply to a condition that ought to be determined by human needs, a mode of human conduct adapted to production as an end in itself. Into the wishful image of an uninhibited, vital, creative man has seeped the very fetishism of commodities which in bourgeois society brings with it inhibition, impotence, the sterility of the never-changing. The concept of dynamism, which is the necessary complement of bourgeois 'a-historicity'. is raised to an absolute, whereas it ought, as an anthropological reflex of the laws of production, to be itself critically confronted, in an emancipated society, with need..." -- Adorno: 155-156.

Adorno draws on the concept of fetishism in other places. I do not know that the above passage is consistent with Marx and Engels in The German Ideology.

In this next passage he uses the concept of the organic composition of capital to write about how working class consciousness is dimmed:

>"Puzzle-picture. Why, despite a historical development that has reached the point of oligarchy, the workers are less and less aware that they are such, can be surmised from a number of observations. While objectively the relation of owners and producers to the productive apparatus grows ever more rigid, subjective class membership becomes all the more fluctuating. This tendency is fostered by economic development itself. The organic composition of capital demands, as has often been noted, control through technical experts rather than through factory owners. The latter were the counterpart, as it were, of living labour, the former correspond to the share of machinery in capital. The quantification of technical processes, however, their dissection into minute operations largely independent of education and experience, makes the expertise of these new-style managers to a large degree illusory, a pretence concealing the privilege of being appointed. That technical development has reached a state which makes every function really open to all - this immanently socialist element in progress has been travestied under late industrialism. Membership of the elite seems attainable to everyone. One only waits to be co-opted... Preference goes to those who fit in most exactly...That technical forces might permit a condition free of privileges is accredited by all, even those in the shadow, to the social relations which prevent it. In general, subjective class-membership today shows a mobility that allows the rigidity of the economic order itself to be forgotten..." -- Adorno: 193-194.

And, for the last passage I select, Adorno writes about the law of value and, again, the organic composition of capital:

>"Novissimum organum. It has long been demonstrated that wage-labour formed the masses of the modern epoch, indeed created the worker himself. As a general principle the individual is not merely the biological basis, but the reflection of the social process; his conciousness of himself as something in-itself is the iI1usion needed to raise his level of performance, whereas in fact the individuated function in the modern economy as mere agents of the law of value. The inner constitution of the individual, not merely his social role, could be deduced from this. Decisive here, in the present phase, is the category of the organic composition of capital. By this the theory of accumulation meant the 'growth in the mass of the means of production, as compared with the mass of the labour-power that vivifies them'. If the integration of society, particularly in totalitarian states, designates subjects more and more exclusively as partial moments in the network of material production, then the 'alteration of the technical composition of capital' is prolonged within those encompassed, and indeed constituted, by the technological demands of the production process. The organic composition of man is growing. That which determines subjects as means of production and not as living purposes, increases with the proportion of machines to variable capital... Only when the process that begins with the metamorphosis of labour-power into a commodity has permeated men through and through and objectified each of their Impulses as formally commensurable variations of the exchange relationship, is it possible for life to reproduce itself under the prevailing relations of production..." -- Adorno: 228-229.

My understanding of the organic composition of capital is straightforward. I take it to be the ratio of constant capital to variable capital, evaluated either with labor values or with prices of production. I do think about the physical composition of capital goods and of issues associated with depreciation. But I certainly do not go into the cultural effects that Adorno writes about.

Pro-capitalists here go on and on about Marx without getting his ideas correct. It will not help them to discuss doctrines of the Frankfurt school.

Consider the claim that the interest rate is equal to the marginal product of capital. This is part of a theory that disguises the exercise of power in, for example, making investment decisions. I have recently documented that some 'neoclassical' economists know that this equality is not a part of any rigorous theory.

I here explain more.

Consider a particular kind of shovel as a capital good. It has a price. And a price might exist for renting its services. The first is in units of dollars or numeraire units per shovel. The second is in units of dollars per shovel services per day, maybe. Neither are in units appropriate for an interest rate. It is a mistake to say that the interest rate is the rental price of capital, where capital is meant to be a specific capital good. It is true that an interest rate is built into the calculation of net present value for relating the price of a shovel to its rental price.

What units of measurement would support talking about a 'unit of capital'? You can add up a given configuration of plant, machines, fuel, semi-finished goods, and so on by prices. Then a 'unit of capital' would be measured in dollars or numeraire units.

This measure has some defects. The same complex of plant, etc. can have many different measures of its size, given variations in prices. Two different complexes can have the same measure. A numeraire measure of capital is not an appropriate variable to enter a production function, either at the level of the economy or at the level of an individual firm. The numeraire amount of capital cannot be taken as part of the givens in price theory, unlike the available labor and land. A lot of 'neoclassical' models, which consider the allocation of resources among alternatives, from the 1870s on are incoherent for this reason.

You must consider a (small) variation in the quantity of capital when calculating the so-called marginal product of capital. The numeraire quantity of capital varies for two reasons. One is because, given the complex of plant, etc., the prices of these elements varies. This variation is known as the price Wicksell effect. In many models, prices vary with the interest rate. The other variation results from a change in the complex of plant, etc. at a given interest rate. This variation is known as the real Wicksell effect, and is analyzed with the choice of technique.

If the real Wicksell effect were only in the traditional direction, one could define a measure of capital as the sum of real Wicksell effects. With an analogous chain index for output, the marginal product of capital would be equal to the interest rate, in equilibrium. But about two thirds of a century ago, economists discovered that real Wicksell effects can have any direction. The cost-minimizing technique at a LOWER interest rate, around a switch point, can be LESS capital-intensive. (This contradicts the story that a decision to save more drives interest rates down and induces firms to adopt more capital-intensive techniques. A similar story about leisure and wages is also invalid.)

>"One can only wonder what is the good of a quantity of capital or a period of production which, since it depends on the rate of interest, cannot be used for its traditional purpose, which is to determine, the rate of interest." -- Piero Sraffa (1962)

I like to recommend the following (the author's daughter, Kamala, has a certain prominence):

Donald J. Harris (1973). Capital, distribution, and the aggregate production function. American Economic Review 63(1): 100-113.

1. Introduction

Last century and into this one, 'neoclassical' economists noted the lack of theoretical foundation for certain widely used models in economics. Some here have expressed puzzlement at the established proposition that the interest rate is generally not equal to the marginal product of capital. This post quotes three prominent 'neoclassical' economics, over decades, noting the lack of theoretical foundation for such an equality.

For the purposes of this post, I have little to say about my disagreements with these authors. I will note that Sraffians have something to say about microeconomics too. I also do not want to go into here why empirical work with these unfounded models is almost always a kind of humbug.

2. Frank Hahn

Frank Hahn attacks my favorite school of thought. He says:

>"Sraffa ... confined himself to the remark that the [missing] equation cannot be one which demands the equality of the marginal product of 'capital' and the rate of profit. ... the neoclassical economist has the same view but his reasons are not those given by Sraffa." -- Frank Hahn (1982) The neo-Ricardians. Cambridge Journal of Economics. 6(4): 362.

And again:

>"The Sraffian picture of neoclassical theory is this. At any moment of time we can observe something physical called the stock of capital (K) as well as the amount of labor (L). There is a concave production function

>Y = F(K, L)

>where Y is output. In a neoclassical equilibrium all inputs are used and must be paid their marginal products. The latter are known once (K, L) are known. Hence the rate of profit of capital, the real wage and the distribution of income are all known once F(), K and L are known. The concavity of F further implies that the rate of return on capital is non-increasing (generally decreasing) in K. This construction, to be called the parable, Sraffians claim not to be watertight except in the single good economy. In this they are generally correct." -- Frank Hahn (1982: 370)

3. Edwin Burmeister

This is from a standard reference work:

>"Imposing some set of conditions on the technology T() should be sufficient to ensure that the real Wicksell effect is always negative. Such conditions would be of interest - especially if they could be empirically tested - since they would validate the qualitative conclusions derived from the one-good model often used in macroeconomics without any theoretical justification for ignoring aggregation problems. Moreover, Burmeister (1977, 1979) has proved that a negative real Wicksell effect is a necessary and sufficient condition for an index of capital, k, and a neoclassical aggregate production function F(k) defined across steady-state equilibria such that (i) c = F(k), (ii) r = F’(k), and (iii) F’’(k) < 0. Unfortunately, no set of such sufficient conditions is known, but the literature on capital aggregation suggests that they would impose severe restrictions on the technology." -- Edwin Burmeister (1987). Wicksell effects. The New Palgrave

That index is Champernowne's chain index measure of capital.

4. Emmanuel Farhi

Here is Emmanuel Farhi giving a lecture in 2018 agreeing with the above authors. His history of the CCC is in the first half hour. There is an accompanying paper (working paper version here).

5. Conclusion

Economics presents a problem for those concerned with the sociology of 'knowledge'.

1. Introduction

 Prices are not determined by supply and demand.

 I have provided mathematical proofs here before. These proofs present numerical counter-examples. I take the assumptions for so-called neoclassical economics as given. In particular, I assume constant returns to scale and diminishing marginal returns to each factor. Often you will see these assumptions presented as in production functions. My preferred discrete depiction of technology is more applied in practice. The counterexamples have properties that negate the conclusions often said to follow. For example, I have an upward-sloping labor demand curve. If the stories some economists tell were internally consistent, these accepted counter-examples could not and would not exist.

Neoclassical economists have known for decades that they cannot state their assumptions. As an example of confused balderdash, I cite George Borjas, Labor Economics. For an example of a correct textbook, I cite Kurz and Salvadori (1995). I do not know that I would call Opocher and Steedman (2015) a textbook. Woods (1990) iis a textbook. Chapters are followed by problem sets. I do not think you can find PDFs of these books. You can find Sraffa (1960).

2. An Example with Three Produced Commodities

 You could check this example with a spreadsheet. Answers are given, so it can be checked with arithmetic. I outline something like a market algorithm when the wage is given. Two levels of the wage are given. (An example of supposedly educated economists being unwilling or unable to recognize results established sometime last century is here.)

3. An Example with Fixed Capital

This post works through a fixed capital example from Baldone (1974), in Studi Economici. A machine that lasts for three production cycles is an example of fixed capital. I take the interest rate as given. To check, you have to be willing to solve a linear system of four equations in four variables. (I do not go into the centre of a fixed capital system, which reduces that system to one of two equations in two variables.) This exposition asserts that firms will not produce commodities with negative prices.

4. An Example With Two Commodities

This exposition works through an example from Bruno, Burmeister & Sheshinski (1966, p. 545) in the Quarterly Journal of Economics. These are mainstream economists, and that journal, associated with Harvard, is one of the most prestigious in the world. This example has two produced commodities. The example requires you to solve two equations in two unknowns, given the interest rate (also known as the rate of accounting profits).

5. Conclusion

Many more examples like these can be produced, including with smooth production functions, rent, and so on. Empirical examples have been illustrated in the literature. I would have liked to have seen more. Innovation in actually existing capitalist economies is probably more about creating new processes and products, not the choice from an existing cookbook of recipes, as presented in production functions and the theory of supply and demand.

TL;DR: Mainstream economists agreed in the 60s of last century that what they teach is incorrect and illogical.

Update: I want to note this rigorous response elsewhere: "Your friend [me] is stupid." "Because the things they are saying are wrong."