Two Ways To Think About Fixed Capital

1.0 Introduction

This post presents two approaches to fixed capital. The first emphasizes power and convention. It emphasizes that the 'money world', as Mason and Jayadev (2026) put it, is not a direct reflection of physical properties of production. The second is much closer to a determined model, with one degree of freedom.

I have at least one previous post, more abstractly on these themes

2.0 Depreciation as Accounting Conventions and Mediated by the Exercise of Power

Robert Paul Wolff points out that how overhead costs are allocated is a political exercise in many firms. Two managers on the same level might each be in charge of the production of a specific product. Suppose these products are produced in the facility. Each manager wants upper management to see that they are making the most profits for the company. In is in the interest of each to see that as much of possible of the overhead for running the facility is applied to their rival's department.

A given machine might be used in multiple production processes, resulting in the production of different products. The allocation of overhead costs here follows the above logic.

Sometimes (many times?), no fact of the matter exists for how to allocate costs. As I understand it, the Generally Accepted Accounting Principles (GAAP) includes different conventions for depreciation. Some models I have seen assume radioactive decay so to speak. Tax law specifies what can be allowed.

3.0 Depreciation and the Economic Life of Machines as an Aspect of Prices of Production

Another way of thinking about fixed capital is as in Sraffa (1960). Enough equations are given for prices to be determined, corresponding to a given wage or rate of profits. The data include inputs and outputs, in disaggregated physical terms, for all combinations of ages of machines. These detailed specifications are not based solely on the age, but the entire history of each machine.

Alessandro Roncaglia showed, back in the 1970s, that a countable infinity of equations can arise when production processes can require inputs of combinations of machines. The theory of pure fixed capital includes assumptions that rule out this possibility.

Sraffa derives the formula for an annuity from his treatment of a machine of constant efficiency. But the analysis generalizes. This approach is in tension with the first approach.

4.0 Conclusion

I will continue exploring mathematical puzzles. I like to think that Sraffa presents the elements of an alternative theory, not just an immanent critique of 'neoclassical' theory. The analysis points outside itself.

Reference

• Mason, J. W. and Arjun Jayadev. 2026. Against Money. University of Chicago.

Jack Birner On The Cambridge Capital Controversy

I have been rereading Jack Birner's 2002 book, The Cambridge Controversies in Capital Theory. Birner is an economist of the Austrian school. He probably generally disagrees with me on lots of matters. Torward the start of the introduction, he writes:

"Four decades ago the best minds in economics were engaged in a confrontation which the entire profession followed in the pages of the leading journals almost as if it were a soccer match. It has become customary to distinguish two opposing groups of economists to the debate..." -- Jack Birner (2002: 1)

And he expresses astonishment that the results of this dispute are ignored:

"What I do want to draw attention to is that the conclusions reached in that debate constitute a rare example of a set of formally proven, uncontestable, undeniably true and reliable results in economics... They can be summarized by saying that the K of the production function that modern economists so confidently and fully rely on for their theoretical and empirical work can only be used in conditions where there is only a single, homogeneous capital good. One does not need to have a degree in economics to know that in reality this is not the case. The economy consists of a bewildering variety of buildings, machines, software, skills and ways of organizing production. And as everyone who has filed a corporate tax declaration knows, it is not even possible to give more than a rather inexact estimate of their value. In other words, not only is there no intuitive justification for the use of aggregate, homogeneous K, we have proofs by Nobel-calibre economists assisted by 100 per cent certain mathematical techniques that demonstrate without a shred of doubt that this K cannot and should not be used for the objectives it is currently used for. Nevertheless, economists go about their business as if these proofs did not exist. That some of them are the very same people who produced these proofs earlier makes things even more curious. The fact that production functions with the same aggregate K figure prominently in all current textbooks of macroeconomics is worse than curious: it is deeply worrying." -- Jack Birner (2002: 1-2)

I do not think the situation is different today. I agree with Birner that the overall point of the CCC is not at all clear from the details of the match. The participants were worrying about local details. I think more was at stake than an aggregate theory. I like to emphasize the labor 'market' in my expositions. Fabio Petri, among others, emphasizes mistakes in what the early marginalists thought could be consistently taken as given in their theory.

Birner considers the role of idealizing assumptions in mathematical models. He considers the relations of such ideal models to models that more 'factual', that is, closer to being able to be applied empirically.

The trend, for decades, in the philosophy of science is to be descriptive, to try to understand how specialists in specific disciplines become convinced of their ideas. The CCC poses a problem for the methodologist.

I'm am doubtful about Birner's methodology at points. He draws upon some scholars I like. For example, he draws on Arthur Koestler's The Sleepwalkers: A History of Man's Changing Vision of the Universe. Koestler points out that Copernicus was focused on narrow points. One of the virtues of a geocentric model, for him, was that it got rid of equants. An equant is a circular orbit that has uniform velocity around a point displaced from its center.

Likewise, economists in the CCC were focused on narrow points about, say, Samuelson's surrogate capital and Robinson's pseudo-production function. For Birner, Sraffa and Garegnani were about the only ones awake.

In some sense, Birner does not resolve his problem. He concludes most economists are still asleep.

Socialism Succeeding In Emilia-Romagna

Emilia-Romagna is a region in Italy, north of Tuscany. I have written about its capital, Bologna, before.

About a third of the gross domestic product of Emilia-Romagna is produced by co-operatives. About two thirds of those who reside in Emilia-Romagna participate in co-ops in some ways. (See this article from John Duda.) Apparently, co-ops in Italy go back to the nineteenth century, surviving through the fascists in the twentieth century.

Article 45 of the 1947 Italian constitution promotes co-ops. It states:

The Republic recognises the social function of co-operation of a mutually supportive, non-speculative nature. The law promotes and encourages co- operation through appropriate means and ensures its character and purposes through appropriate checks.

The law safeguards and promotes the handicrafts.

A capability for a worker to take unemployment benefits at once to set up a co-op is one of the provisions of the 1985 Macora law.

A society with a large co-operative segment will have related institutions. Co-ops will market to each other. Scholars, such as Vera Zamagni at the University of Bologna, will study them. Competition among co-ops might be less cut-throat. The study of management and administration at academic institutions will have curriculum supporting co-ops. Mutual banks might be set up to loan to co-ops, and other financial institutions will have more practice in making such loans. Co-ops might set up institutes to perform research into processes and products improving their technology.

The 1986 book, The Second Industrial Divide: Possibilities for Prosperity, by Michael J. Priore and Charles Sabel, is supposed to be of interest on this topic.

Anomalous Switch Points

I have a new working paper at the Centro Sraffa. The abstract follows:

Abstract: This article presents examples of models of rent with decreasing wage frontiers; with unique, square cost-minimizing techniques at a given rate of profits; but without the wage maximization property. Anomalous switch points are highlighted, where an anomalous switch point has properties that contrast with generic switch points in models of circulating capital. This article presents a numeric example of a switch point along a single wage curve, with no other wage curve intersecting at the switch point. Other numeric examples are of switch points in which only the scale, not the operated processes, vary between the cost-minimizing techniques at the switch point. A fake switch point is presented in which prices vary only for goods which are not commodities under the non-cost minimizing technique, also known as ghost commodities.

The Roosevelt Dime And Fluoridated Water: Communist Plots

Franklin Delano Roosevelt died in 1945, and World War II ended with the Japanese surrender in August. Germany had surrendered in May. The Roosevelt dime was introduced in 1946. John Sinnock, an artist at the mint, designed the obverse. His initials are under Roosevelt’s head.

The Soviet Union was the ally of the United States in fighting the fascists. This quickly changed. Somehow anti-communists became convinced that the J. S. on the Roosevelt dime stand for Joseph Stalin. I don't know what advantage the communists were supposed to get out of this plot.

When I first saw Dr. Strangelove, I thought the idea that fluoridated water was a communist plot was quite comic. I did not realize that Kubrick did not make this up. Anti-communists believe this. I do not know if they talk about, "Sapping our precious bodily fluids," as General Jack D. Ripper does in the movie.

I have documented some other stupid stuff anti-communists and anti-Marxists have said.

On Building On Pasinetti's Lectures On The Theory Of Production

I have been re-reading Pasinetti's 1977 book. I claim I am original in partitioning parameter spaces with fluke switch points, concrete numerical examples, certain diagrams for visualizing certain analyses, and extending the capital critique to non-competitive markets. I have noted that participants in the 1966 QJE symposium, including Pasinetti, explicitly noted the possibility of fluke switch points.

Pasinetti’s Lectures contain:

• The algebra repeated in my derivation of Hayek's triangle (p. 91, p. 118).
• An explanation of how a switch point can occur along a single wage curve. The numeraire is a basic good. Two techniques differ in the method or process for producing a non-basic good (p. 161).
• A fluke case with three or more wage curves intersecting at a switch point (p. 164).

The first is an elaboration of Sraffa's reduction to dated labor quantities. I do not feel obligated to cite Newton when I take a derivative. This reduction is close to that. I do not see others linking up this analysis to Hayek's triangles, though,

Pasinetti does not provide a figure or numeric example illustrating the second point. Land is non-basic. Perhaps I should note this in my example with fixed capital and rent.

Pasinetti does provide a figure with three wage curves intersecting in a single switch point. But citing articles from 1966 is sufficient.

C129.4r: Harcourt on Translation Of Sraffa (1925)

This letter is from G. C. Harcourt to Piero Sraffa. As I understand it, Sraffa later refused permission for this translation to be published while he was alive. The translation now available is from Alessandro Roncaglia and John Eatwell.

Adelaide, South Australia 5001
Telephone: 23 4333

Department of Economics
14th April 1970.

Piero Sraffa, Esq.,
Trinity College,
CAMBRIDGE, U.K.

Dear Piero,

Just a short note to say how delighted I was that you will let Mario Nuti translate the Italian version of your 1926 article for Australian Economic Papers. We will, of course, honour strictly your conditions. It really is very generous of you and I personally am extremely grateful.

I hope to be in Cambridge next January for 4 – 6 weeks and hope very much that we may meet then. I hear from Vincent from time to time, he seems to be flourishing. I have just come back from three marvellous months in Japan. I wrote a book on capital theory while there, expanding the assertions of my survey article into, I hope, persuasive arguments.

With all good wishes,

Yours ever,
Geoff. [Handwritten]
G. C. HARCOURT
Professor of Economics

Some Cambridge Controversies in the Theory of Capital is the book Harcourt mentions writing while visiting Japan. I do not know who Vincent is.