Wednesday, January 01, 2025

Welcome

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

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

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

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

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

Saturday, March 16, 2024

Elsewhere

  • Matt McManus on Thomas Sowell.
  • A review of Adam Shatz's biography of Frantz Fanon.
  • Nathan Robinson interviews Kohei Saito on degrowth.
  • I have not read Bob Rowthorn on neo-ricardianism in decades. I wish NLR made PDFs of old articles freely available.

Monday, March 11, 2024

To Do: Perverse Switch Points And The Economic Life Of A Machine

Table 1: Lower Rate of Profits Around A Switch Point
Traditional Marginalist Story'Perverse' Marginalist Story
Traditional Austrian StoryNegative real Wicksell effect, greater net output per workerPositive real Wicksell effect, smaller net output per worker
Longer economic life of machineLonger economic life of machine
'Perverse' Austrian StoryNegative real Wicksell effect, greater net output per workerPositive real Wicksell effect, smaller net output per worker
Shorter economic life of machineShorter economic life of machine

I have been thinking about perturbations of coefficients in a model of fixed capital. This research can be redirected to find examples to fill in the above two-by-two table. Under obsolete marginalist teaching, a lower rate of profits encourages firms to addopt more capital-intensive techniques. At least two measures of capital intensity are available. Burmeister champions a measure of real Wicksel effects. Böhm-Bawerk championed a measure of the period of production which I am identifying, in this context, with the economic life of a machine.

The upper-left entry is the only one that conforms to the traditional story with both measures. I want to show that all four entries are possible. By perturbing an example from Salvadore Badone, I can fill in three of the entries, all but the bottom right. By perturbing an example of a 'one good' model, I can fill in that square and repeat two others. I also have an example from Bertram Schefold. I'd like to find a single example with perturbations that can fill in all four squares.

I want to recall that this work complements the corn-tractor model from Ian Steedman. Around each switch point, a different type of tractor is produced in Steedman's model, unlike in these examples. Each tractor works at constant efficiency, while I allow efficiency to vary. We both look at variations of the economic lives of machines. And this analysis is examining an issue independent of capital-intensity, as usually argued about in the Cambridge Capital Controvery. Demonstrating this independence is rather the point of filling in the above table.

I need a survey of analyses of fixed capital that does not end with a pure fixed capital model. Or, at least, I need to summarize a paper from Biao Huang. Perhaps I can avoid such a survey by just citing a model of pure fixed capital for existence but otherwise de-emphasize it. My goal is to be as terse as possible, with illustrations.

I also need to say something about why economists of the Austrian school should care. It seems to me that such economists often say that they have long ago developed their theory where it no longer relies on aggregate measures or physical measures of capital-intensity. I want to assert that they have not succeeded and still implicitly rely on the intuition from previous theory. Saverio Fratini makes a similiar case. It seems to me that I just need to note the existence of these claims and argue that the economic life of machines is one aspect of the Austrian theory of capital.

A difficulty arises of where to publish this. My previous version was rejected from Metroeconomica. Their editors, reviewers, and readers are unlikely to be astonished by these claims. On the other hand, some editors and authors of mainstream journals would claim they have long ago moved to and then transcended abstract models which this sort of work does not address. Yet they continually have a non-articulated background intuition inconsistent with the theory of prices of production. Fabio Petri has long argued along these lines.

Wednesday, March 06, 2024

New Interpretations Of Marx

This post is basically complaining that I cannot keep up.

I think I am fairly informed on Karl Marx. I do not read German, and I have not even read some early works. My area of concentration is reading Capital as a work of mathematical economics, which cuts against the subtitle and, maybe, de-emphasizes a break with classical, especially, Ricardian political economy.

More generally, I thought Marx generally praises the tremendous increase of productivity brought about by the bourgeoisie. He downplays the accompanying environmental degradation. Imperialism extends capitalism into non-European colonies. Marx deplores the violence, but thinks rationalization of such societies is progress.

As I understand it, some of the literature below challenges these ideas. This is partly because of the current context. But it is also because of new texts brought into circulation by the second attempt at a Marx-Engels-Gesamtausgabe (MEGA2). David Ryazanov led the first attempt at MEGA. Stalin first dismissed him to internal exile, then killed him in one of his purges. I have not read him, but I gather Musto draws on Marx's reflections from visiting Algiers on a doctor's recommendation. Anderson, I guess, draws on journalistic writings. These two offers re-evaluate what Marx has to say about colonialism. I am currently reading Soren Mau. The instruments and violence and intellectual hegemony of those presently the interests of capitalists as universal interests help maintain the reproduction of capitalism. Mau looks at a third means for such reproduction.

And we also now have available a new translation of the first volume of Capital. From Heinrich, I learned that the structure of the first chapter was quite different in the first edition. Some turns of phrase, such as, "Moneybags must be so lucky", come from the Moore and Aveling's english translation.

Anyways, here are some recent works on Marx:

I think a tendency exists to treat capital as something like an emergent, over-arching subject. One can see this in writing from Ian P. Wright. Philip Mirowski argues markets are computing automata, and computers are often taken as models of the mind these days. Another book I want to consider reading is Benjamin Labatut, 2023, The Maniac, Penguin Random House. This is a novelization of the life of Johnny Von Neumann.

Saturday, March 02, 2024

Labor Values And Invariants

1.0 Introduction

This post is an attempt to work through some linear algebra that some have used to understand Karl Marx's Capital. I have recently explained how, in a simple model, prices of production are equal to labor values if the organic composition of capital does not vary among industries. That special case is the setting of volume 1.

In capitalism, workers rent themselves out to their employers. They work longer, under the dominion of capital, than needed to produce the commodities which they purchase with their wages. Marx explains the returns to ownership (profits, interest, rent, etc.) by the distinction between the use value and the exchange value of labor power.

This post removes the special case assumption. It considers certain relationships between the system of labor values and the system of prices of production. These relationships are highlighted towards the start of volume 3. I ignore Hegel, on his head or otherwise.

2.0 Quantity Flows

Suppose a capitalist economy is observed at a given point in time. n commodities are being produced, each by a separate industry. Suppose the technique in use can be characterized by a row vector a0 and a n x n square matrix A.

The jth element of a0 is the amount of labor directly employed in the jth industry in producing one unit of a commodity output from that industry. "We suppose labour to be uniform in quality or, what amounts to the same thing, we assume any differences in quality to have previously been reduced to equivalent differences in quantity so that each unit of labour receives the same wage…" - Piero Sraffa (1960).

The jth column of A is the goods used up in producing one unit of a commodity output. For example, suppose iron is produced by the first industry and steel is produced by the second industry. a1,2 is then the kilotons of iron needed to produce a kiloton of steel. Assume that every good enters directly or indirectly into the production of each commodity. Iron enters indirectly into the production of tractors if steel enters directly into the tractor industry. Assume a surplus product, also known as a net output, exists.

Let y be the column vector of net outputs and q the column vector of gross outputs, both in physical terms. In Leontief's work, y is taken as given. Gross outputs and net outputs are related as:

y = q - A q

Or:

q = (I - A)-1 y

The labor force needed to produce this net product is:

a0 q = a0 (I - A)-1 y = 1

I have taken units in which labor is measured to be such that this labor force is unity. Employment is such that the net output is produced, the capital goods in producing the net output are reproduced, the capital goods used in producing those capital goods are reproduced, and so on.

3.0 Labor Values

Let ej be the jth column of the identity matrix. The labor force needed to produce this net output is:

vj = a0 (I - A)-1 ej

That is, the (direct and indirect) labor needed to produce a net output of one unit of the jth commodity is vj. The row vector of labor values is:

v = a0 (I - A)-1

4.0 Prices of Production

At any time, market prices are such that different industries are making different rates of profits. Under competitive conditions, without barriers to entry in the various industries, a kind of leveling process is going on.

One can imagine a vector of prices such that this leveling process is already completed with the observed technique and wage. Let p be that row vector of prices of production, with all industries obtaining the same rate of profits.

I need an assumption about the composition of commodities purchased from the wage, w, since I want to explore the labor value embodied in the wage. Accordingly, assume that the wage is a proportion of the final product. The wage ranges from zero to unity, inclusive. The physical composition of the wage is w y. Wages are advanced. Define:

A*(w) = A + w y a0

I gather the vector operation at the end of the above expression is the outer product. Prices of production satisfy the equation in the following display:

p A*(w) (1 + r) = p

where r is the rate of profits. That is, p is a price vector consistent with the observed technique and wage.

By the Perron-Frobenius theorem, the eigenvalue of A*(w) with the maximum modulus is real, positive, and does not exceed unity. The corresponding rate of profits is non-negative. The eigenvector consists of all positive entries. Thus a solution exists for the above equation. Furthermore, the wage and the rate of profits are related by a decreasing function. The maximum wage occurs at a rate of profits of zero. The maximum rate of profits is finite and occurs at a wage of zero.

Prices of production have been found up to a scaling factor. They are generally not proportional to labor values, as Ricardo and Marx knew.

5.0 Invariants

The scale for prices of production can be fixed by specifying a numeraire. Consider, instead, the imposition of an identity between the system of labor values and the system of prices of production.

5.1 Case 1: Total Gross Output

The labor value of gross output is equal to the price of gross output if and only if:

v q = p q

Imposing the above condition fixes the scale for prices.

5.2 Case 2: Total Net Output

Alternatively, the labor value of net output is equal to the price of net output if and only if:

v y = p y = 1

I have taken advantage above of the scaling of units of labor time. This invariant is my favorite of the three invariants considered here.

5.3 Case 3: The Rate of Profits

The labor value of advanced capital is v A*(w) q, while its price is p A*(w) q. The labor value of profits is:

(1 - w) v y = (1 - w)

The rate of profits does not differ between the system of labor values and the system of prices if and only if:

(1 - w)/[v A*(w) q] = (1 - w) p y/[p A*(w) q]

6.0 Concluding Observation

The above post has defined three invariants, each equating a sum or ratio of labor values to the corresponding sum or ratio in the system of prices of production. Only one invariant can generally hold, though, in the given model. This has led to quite a bit of literature arguing that one of these or other invariants is central to Marx's argument.

Some have another approach. They adopt another model in which all three invariants hold. In fact, more than one such model has been developed.

An approach I find of interest looks at a special composition of final output. Whatever the composition of the final output, one can iterate by looking at the composition of the capital goods used in producing that final output. A number of iterations leads to a composite commodity of close to the output of something like Marx's industry of average organic composition of capital.

Or one can retain an interest in how labor is allocated among industries, while exploring prices of production with an arbitrary numeraire. The fundamental theorem of Marxism holds in this setting. Must one draw quantitative relationships between the system of labor values and the system of prices of production?

Others might want to explore the historical and empirical evolution of the parameters of the model in the post and related models.

Reference

Saturday, February 24, 2024

Utility Maximization A Tautology?

Economists proved over half a century ago that certain stories are unfounded in the theory. For example, one might think that if some workers are involuntarily unemployed, a drop in real wages would lead to a tendency for the labor market to clear. The Cambridge Capital Controversy revealed some difficulties. In response, some economists turned to the Arrow-Debrue-McKenzie model of intertemporal equilibria in which it is not clear that one could even talk about such concepts. The Mantel-Sonnenschein-Debreu theorem shows that this model lacks empirical content. Utility theory provides a closure for some models. Formally, one can demonstrate the existence of equilibria under certain assumptions. But existence does not get one very far.

My purpose of this post is to note that some saw utility theory as a useless tautology at the time of the marginal revolution:

"It is interesting, in this connection, that the earliest critics saw in the theory of marginal utility what we have called a behaviourist theory of choice ... and used exactly the same arguments against it which will be used below against this latter version. Thus [John] Cairnes wrote about Jevon's theory: 'What does it really amount to? In my apprehension to this, and no more - that value depends upon utility, and that utility is whatever affects value. In other words, the name "utility" is given to the aggregate of unknown conditions which determine the phenomenon, and then the phenomenon is stated to depend upon what this name stands for.' Jevon's theory was believed to say no more than this: 'that value was determined by the conditions which determine it - an announcement, the importance of which, even though presented under the form of abstruse mathematical symbols, I must own myself unable to discern'. Some Leading Principles of Political Economy, 1874, p. 15.

[John] Ingram took the same view in A History of Political Economy, 1888, ed. by Ely, 1915, p. 228 and passim. Cairnes, Ingram, and other early critics of marginal utility had, however, directed their criticism also against the mathematical method generally, and the discussion went soon into other channels. The marginalists met the criticism by claiming to be proponents of logical and mathematical method and their tautological psychology thus escaped its well-deserved criticism." -- Gunnar Myrdal (1953) The Political Element in the Development of Economic Theory (trans. by Paul Streeten, Routledge & Kegan Paul, p. 231.

Obviously, Cairnes and Ingram could not have known about results demonstrated a century later. Utility theory manages simultaneously to not say anything about market phenomena, to not be good armchair theorizing, and to be empirically false at the level of the individual.

Friday, February 23, 2024

Elsewhere