Wednesday, January 01, 2020


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.

Sunday, September 16, 2018

Normal Forms for Switch Point Patterns

My article with the post title is now available at the Review of Behavioral Economics. The abstract follows:

Abstract: The choice of technique can be analyzed, in a circulating-capital model of prices of production, by constructing the wage frontier. Switch points arise when more than one technique is cost-minimizing for a specified rate of profits. This article defines four normal forms for variations in the number and sequence of switch points with a perturbation of, for example, a coefficient of production. The 'perversity' of switch points that appear on and disappear from the wage frontier is analyzed. The conjecture is made that no other normal forms for local patterns of co-dimension one exist.

Saturday, September 15, 2018


  • Maeve Cohen, the director of Rethinking Economics, notes the absurdism of undergraduate economics teaching, even after the Global Financial Crisis. In this one page article in Nature, she calls for greater pluralism in teaching. (This has led to the usual whining and silliness in the usual places.)
  • The American Economic Association has a moderated discussion board. I suspect much of the discussion will be too focused on narrow questions for interest by non-economists.
  • Thomas Piketty, Emmanuel Saez, and Gabriel Zucman have estimates for income in the United States, over time, for various percentiles. These can be called distributional national accounts.
  • Yanis Varoufakis calls for an international movement to fight both a re-insurgent fascism and establishment globalists.
  • Georgist single-taxers are not too my taste. I found this website for the New Physiocratic League colorful. I find intriguing the concept of certifying a political party's platform.

Saturday, September 01, 2018

Theses For Debate In Reading Marx

I present four claims about Marx's Capital. I strive for topics more general than, for example, squabbles about the transformation problem. I suggest that some of these claims present a useful focus for reading Marx's book, even if part of your focus is arguing why the claim is wrong. If this were more than a blog post, I would need to cite various Marxists and scholars that inspired me.

Thesis I: Capital is organized around a model of a pure, two-class capitalist economy.

I think the above claim is helpful in making sense of the opening chapters of Volume 1 and of Volume 2. In Volume 2, I am thinking of the analysis of the analysis of various circuits, as well as the models of simple and expanded reproduction.

This claim separates out the historical material and the analysis more sharply than some commentators on Marx accept. I guess it is consistent with some of Marx's use of Blue Books filed by factory inspectors in Britain. Historical material that goes beyond a model of pure capitalism includes the analyses of primitive accumulation in pre-capitalist formations and of the development of machinery and manufacture. I think of the replacement of the putting-out system, handicraft, and domestic industry by factories.

Thesis II: Capital continues the tradition of classical political economy; it does not represent a sharp break with this tradition.

One can argue Marx saw William Petty, Francois Quesnay, Adam Smith, and David Ricardo, for example, as having applied a scientific method of abstraction to identify essences that lie behind the surface phenomena of market prices. Of course, Marx had many criticisms of his predecessors. He thought Smith had not sufficiently distinguished labor that was and was not productive of surplus value. Even Ricardo did not distinguish (abstract, social) labor from labor power. Marx argued his distinction between constant and variable capital was more fundamental, in some sense, that the classical political economy distinction between fixed and circulating capital. And the classical did not talk about surplus value in general, instead of manifestations in the form of profits, interest, and rent.

This claim of continuity can also be argued to be consistent with Marx's contrast of vulgar and scientific political economy. Not everybody in the time of the classics, including Adam Smith, were thoroughgoing in the application of their scientific method.

But some of what Marx has to say about illusions generated by competition is in tension with this claim of continuity. He was interested in what social conditions made possible the development of political economy. The classical political economists championed the rising bourgeois before the social question became sufficiently biting. And what about the sarcasm and irony in Capital.

Thesis III: The system of labor values is a reality behind the appearance of freedom in market transactions.

In some sense, labor values provide a sub-basement underlying a building more obvious to our sight.

A counter thesis would be based on a Wittgenstein-like reading of Capital. Nothing is hidden, but markets, like languages, are befuddling. Marx is presenting arrangements in a therapeutic treatment to dissolve confusions. This also gets into some readings of Sraffa's work.

Thesis IV: One can accept the analysis in Capital as a way of understanding the world, independently of a any position on the desirability of changing it, either through a revolution or otherwise.

Friday, August 24, 2018

A Semi-Idyllic Golden Age

1.0 Introduction

This post presents a model of a steady state with a constant rate of growth in which:

  • Total wages and total profits grow at same rate.
  • Neutral technical change increases the productivity of labor in all industries.
  • The wage per hour increases with productivity.
  • Each worker continues to consume the same quantity of produced commodities.
  • But each worker takes advantage of increased productivity to work less hours per year.

In these times, when concerns about global warning are so important, one would also want to see a suggestion of a reduced ecological footprint. So this model of a steady state is only semi-idyllic.

I do not consider anything in the mathematical model below to be original. I outline it to raise the question whether such a growth path is possible under capitalism. The model demonstrates logical consistency, but cannot demonstrate that details abstracted from in the model would prevent its realization.

2.0 The Model

Consider a closed economy with no foreign trade. Industries are grouped into two great departments. In Department I, firms produce means of production, also known as capital goods. The output of Department I is called ‘steel’ and measured in tons. In Department II, firms produce means of consumption, also known as consumer goods. The output of Department II is called ‘corn’, measured in bushels. Both steel and corn are produced from inputs of steel and labor.

Constant coefficients of production (Table 1) are assumed to characterize production in each year. All capital is circulating capital. Long-lived machines, natural resources, and joint production are abstracted from in this model. Free competition is assumed. Labor is advanced, and wages are paid out of the net output at the end of the year. Workers are assumed to spend all of their wages on means of consumption. Profits are saved at a constant proportion, s.

Table 1: Constant Coefficients of Production
a0, 1(t)Labor required as input per ton steel produced in year t.Person-Hrs per Ton
a1, 1Steel services required as input per ton steel produced.Tons per Ton
a0, 2(t)Labor required as input per bushel corn produced in year t.Person-Hrs per Bushel
a1, 2Steel services required as input per bushel corn produced.Tons per Bushel

Suppose coefficients of production for steel inputs are constant through time but labor coefficients exhibit a growth in labor productivity of 100 ρ percent:

a0, j(t + 1) = (1 - ρ) a0, j(t), j = 1, 2

Let Xi(t), i = 1, 2; represent the physical output produced in each department in year t and available at the end of the year. Furthermore, suppose the price of steel, p, and the rate of profits, r, are constant. Let outputs from each of the two departments grow at a constant rate of 100 g percent:

Xi(t + 1) = (1 + g) Xi(t), i = 1, 2

Certain quantity equations follow from these assumptions. The quantity of capital goods added each year must equal the capital goods remaining after reproducing those used up in producing total output, in both departments:

g [a1,1 X1(t) + a1,2 X2(t)]
= X1(t) - [a1,1 X1(t) + a1,2 X2(t)]

The person-years of labor employed relates to labor coefficients and gross outputs:

L(t) = a0, 1(t) X1(t) + a0, 2(t) X2(t)

Price equations are:

p a1, 1 (1 + r) + a0, 1 w(t) = p
p a1, 2 (1 + r) + a0, 2 w(t) = 1

These equations embody the use of a bushel corn as numerate. w(t) is the wage per person-hour, paid out at the end of the year out of the surplus.

These assumptions and parameters are enough to depict Table 2. The column labeled "Constant capital" shows the value of advanced capital goods, taking the output of Department II as the numeraire. The column labeled "Variable Capital" depicts the wages paid out of revenues available at the end of the year. The surplus is what remains for the capitalists.

Table 2: A Tableau Economique
Ip a1,1 X1(t)w(t) a0,1 X1(t)p a1,1 X1(t) rp X1(t)
IIp a1,2 X2(t)w(t) a0,2 X2(t)p a1,2 X2(t) rX2(t)

I make one further assumption. Workers spend what they get, and capitalists save a constant ration, s, of their profits. With these assumptions, one can calculate the bushels corn that the workers and capitalists in Department I want to purchase, at the end of each year, from Department II. Likewise, one can calculate the numeraire value of the steel that capitalists in Department II want to purchase from Depart I. Along a steady state, these quantities must be in balance:

[a0, 1(t) w(t) + (1 - s) p a1, 1 r] X1(t)
= p a1, 2 [1 + s r] X2(t)

This completes the specification of this model of expanded reproduction with technical change uniformly increasing the productivity of labor.

3.0 The Solution

Output per labor hour is found by solving the quantity equations:

X1(t)/L(t) = a1, 2 (1 + g)/β(t, g)
X2(t)/L(t) = [1 - a1, 1 (1 + g)]/β(t, g)


β(t, g) = a0, 2(t) + [a0, 1(t) a1, 2 - a0, 2(t) a1, 1](1 + g)

That is:

Xi(t)/L(t) = [1/(1 - ρ)t] [Xi(0)/L(0)], i = 1, 2

The path of employed labor hours falls out as:
L(t) = (1 - ρ)t (1 + g)t L(0)

The number of employed person-hours decreases if:

ρ > g

The above expresses the condition that the labor inputs needed to produce a unit of output, in both departments, decrease faster than the rate of growth in both departments.

The price equations are also easily solved. Given a constant rate of profits, the price of steel is constant as well:

p = a0, 1(0)/β(0, r)

The wage per person-hour increases with productivity:

w(t) = [1 - a1, 1 (1 + r)/β(t, r) = [1/(1 - ρ)t] w(0)

The trade-offs between consumption per worker and the steady-state rate of growth and between the wage and the rate of profits have the same form.

These solutions can be substituted into the balance equation. It becomes:

[1 - a1, 1 (1 + s r)] (1 + g) = [1 - a1, 1 (1 + s r)] (1 + s r)

Suppose the rate of profits falls below its maximum (where the workers ‘live on air’) or not all profits are saved. Then this is a derivation of the "Cambridge equation":

r = g/s

A steady rate of growth, when the workers consume their wage, requires that the rate of profits be the quotient of the rate of growth and the savings rate out of profits.

4.0 Demographics and Institutions

I make some rather arbitrary assumptions about demographics and institutions. Suppose the number of person-years supplied as labor grows at the postulated rate of growth:

LS(t + 1) = (1 + g) LS(t)

with LS(t) measured in person-years. Let the number of hours in a standard labor-year, α(t) decrease at the same constant rate as the growth in productivity:

α(t + 1) = (1 - ρ) α(t)

The rate at which the total supply of labor-hours increases is easily calculated:

α(t + 1) LS(t + 1) = (1 - ρ) (1 + g) α(t) LS(t)

Under these assumptions, the supply of labor-hours grows at the same rate as the demand for labor-hours. Total wages and total profits increase at the same rate, 100 g percent. The wage per worker increases at the same rate as the standard length of a labor year declines. Thus, workers consume a constant quantity of commodities, but they take increased productivity in steadily increased free time.

5.0 Discussion and Conclusions

What should one postulate about money in this model? One could assume the money supply grows endogenously, along with commodities. Or, perhaps, the velocity of the circulation of money increases with productivity. A continuous decrease in the money price of corn is another logical possibility. Perhaps Rosa Luxemburg was right, and an external source of demand from less developed regions and countries is needed to support expanded reproduction. Or Kalecki is correct, and military spending by the government will do.

I do not know if this model describes any existing capitalist economy. It does not describe the post-war golden age. In that time, at least in the United States, workers took increased productivity in increased consumer goods. (I think the memory of the Great Depression, the occurrence of World War II, and the existence of the Soviet Union has something to do how this worked out.) Could any capitalist economy function like this? Somehow, an advertising industry is not encouraging workers to consume ever more produced commodities, or they ignore such messages. They continually have more freedom. Yet, they always spend a bit of time under the domination and direction of their employers. Will the capitalists tolerate this?

Monday, August 20, 2018

Samir Amin (1931-2018)

Despite the label at the bottom of this post, this is not really a profile of Amin. I happen to have started reading Modern Imperialism, Monopoly Finance Capital, and Marx's Law of Value (Monthly Review Press, 2018) last month. Here are a couple of quotations:

"Vulgar economics is obsessed with the false concept of 'true prices,' whether for ordinary commodities, for labor, for money, for time, or for natural resources. There are no 'true prices' to be 'revealed' by the genius of the 'market.' Prices are the combined products of rates of exploitation of labor (rates of surplus-value), of competition among fragmented capitals, and the deduction levied in the form of 'oligopoly rents,' and of the political and social conditions that govern the division of surplus-value among profits, interest, ground rents, and extractive rents." -- Amin, p. 99.

"Marx's criticism of the classic bourgeois political economy of Smith and Ricardo concluded by shifting from analysis centered on 'the market' ... to one centered on the depths of production where value and the extraction of on surplus value are determined. Without this shifting of the analysis from the superficial to the essential, from the apparent to the concealed, no radical critique of capitalism is possible...

The law of value formulated by Marx, based on the concept of abstract labor, expresses the rationality of the social utility (the utility for society) of a defined use value. This rationality transcends that which governs the reproduction of a particular mode of production (in this case, the capitalist mode of production). Under capitalism, rationality demands the accumulation of capital, itself based on the extraction of surplus value. The price system frames the operation of this rationality. Economic decisions in this framework ... will be different from those that might be made on the basis of the law of value that would define, in the socialism to come, the mode of social governance over economic decision making.

Bourgeois economic theory attempts to prove that the mode of decision making in the framework of its system of prices and incomes produces a rational allocation of labor and capital resources synonymous with an optimal pattern of output. But it can reach that goal only through cascading tautological arguments. To do so it artificially slices productivity into 'components' attributed to 'factors of production.'

Although this pattern of slices has no scientific value and rests on tautological argument, it is 'useful' because it is the only way to legitimize capital's profits. The operative method of this bourgeois economics to determine 'the wage' by the marginal productivity of 'the last employee hired' stems from the same tautology and breaks up the unity of the collective, the sole creator of value. Moreover, contrary to the unproven affirmations of conventional economics, employers do not make decisions by using such 'marginal calculations.'" -- Amin, pp. 232-234.

I have several other books by Amin on my bookshelf:

  • Samir Amin (2006). Samir Amin: A Life Looking Forward: Memoirs of an Independent Marxist. Zed Books.
  • Samir Amin (1998). Spectres of Capitalism: A Critique of Current Intellectual Fashions. Monthly Review Press.
  • Samir Amin (1997). Capitalism in the Age of Globalization: The Management of Contemporary Society. Zed Books.

As I understand Amin is most well known for inventing the word "Eurocentrism" and for extending the law of value to the law of worldwide value.

Amin builds on the concept of the "surplus", as developed in the work of Paul Baran and Paul Sweezy. One can formalize this notion in a model of a developed country with three departments, for producing capital goods, consumption goods, and luxuries. The last department is not in Marx's models of simple and expanded reproduction. This department is needed to address the problem of realization in an age of monopoly capital.

When it comes to realization problems, there is a long tradition among Marxists of looking at open economies, with advanced industrial capitalist economies trading with less developed peripheral regions or countries. Amin, an Egyptian trained in Paris and working in Dakar, was well positioned to develop these ideas of North-South trade. In the book mentioned above, he often talks about extending Marx's law of value to the law of worldwide value. I gather his ideas are partly the result of a critical engagement with Andre Gunder Frank's work, which I do not know.

To my mind, you can find similar ideas, about monopoly and finance capital and imperialism, going back to the time of the Second International. Amin mentions Rosa Luxembourg, but, as I recall, is critical of her. By the way, he groups Sraffa with bourgeois economists.

I was hoping to find Amin providing an exposition of a mathematical model in Modern Imperialism. He does provide some, but mostly he sticks with numerical examples and historical analysis. He says that this is, partly, to make his work accessible to a larger audience. Also, I am not sure that a mathematical model of the whole is appropriate for monopoly capital. I guess if I want to explore more, I should look at his 1974 book, Accumulation on a World Scale.

Saturday, August 11, 2018

Economists In Popular Fiction

Apparently, a character in a current movie, Crazy Rich Asians is an economist. Dan Kopf considers whether she is a good economist. In a couple of recent tweets, Paul Krugman reacts:

"Actually, I can fill this gap.

"There was a movie titled The Internecine Project ... with James Coburn as a chairman of the Council of Economic Advisers who gets a bunch of people to kill each other to hide his evil past. Sounds good to me, but the movie was terrible." -- Paul Krugman, 9 August 2018

I do not know about the movie versions, but I can name a couple of book series with characters who are economists:

  • Meyer is the sidekick in John D. MacDonald's Travis McGee mystery series. Meyer's houseboat is the John Maynard Keynes, until it is blown up. He replaces it with the Thorstein Veblen.
  • The love interest in the Bourne Identity series is an economist. If I recall correctly, Jason Bourne first meets her by carjacking and kidnapping her, and then forcing her to drive with him to Paris.

I don't think you can count the Marshall Jevons' mystery series, since that is a pen name for two economists.