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.

Saturday, January 19, 2019

Elsewhere: Popular Writing On Modern Monetary Theory

Some articles:

I do not assert that all points in these articles are well-taken.

I think of MMT as descriptive. It combines endogenous money, functional finance, and chartalism. Much of its empirical evidence consists of qualitative descriptions of how financial institutions and central banks operate. One can imagine a policy regime where unemployment and inflation are addressed by changes in the level of taxes and government spending, with monetary policy is a more passive attempt to keep interest rates permanently low. This would contrast with one where central banks are more responsible, through interest rate policy, with addressing unemployment and inflation. An analysis of the implications of such treatments need not be normative.

(Some asides: As a contrast, Josh Barro could have brought up his father, Robert's, treatment of Ricardian equivalence, which Ricardo rejected. Doesn't Marx, in chapter 1, volume 1 of Capital have an incorrect theory in which barter precedes money?)

Saturday, January 12, 2019

What Is Pure Capitalism?

1.0 Introduction

This post is fairly stream of consciousness. It is a bit more about how many find me odd.

I have previously mentioned, as an aside, Kozo Uno and his reading of Marx's Capital as a theory of pure capitalism. I like this idea, although it needs to be noted Marx had a lot to say in Volume I about concrete practices in his day and the historical development of capitalism. The theory and history are entwined. But Marx certainly presents the capitalist, not as a person, but as an embodiment of capital, in some sense.

I often bring a book with me when I go out to eat by myself. Sometimes people ask me what I am reading. For example, I have lately been re-reading the first volume of Capital; Marx's Value, Price, and Profit; and Böhm-Bawerk's Karl Marx and the Close of his System.

2.0 Small Businessmen Do Not Exist in Pure Capitalism

Many I run into are small businessmen, that is, petty bourgeois, in Marxist phraseology. I think of restaurant owners, general handymen, providers of mowing and plowing services, owners of auto repair shops, landscaping artists, and even one movie producer, musicians, consultants on Information Technology and Information Assurance, and so on. They do not obtain income solely from returns to capital, but, rather, from some combination of labor and capital. Their labor includes general scut work, managerial direction, and strategic planning. (Which of these tasks comprises the labor of superintendence?) Some have partners with finance capital invested in the business, often family members. Some sometimes have a few employees, and some have many more.

Maybe this is politeness, but I often say that Marx is not writing about you. I do not want to try to explain that capitalism restricts even your agency. I think many are conscious of trade-offs in staffing too much or too little on any given day, on the level of service provided, and on ensuring that staff do not quit. I bet many might agree that some staff that fall into the category of so-called unskilled labor, such as bartenders, baristas, waiters, bussers really know a lot about their tasks, do them well, and would take much time to train replacements. When they bid on jobs, they are conscious of socially necessary labor time and are worried about whether, for some reason not necessarily within the control of the worker, a job might take longer than assumed in the calculations which a bid was based on. Yet they feel that, with competition as it is, they cannot include a reserve time or even fully charge their own time. (Come to think of it, I am not including here those I know who make their income from profit on alienation, by buying collectibles low and selling high.)

I am more likely to explain to workers that the business owners' income comes from value added by their labor but not paid out in their wages. I also say that my income from Apple also comes from the exploitation of workers, and that this would be so even if Foxconn was not treating their workers so badly that they had to line their dorms with nets at ground level. And, of course, I am a consumer of commodities produced under capitalism. I am amused to attempt to explain that the labor theory of value can be seen not to work, as a theory of price, because of the existence of such products as wine and whiskey.

If you think about it, small businessmen do not fit in with the abstraction of pure capitalism since their earnings do not come solely from capital. Self-employed artisans and those close to such are, for Marx, survivors from a period of time before capitalism was fully developed. With John Kenneth Galbraith, I think this sector, however, will always exist, aside with the large corporate sector, in which many are somewhat sheltered, for a time, from the gales of competition.

3.0 Workers with Savings Do Not Exist in Pure Capitalism

Many skilled workers in the United States have savings, often in the form of mutual funds. They might not be able to access this wealth immediately, without a penalty, if it is in a 401K or Individual Retirement Account (IRA). (Defined-benefit pensions are now rare.) My casual empiricism is consistent with the observation that a tiny fraction of the population owns most of the wealth in the United States.

Here is another class of people whose income consists of returns to both labor and ownership of capital. And they have deferred not only the day-to-day management of the firms they indirectly have ownership shares in, but even decisions about investing and disinvesting in such firms to paid professionals. Does it matter to how the system works whether these savings are managed by financial experts on Wall Street or specialists more closely connected to labor unions? How should analyze executives corporate suites whose income is often classified as salaries, but anyways seems to have something to do with being in a class with control, but not ownership of the means of production? (I have not actually read that book or the one linked above by Drucker.)

4.0 Conclusion

So what kind of society is Marx describing abstractly? I think that in pure capitalism, some capitalists should be making investment decisions, but not being paid for labor power. Perhaps we want to think of the mid-nineteenth century when industrialists like John D. Rockefeller, Andrew Carnegie, or Karl Wittgenstein were starting out, but before they had obtained oligopolistic power.

One can build on this model to describe historic capitalism. You might think my account of small businesses shows something about a system organized around the production of commodities by means of commodities. Others have developed analyses of monopoly and finance capitalism. In the Post Keynesian tradition, Richard Kahn, Nicholas Kaldor, Luigi Pasinetti, and Joan Robinson had developed a model in which workers save, but investment decisions are driven by another class. Maybe a different model is more appropriate for the neoliberal era after the end of Bretton Woods, and in which workers do not seem to find their wages growing with productivity.

Friday, January 04, 2019

Linear Programming, M-C-M, and C-M

1.0 Introduction

Consider typical Linear Programs (LPs) for formulating the theory of firm in classical and neoclassical economics. I claim that the classical theory can be formulated as M-C...P...C-M, and that the neoclassical theory of production is something like C...P...C-M.

The notation is from Marx. For Marx, simple commodity circulation is represented as C-M-C. A commodity is sold for money, and then that money is used to buy another commodity. An owner of a use value trades it for a more desired use value. The formula M-C-M characterizes capitalism. A capitalist buys commodities so as to later sell commodities to somehow obtain more money. The goal is the accumulation of capital, not the acquisition of commodities.

2.0 Classical Theory of Production

For the classical theory, I had a recent presentation here. This is the price-side of John Roemer's Reproducible Solution (RS). The question is what must prices be such that firms can be willing to choose to produce commodities such that capital goods are reproduced (perhaps on an expanded scale), so that the economy will continue.

For ease of exposition, I might as will assume all commodities are basic commodities (in Sraffa's sense) and that there is no choice of technique. I define the following variables:

  • ω: A N-element column vector of commodities in existence at the start of the year.
  • a0: A N-element row vector of labor coefficients for each industry.
  • A: A N x N Leontief matrix, with each column listing the coefficients of production for each industry.
  • w: The wage.
  • p: A N-element row vector of prices for each produced commodity.
  • q: Decision variables. A N-element column vector of the quantity of each commodity to produce.
  • r: Decision variable. The rate of profits.

Each firm begins with an inventory of produced commodities, after having sold those needed for consumption last year. A firm chooses quantities to produce, q, to:

Maximize {p - [p A + a0 w]} q

such that

p A qp ω
qi ≥ 0, i = 1, 2, ..., N

The dual LP is to choose the rate of profits, r, to:

Minimize p ω r

such that:

p A(1 + r) + a0 wp
r ≥ 0

Some theorems from duality theorem are useful here. If a decision variable is positive in an optimal solution to the primal LP, the corresponding constraint is met with equality in the dual LP. In this simple presentation, where all commodities must be produced for the economy to be smoothly reproduced, all decision variables in the primal LP must be positive. Consequently, all constraints must be met with equality in the dual LP. That is, the dual LP provides a system of N equations in N + 2 price variables. An introduction of a choice of technique yields a justification of Kurz and Salvadori's direct method.

Commodities appear on the right-hand side of the constraint in the primal LP. And the decision variables are the commodities to be produced. But the constraint is that the value of the capital goods advanced be less than the value of the given inventory. Likewise, the capitalists are trying to maximize the increment of value. Realization problems are abstracted from here. One assumes that markets exist where one can trade inventory for more appropriate commodities for production plans, and likewise produced commodities can be sold. So the LP can be characterized as M-C-M'. It describes the wealth of society as "an immense accumulation of commodities."

3.0 Neoclassical Theory of Production

For the neoclassical theory, you can look at an appendix in Pasinetti (1977). Neoclassical theory is about the allocation of given resources. I define the following variables:

  • b: A M-element column vector of (unproduced?) factors of production available at the start of the year.
  • A: A M x N Leontief matrix, with each column listing the coefficients of production for each process.
  • p: A N-element row vector of prices for each produced commodity, with repeated prices for commodities with more than process for producing them.
  • q: Decision variables. A N-element column vector of quantities to produce with each process.
  • w: Decision variables. A M-element column vector of shadow prices.

The factors of production need have no relation to produced commodities. Don't think of seed corn and harvested corn. Think rather of various kinds of land, ores, and such-like for factors; and of consumer goods for produced goods. The managers of firms, in neoclassical theory, choose the levels, q, of operation of each process to:

Maximize p q

such that

A qb
qi ≥ 0; i = 1, 2, ..., N

The dual LP is to choose shadow prices w

Minimize bT w

such that

AT wpT
wj ≥ 0; j = 1, 2, ..., M

If a process is not operated in the solution to the primal LP, its cost, at shadow prices, exceeds the price of its outputs. If a given resource has a positive shadow price in the solution to the dual LP, it will fully used in the primal LP. Or, if it is not fully used (its constraint in the primal LP is met with inequality) then its shadow price will be zero.

The neoclassical theory ends up with C-M as a description of produced commodities being sold on markets. Its starts with use-values, though. So I guess it can be represented at, a high-level, as C-M alone.

4.0 Conclusion

I have previously contrasted post-Sraffian price theory and the neoclassical theory of value. The former is about an analysis of what needs to be the case for the reproduction of society. The latter is about the allocation of scarce resources. This post has introduced another contrast. Post-Sraffian price theory applies to a capitalist society, in which the accumulation of monetary value is an end of itself. I am not sure what kind of society, if any, can be described by the neoclassical theory of production. I guess neoclassical economics makes a bit more sense when it is used to described a series of temporary equilibria strung together.

  • Robert Dorfman, Paul A. Samuelson, and Robert M. Solow. 1958. Linear Programming and Economic Analysis
  • Heinz Kurz and Neri Salvadori. 1995. The Theory of Production: A Long-Period Analysis.
  • Luigi L. Pasinetti. 1977. Lectures on the Theory of Production
  • John Roemer. 1979. Analytical Foundations of Marxian Economic Theory
  • Robert L. Vienneau. 2005. On labour demand and equilibria of the firm. Manchester School: 73: 612-619.

Friday, December 28, 2018

Foreign Trade And Non-Uniform Rates Of Profits

This post raises a question. Supposedly, the classical concept of prices of production with non-uniform rates of profits can be recast as a theory of foreign trade. I do not see how wages can properly be treated in such recasting.

D'Agata (2018) and Zambelli (2018) are two recent papers that argue prices of production can be formulated with non-uniform rates of profits. They argue that this introduces a certain indeterminateness into prices, as in some of my examples of foreign trade. Both D'Agata and Zambelli cite Adam Smith and David Ricardo to justify their models as of classical inspiration. If somebody is to draw on this research for a theory of foreign trade, I hope they cite this passage from Adam Smith:

… every individual … endeavors as much as he can both to employ his capital in the support of domestic industry, and so to direct that its produce may be of the greatest value; every individual necessarily labours to render the of the society as great as he can. He generally, indeed, intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he only intends his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in so many other cases, led by an invisible hand to promote an end which was no part of his intention.

I suspect many propertarians are not aware that Smith was arguing that a lack of foreign direct investment is desirable, that enough barriers exist against entrepreneurs investing in other countries that no need exist for certain protectionist laws to be passed by government.

D'Agata models non-uniform rates of profits as arising due to both "objective and idiosyncratic factors affecting producers' investment decisions". Objective factors are modeled by different groups of producers having access to different techniques of production for producing the same commodities. For example, firms in England and Portugal might have access to different techniques for producing corn and wine, as in Ricardo's Principles. I guess countries having different endowments of land and labor, thereby limiting the scale at which some processes can be operated, is also an objective factor important to the theory of foreign trade.

Idiosyncratic factors are formalized by different producers having different valuation functions, where a valuation function is a continuous, strictly increasing function of the rate of profits obtained in a given industry. In terms of the theory of foreign trade, one might model entrepreneurs in England all having identical valuation functions, while entrepreneurs in Portugal have another valuation function, common among the Portuguese. Each valuation function might be assumed not to vary among industries. For example, English entrepreneurs value the rate of profits made in making corn the same as the rate of profits made in making wine.

From these considerations, one can obtain a theory of foreign trade in which:

  • Countries differ among themselves in the technology or endowments they have access to.
  • In a full employment position with balanced trade, countries specialize in the production of different commodities.
  • In such an equilibrium position, the rate of profits varies among countries.

(I do not claim such a theory is complete, since it does not consider Keynesian effective demand, paths with unbalanced trade, fluctuations in exchange rates, and so on.)

When I have tried to develop such a theory of foreign trade, I have created examples in which the wage also varies across countries. This is easy to justify based on an assumption of a lack of a free movement of people across national borders. But how is this idea formalized in D'Agata's approach?

  • Antonio D'Agata, 2018. Freeing long-period prices from the uniform profit rate hypothesis: A general model of long-period positions. Metroeconomica 69: 847-861.
  • Stefano Zambelli, 2018. Production of commodities by means of commodities and uniform rates of profits. Metroeconomica 69: 791-819.

Wednesday, December 26, 2018

Robert Visits An American Grave: Frederick Douglass

Frederick Douglass was an escaped slave, a great abolitionist orator, and generally a great American. Not too long ago, I read one of his autobiographies. Of his speeches, I am most likely to recognize bits from his 1952 observations on independence day. (Eldridge Cleaver quotes it in Soul on Ice.) This part is fierce:

What, to the American slave, is your 4th of July? I answer: a day that reveals to him, more than all other days in the year, the gross injustice and cruelty to which he is the constant victim. To him, your celebration is a sham; your boasted liberty, an unholy license; your national greatness, swelling vanity; your sounds of rejoicing are empty and heartless; your denunciations of tyrants, brass fronted impudence; your shouts of liberty and equality, hollow mockery; your prayers and hymns, your sermons and thanksgivings, with all your religious parade, and solemnity, are, to him, mere bombast, fraud, deception, impiety, and hypocrisy — a thin veil to cover up crimes which would disgrace a nation of savages. There is not a nation on the earth guilty of practices, more shocking and bloody, than are the people of these United States, at this very hour.

Frederick Douglass is buried in Mount Hope Cemetery in Rochester, NY. This is a family plot, with his widow at his left.

Tuesday, December 18, 2018

Variation Of Gains From Trade With International Prices

Figure 1: Intercepts of Production Possibilities Frontiers for England
1.0 Introduction

In this example, gains and losses from trade vary with international prices. Given rates of profits are compatible with an interval of relative international prices for linen and corn, when trade exists only in consumer goods. I explore whether, when trade exists in capital and consumer goods, more than one pattern of specialization among countries is possible, depending on relative international prices. I am beginning to think that specialization, in this model, in corn and linen is infeasible, except in knife-edge cases.

The theory of comparative advantage provides no valid justification for the abolition or the lowering of tariffs. Unregulated international trade is not about efficient use of an international allocation of resources. Many existing textbooks, including Krugman and Obstfeld's, should be ripped up, and the authors should start again.

2.0 Technology, Endowments, And The Rate Of Profits

I assume each of two countries (Tables 1 and 2) have a fixed-coefficients technology for producing three commodities. The technology varies between countries, although it has the same structure in both. Steel is the only capital good. Each commodity can be produced, in a year, from inputs of labor and steel. A coefficient of production shows the quantity of an input needed per unit output. For example, in England, one person-year and 1/30 tons of steel must be purchased per square meter of produced linen. Steel is totally used up in production, and constant returns to scale obtains.

Table 1: Coefficients of Production in England
Labora0, 1(E) = 1a0, 2(E) = 8a0, 3(E) = 12
Steela1, 1(E) = 1/5a1, 2(E) = 1a1, 3(E) = 1

Table 2: Coefficients of Production in Portugal
Labora0, 1(P) = 6/5a0, 2(P) = 12a0, 3(P) = 20
Steela1, 1(P) = 1/4a1, 2(P) = 2a1, 3(P) = 3/2

I take endowments of labor as given, as in the Ricardian model of foreign trade. Let England and Portugal both have available a labor force consisting of one person-year. So Production Possibilities Frontiers (PPFs) are found per person-year. By assumption, workers neither immigrate nor emigrate. In this model, full employment is assumed.

I also take the rate of profits as given, at 100 per cent in England and at 20 percent in Portugal. I assume that financial capital cannot flow between countries. So the rate of profits need not be the same across countries.

3.0 Summary

I apply my usual analysis to determine patterns of specialization, given technology, endowments, and rates of profits in each country. When foreign trade is possible in corn and linen, but not steel, the domestic price of steel and the wage in each country must be such that the going rate of profit is earned in producing steel. Likewise, firms in, say, England make neither extra profits nor incur extra costs in producing the consumer good in which England specializes. The firms would incur extra costs if they were to produce the other consumer good. The same principles extend to the case in which foreign trade is possible in all produced commodities.

In this analysis, which is an example of a small country model, prices for goods bought or sold in foreign trade are taken as given by firms in all countries. I find prices and specializations which are consistent with the given parameters. One can draw Production Possibility Frontiers (PPFs) for each country, given prices in foreign markets and specializations. A PPF shows possible baskets of consumer goods when labor is fully employed. In this model, each PPF is a decreasing function in the first sector of the two-dimensional space formed by quantities of corn and linen. Such a PPF is fully specified by the intercepts. The intercept with the corn axis is maximum amount of corn that can be consumer, per employed worker, given that no linen is consumed. Similarly, the intercept with the linen axis is the maximum amount of linen that can be consumed. Figure 1, above, and Figure 2, show the intercepts for the PPFs for England and Portugal, respectively.

Figure 2: Intercepts of PPFs for Portugal

In the example:

  • When foreign markets exist only for corn and linen:
    • England specializes in the production of linen (and steel), while Portugal specializes in corn (and steel).
    • England suffers a loss from trade, except when the international relative price of linen is at its highest feasible level.
    • Portugal obtains a gain from trade.
    • England’s loss and Portugal’s gain is smaller for larger relative prices of linen on international markets.
  • When foreign markets exist for steel, corn, and linen:
    • For a relatively small ratio of the international price of linen to the international price of corn, England specializes in corn and linen, and Portugal specializes in steel.
      • In this range, prices compatible with England specializing in linen and Portugal specializing in steel and corn provide England with extra profits in producing corn.
      • This case is infeasible. England only obtains steel by trading corn for it. England is unwilling to trade linen for steel, and Portugal is unable to acquire linen by selling steel.
    • For a relatively large ratio of the international price of linen to the international price of corn, England specializes in linen, and Portugal specializes in steel and corn.
      • In this range, prices compatible with England specializing in corn and linen and Portugal specializing in steel provide Portugal with extra profits in producing corn.
      • England obtains a gain from trade, as compared to when foreign trade is only possible in consumer goods
      • For a low price of linen in this range and a consumer basket heavily weighted to corn, England suffers a loss from trade, as compared to autarky.
      • Otherwise, England obtains a gain from trade, as compared to autarky.
      • Portugal’s PPF is identical to what it would be if foreign trade were possible only in consumer goods.
      • Accordingly, Portugal obtains a gain from trade, as compared to autarky.