Capital As A Social Relationship

Home Depot Sells Consumer Goods

1.0 Introduction

The lumber in the above picture may look like an immense accumulation of capital goods, where capital goods are a type of commodity. But, I argue, these commodities should properly be thought of as consumer goods.

2.0 A Keynesian Perspective

John Maynard Keynes, in The General Theory of Employment, Interest and Money, was interested in the sources of aggregate demand. Aggregate demand is demand for commodities, and an increase in this demand leads to an increase in waged labor. So, for Keynes, capital goods are goods whose use would be accompanied by labor being paid wages.

Home Depot and Loewes market to the Do-It-Yourselfer. (I assume building contractors buy in bulk, and purchase most of their stuff elsewhere.) The purchaser of products from these commercial enterprises may intend to construct a deck, erect a shed in their backyard, or remodel a kitchen or bathroom. But the work in completing this products will not be paid a wage. That is, as far as aggregate demand in a capitalist economy goes, the lumber pictured acts like a consumer good, not a capital good.

3.0 A Classical Perspective

Classical economists, such as Adam Smith, distinguished between "productive" and "unproductive" labor. Unproductive labor is that labor which is paid for out of revenue, not out of a capital fund. Unproductive labor does not earn a profit, even tendentially:

"There is one sort of labour which adds to the value of the subject upon which it is bestowed: there is another which has no such effect. The former, as it produces a value, may be called productive; the latter, unproductive labour. Thus the labour of a manufacturer adds, generally, to the value of the materials which he works upon, that of his own maintenance, and of his master's profit. The labour of a menial servant, on the contrary, adds to the value of nothing. Though the manufacturer has his wages advanced to him by his master, he, in reality, costs him no expence, the value of those wages being generally restored, together with a profit, in the improved value of the subject upon which his labour is bestowed. But the maintenance of a menial servant never is restored. A man grows rich by employing a multitude of manufacturers: he grows poor by maintaining a multitude of menial servants." -- Adam Smith, Wealth of Nations, Book II, Chapter 2.

I think of a typical example of unproductive labor as the work of a carpenter hired by a 18th or 19th century British aristocrat to build him a chest with wood that the aristocrat's estate provides. I guess such an estate would support all sorts of servants in the surrounding community. But profits would not be earned on their wages, either by these servants or by their employers.

So, even if the purchaser of the lumber products under consideration here hired some helpers or, perhaps, compensated some assistants with food or drink, these products would still not be capital goods.

4.0 A Neoclassical Perspective

A neoclassical might abstract from all these considerations of institutions, particularly for those that constitute capitalism. And the neoclassical economist might classify as capital those goods that last for many periods, providing a flow of services. (I think you can find this perspective in Leon Walras; he certainly distinguishes between a flow of services and the stock of goods.) At the highest level of abstraction, whether the owner of a capital good is a firm or a household is irrelevant. Furthermore, home improvements will increase the price that a house can fetch if you decide to sell it. If you rent it out, you will acquire what Alfred Marshall described as a quasi-rent from these home improvements.

Note, though, that this perspective abstracts from the distinction between goods, that once produced, are given in quantity at a point in time and, say, an annual cycle of (re)production of commodities needed to sustain a capitalist economy. As can be seen on the first page of the first chapter of David Ricardo's Principles of Political Economy and Taxation, classical economic theory focuses on the latter aspect.

Preliminary Thoughts on Volume Two of the Collected Papers of Robert Paul Wolff

1.0 Introduction

I have been reading From Each According to His Ability: Essays on Karl Marx and Classical Political Economy, by Robert Paul Wolff. This is a collection of essays, including critiques of Wolff's views by John Roemer and David Schweickart with Wolff's responses. I have read at least two¹ of these essays before². Many of these essays build on two books Wolff has written³. This book is available only as an E-book⁴. Some typographic errors exist here and there. It is basically self-published, with Wolff getting permission from various journals to republish the essays not originally presented on his blog.

These essays concentrate on two main themes. One is a formal presentation of Marxist political economy, developed by Piero Sraffa and others. The other is an interpretation of the curious literary style of Marx's Capital, in which commodities are treated as persons, persons are personifications of abstract classes, and the argument in the first chapter for the labor theory of value⁵ is difficult to take seriously.

2.0 A Formal Interpretation of Marx

Wolff is impressed with how Sraffians and analytical Marxists have (or should have) transformed our understanding of economics. Before this recent development, Marxists tended to concentrate on philosophical themes of alienation in Marx's early works, historical materialism, and cultural criticism. Marx's economics seemed to be in the trash bin of history:

"There has, in the past two decades, been an enormous world-wide upsurge of serious interest in, and rigorous investigation of, the central theses of the political economy of Karl Marx. Such doctrines as the labour theory of value, which for almost a century were ridiculed as outmoded ideology, as superstition, as metaphysics, are now taken seriously and debated with the aid of the most sophisticated tools of modern formal analysis. What began primarily as an activity of mathematical economists has now become a philosophical endeavor as well, with the result that the rediscovery of Marx is taking on a broader and deeper dimension." -- Robert Paul Wolff, "A Reply to Professor Schweickart"

I think Wolff is too optimistic here. I, of course, agree that a rigorous, formal, reconstruction of classical and Marxian economics is now available to economists. It is my impression, however, that, due to the sociology of the profession, most economists are unaware of the existence of this approach. I expect them to be still echoing seriously outdated mistakes about Marx's economics being ideology, superstition, and metaphysics. At least, I do not expect this formal reconstruction to be available in textbooks widely used by economists up through graduate school.

For his formal analysis, Wolff draws on definitions of labor values in terms of quantity flows between industries, as expressed in Leontief input-output matrices for self-reproducing capitalist economies. Prices of production are similarly calculated from such inter-industry quantity flows and an external specification of the distribution of the surplus. Wolff quotes Adam Smith on how a process akin to gravitation will lead market prices to approach prices of production, but does not otherwise analyze this claim extensively.

Wolff notes that both Ricardo and Marx were aware that prices of production generally deviate from labor values. Wolff discusses Marx's solution to the transformation problem, and what Wolff calls "conservation laws"⁶. The equality of surplus value with, to a first approximation, profits, seems to be primary with Wolff. He points out that this equality can be obtained by a specification of the appropriate numeraire. So he brings in a second equality between total value produced in a given time and the total output, evaluated at prices of production. Because of a dimensional analysis, Wolff's ends up interpreting Marx as claiming a general equality between the ratio of surplus value to total value and the ratio of profits to the prices of output. And, in consistency with the traditions upon which Wolff draws, he argues that Marx's claim is mistaken, except in special cases⁷.

Marx, however, assumes the labor theory of value in Volume 1, to explain the origin of profits. As I read Wolff, he does not think Marx's difficulties with solving the transformation problem invalidates the Volume 1 analysis. Marx's innovation in Volume 1 is to introduce the distinction between labor and labor power, where the latter is the labor value embodied in the commodities purchased by (non-saving) workers for consumption. For Wolff, what Morishima has dubbed the Fundamental Theorem of Marxism seems, at first glance, to justify Marx. A surplus is available to be distributed to capitalists as profit and to landlords as rent if and only if labor is exploited. That is, the labor value of output net of the labor value of capital goods consumed in producing that output must exceed the labor-value of labor power for a profit to exist.

For Wolff, the most serious objection to Marx's economics seems to be that this Fundamental Theorem is true for all commodities, not just labor-power. Surplus value exists, for example, if and only if corn is exploited. Wolff thinks he has an answer to this objection. Labor power is different than other commodities in that it is produced outside of capitalist relations, in some sense. Household production, outside of slavery, need not obtain the general rate of profits used in calculating prices of production. Furthermore, workers in selling their labor power must put their wills under the direction of the capitalists⁸.

3.0 Literary Matters

Wolff's literary analysis of Capital concentrates on the opening chapters. He thinks Marx adopted a style appropriate for his material. When observing a capitalist economy, all trades in the market look like they are made between equals, at least under competitive conditions. For Marx, this is a mystifying illusion resulting from commodity fetishism. Furthermore, Marx treats the labor theory of value with a certain amount of irony. For Marx, according to Wolf, labor values are not a physical embodiment of past labor, but the result of social relationships.

Why does Marx write in a ironic, mystifying style? To see that there is a problem in treating commodities as naturally commensurable and in accounting for the source of profits. If all commodities trade at labor values, how can profits arise? How can workers be said to be exploited, in a descriptive sense? Marx wants the reader to see that the reality thrown up by capitalist economies is topsy-turvy, and that these are questions that need to be asked and answered.

4.0 Conclusion

These essays reflect a perspective developed in the late 1970s and in the 1980s. You can find, on Wolff's blog, some commentators pointing out, for example, the Temporal Single System Interpretation (TSSI) of Andrew Kliman and others. I happen to agree with Wolff's perspective. But the reader should be aware that Wolff has not addressed more recent developments, either in Marxist and Sraffian economic theory, or in literary criticism⁹.

Wolff, being disappointed in the reception of the second of his books on Marx, never wrote a planned third book to integrate his mathematical formalist perspective on Marx and his ironic reading of Marx. The essays in the fourth section of this volume of his collected papers provide a start to such integration. But I have yet to read this section.

Footnotes

1. I think some other chapters might have been blog posts. At least, there is some redundancy, either among chapters or between chapters and other things Wolff has written.
2. "Ricardo's Principles", originally a series of blog posts (for example) in 2011, and Wolff (1982).
3. Understanding Marx and Moneybags Must Be So Lucky.
4. Is it available only in a Kindle format?
5. I refer to Marx's supposed search for a "common element" in commodities, an argument that Wolff says is entirely meretricious.
6. Elsewhere, I have written about these conditions as "invariants".
7. When all commodities are produced with the same organic composition of capital or when the output of the economy is in standard proportions.
8. Wolff's disputes with Roemer and Schweickart are over the precise statement of this claim and its validity.
9. See Kornbluh (2010) for a recent literary reading of Marx's Capital drawing on postmodern theory. Kornbluh also sees Marx style as attempting to defamiliarize capitalism so as to explain the mystifications produced in a capitalist economy.

References

• Anna Kornbluh, "On Marx's Victorian Novel", Mediations, V. 25, No. 1 (Fall 2010).
• Robert Paul Wolff, "Piero Sraffa and the Rehabilitation of Classical Political Economy", Social Research (Spring 1982).
• Robert Paul Wolff, Understanding Marx (Blackwell, 1985). (I have not read this.)
• Robert Paul Wolff, Moneybags Must Be So Lucky: On the Literary Structure of Capital (University of Massachusetts Press, 1988).

Economists For The General Reader

What economists would you expect somebody with a general university education to have heard of? My list is quite short:

• Adam Smith
• Karl Marx
• John Maynard Keynes

I expect these authors to function mostly as symbols in the popular consciousness. I might expect Americans above a certain age to have heard of John Kenneth Galbraith and Milton Friedman. Would they have heard of Paul Samuelson? He did have a column in Newsweek for a while. I first became aware of the existence of Joan Robinson by seeing a reference to her as the "British Galbraith". From what I've read, Nicholas Kaldor also had a certain public presence in Britain for a certain generation.

Given the highly technical nature of academic economists these days, it is hard for economists to invite the public into their discussions. I guess a theme of this blog is that most academic economists are not to be trusted. Others, such as Steve Keen, Fred Lee, and Bill Mitchell say fairly much the same. But I am not opposed to thinking of economics as a technical subject. I do not think I have resolved a tension here in my own mind.

Knowledge/Power

Figure 1: Paul Krugman And Bill O'Reilly Talk To Tim Russert

"My problem was ... to pose the question, 'How is it that at certain moments and in certain orders of knowledge, there are these sudden take-offs, these hastenings of evolution, these transformations which fail to correspond to the calm, continuist image that is normally accredited?' But the important thing here is not that such changes can be rapid and extensive or, rather, it is that this extent and rapidity are only the sign of something else - a modification in the rules of formation of statements which are accepted as scientifically true. Thus, it is not a change of content (refutation of old errors, recovery of old truths), nor is it a change of theoretical form (renewal of a paradigm, modification of systematic ensembles). It is a question of what governs statements, and the way in which they govern each other so as to constitute a set of propositions that are scientifically acceptable and, hence, capable of being verified or falsified by scientific procedures. In short, there is a problem of the regime, the politics of the scientific statement. At this level, it's not so much a matter of knowing what external power imposes itself on science as of what effects of power circulate among scientific statements, what constitutes, as it were, their internal regime of power, and how and why at certain moments that regime undergoes a global modification.

It was these different regimes that I tried to identify in The Order of Things, all the while making it clear that I wasn't trying for the moment to explain them, and that it would be necessary to try to do this in a subsequent work. But what was lacking here was the problem of the 'discursive regime', of the effects of power peculiar to the play of statements. I confused this too much with systematicity, theoretical form, or something like a paradigm. This same central problem of power, which at that time I had not yet properly isolated, emerges in two very different aspects at the point of junction of Madness and Civilization and The Order of Things." -- Michel Foucault, "Truth and Power", reprinted in The Chomsky-Foucault Debate: On Human Nature, The New Press (2006), pp. 144-145.

I do not know that I understand Michel Foucault, and I have not read much that he wrote towards the end of his life. I had thought Foucault's discursive formations were to be grouped with Thomas Kuhn's paradigms and Imre Lakatos's scientific research program. To me, economics is like medicine, psychiatry, and penology. It fits in well with the disciplines that Foucault analyses. Superficially, the epistemic status of these disciplines is more questionable than a hard science. And they have been used to help nation states categorize, partition, and rule their subjects since, say, the eighteenth century. But I want to drop talk of science for now. I look at a concrete example to help me understand what Foucault might mean when he talks about government, power, the political economy of the sign, a discursive regime, and politics. Doubtless, I will miss many, many nuances here.

You can see many commentators and supposed experts in the media, although, for many, I am none too clear in what area they are expert. (I have in mind such people as Rush Limbaugh, Bill O'Reilly, and even Wolf Blitzer and Thomas Friedman.) Many write best-selling books. A book store will classify them, when they come out, in a section labeled "current events". I suppose libraries will put them somewhere in social sciences. People with the sort of media presence I have in mind can be said to benefit from a sort of power for their statements. From an analytical point of view, you might know a drunk at the end of your local bar who is more worth listening to. Yet these commentators react to one another, take each other seriously, and end up having effects on laws that are passed. At least one kind of power circulates among their statements, a power that is not easily available to those taking their own way at your local.

Foucault also writes about power being productive, not solely a matter of prohibitions. How does the above clip illustrate this theme? Those who have power circulating their statements can sometimes dismiss others as living in a "fantasy world". But I think the power we see in right wing commentators in America extends to individuals in communities across the country. You can find many who think they keep informed by watching TV news. And they will have conversations with one another, maybe conversations that you could not participate in without being seen as rude, dismissive, and condescending. Some of these people might even participate in governing your community by participating in, say, the school board, the city council, or state government. Within such groups, you might find an intellectual who has read, for example, Hayek's Road to Serfdom on Glenn Beck's recommendation. So this power I am vaguely pointing at helps form local communities, as well as national discourse.

I consider Krugman to be at a different level of seriousness than the other two people in the above clip. Still these questions arise for him. What power gets his statements listened to and to circulate widely? It would be a mistake to classify his statements solely as part of the academic discipline of economics. For example, his newspaper columns about the Iraq war do not have much to do with economics. And a regime in which he occupies the acceptable left wing of the public face of economics seems quite limiting to me. When Krugman debates Keen through their blogs, it seems clear who is doing the other more of a favor to acknowledge the existence of the other's work, whatever you make think of the outcome of that debate.

I trust that one can see that in merely acknowledging the existence of political power that allows Krugman's statements to circulate, I am not thereby criticizing their content or what Krugman does with this non-personal power. In fact, I think Krugman has quite often acknowledged the power of his platforms and talked about how that influences his topics. As far as I know, he does not read Foucault. (Has not Brad DeLong written a bit on Foucault?) I am not sure what Krugman has said about his willingness to participate in the sort of hurlyburly babble seen in the above clip, other than that he sometimes has a book to promote. I suppose the bit where he leans back and rolls his eyes at the ceiling is comment enough on his particular antagonist there. I think Krugman would even be receptive to claims about the lack of agency of the author. He is rarely as forthright as in the above clip about calling a lie, "a lie". And he knows that his conventions do not allow him to comment on nonsense spouted by his fellow columnists, except very elliptically.

By the way, the video clip above is not directly from a major network. Apparently, it was put on YouTube with annotations added by Jim Gilliam. And, of course, I do not claim the power of those you might see babbling on your television.

Trends in Hardware and Software Costs as an Example of Structural Economics Dynamics

Empirical Trends in Costs for Computer Systems

1.0 Introduction¹

Over time, the proportion of the cost of computer systems consumed by software has tended to rise. Figure 1, originally in Boehm (1973) illustrates. In this post, I offer a theoretical explanation of this empirical observation. One might take this post as an illustration of an empirical use of the Labor Theory of Value.

2.0 The Model

Assume a computer system consists of equal amounts of hardware and software, both measured in some standard units^{1, 2}. Earlier computer systems delivered less units, while current computer systems deliver more. Next, assume that both hardware and software are produced directly from labor³.

2.1 Definitions and Assumptions

Let l_h be the staff-hours needed to produce a unit of hardware. Define ρ_h to be the rate of growth of labor productivity in the hardware industry:

ρ_h = - (1/l_h)(dl_h/dt)

Similarly, let l_s be the staff-hours needed to produce a unit of software, and define ρ_s to be the rate of growth of labor productivity in the software industry:

ρ_s = - (1/l_s)(dl_s/dt)

The last assumption is that the rate of growth of productivity is higher in producing hardware:

0 < ρ_s < ρ_h

One last variable must be defined. Let p be the ratio of labor costs to total system costs for a software system:

p = l_s/(l_h + l_s)

This completes the exposition of the model assumptions and variable definitions.

2.2 The Solution of the Model

Some algebraic manipulations with the above definitions yields the following differential equation:

(1/p) (dp/dt) = Δ(1 - p),

where Δ is the difference in the growth rates of labor productivities in hardware and software productivity:

Δ = ρ_h - ρ_s

This differential equation expresses the rate of growth of software cost, as a proportion of total system cost. The solution to this differential equation is:

p(t) = 1/[1 + c exp(-Δ t)]

where c is a constant determined by an initial value:

c = [1/p(0)] - 1

2.3 Numerical Values

Calibrating the model is the last step in the analysis presented here. Suppose 20% of the cost of a system is software in 1960, and that 80% of the cost of a system is software in 1995. The rate of growth of labor productivity is then 8% more in hardware than in software.

Δ = (1/35)[ln(4) - ln(1/4)] ≈ 7.9 %

The integrating constant for the initial value is:

c = 4/exp(-1960 Δ) ≈ 1.1 x 10⁶⁸

Figure 2 shows the relative proportion of system costs, as generated by the model with these parameters. Notice how closely Figure 2 resembles Figure 1. The model provides an explanation of the empirical observations.

Modeled Trends in Costs for Computer Systems

3.0 Conclusion

This post has presented a model, with its attendant idealizations. And that model shows how the empirical observation that productivity increases faster in hardware than software can account for the empirical observation that the cost of computer systems have become mostly software costs. Hardware costs, as a proportion of total system costs have been declining for decades.

Footnotes

1. This post draws on work I did elsewhere decades ago.
2. Floating Point Operations per Second (FLOPs) is a common measure of output in hardware. I suppose one should also specify the power at which these FLOPs are generated.
3. Source Lines Of Code (SLOC) is a common measure of software size. I have heard the analogy that measuring software in SLOC is like measuring the size of a house by the number of nails used in its construction. I guess one could always use Function Points (FPs) as a measure of software.
4. A natural extension would be to assume both hardware and software are produced solely from inputs of labor, hardware, and software. I am not sure if I ever stepped through such a model in this context.

References

• Barry W. Boehm (May 1973). "Software and Its Impact: A Quantitative Assessment", Datamation.
• Luigi L. Pasinetti (1993). Structural Economic Dynamics: A Theory of the Economic Consequences of Human Learning, Cambridge University Press.

Elsewhere

• Steve Denning, a writer for Forbes, describes Milton Friedman as being the source of "The world's dumbest idea". (I have written on Milton Friedman's confusion. incoherence, and lack of integrity, as well as Michael Jensen's (ir)responibility. See also Unlearning Economics.)
• Mike Konczal on Philip Mirowski's new book.
• Henry Scowcroft on the need for communicating economics to the public.
• Michael Lind on supposedly "Econ 101". Noah Smith complains about the public impression of what economists teach.
• Robert Neild on a 1981 anti-monetarism petition. I am especially amused about him losing his cool in a debate with Milton Friedman.
• Mark van Vugt and Michael Price, two psychologists, I gess, comment on Homo Economics. They link to a website which has David Sloan Wilson as editor in chief.
• Floyd Norris, in the New York Times, explains that Steve Keen foresaw the global financial crisis better than Ben Bernanke did.

Who Are The Nine People Prosecuted By The USA For Espionage For Leaking Secrets To The Press?

1.0 Introduction

This is a current affairs post, usually outside what I blog about.

I have found the count in the post title echoed in several publications, for example:

"...Historically, the vast majority of leak-related investigations have turned up nothing conclusive, and several of the nine that have been prosecuted — six already under the Obama administration, and just three more under all previous presidents — collapsed...

...Many people are surprised to learn that there is no law against disclosing classified information, in and of itself. The classification system was established for the executive branch by presidential order, not by statute, to control access to information and how it must be handled. While officials who break those rules may be admonished or fired, the system covers far more information than it is a crime to leak.

Instead, leak prosecutions rely on a 1917 espionage statute whose principal provision makes it a crime to disclose, to persons not authorized to receive it, national defense information with knowledge that its dissemination could harm the United States or help a foreign power." -- Charlie Savage, New York Times, 9 June 2012.

"Only three times in its first 92 years was the Espionage Act of 1917 used to prosecute government officials for leaking secret information to the press. However, the current administration has already brought six charges under this Act. The accused in all of these cases appear to represent whistleblowers, not those engaged in attempted espionage for foreign governments that 'aid the enemy.'" -- Association for Education in Journalism and Mass Communication

2.0 Possible List

Maybe these are those being discussed:

1. Daniel Ellsberg: Famous for the Pentagon Papers.
2. Anthony Russo: Also involved in disseminating the Pentagon Papers.
3. Samuel Loring Morison: Only person ever convicted, in a trial, for espionage for leaking classified information to the press.
4. John Kiriakou
5. William Binney.
6. J. Kirk Wiebe.
7. Ed Loomis.
8. Thomas Drake.
9. Bradley Manning: Involved with Wikileaks.

Apparently, Scooter Libby was not indicted and tried for espionage. The Espionage Act of 1917 was modified by the McCarran Internal Security Act of 1950, I guess.

3.0 Possible Future Additions

Possibly, Edward Snowden and Retired General James Cartwright (for leaking, maybe, about Stuxnet) will be added sometime to the above list.

(Somewhere in Democracy in America, as I remember it, Alexis de Tocqueville observes that political disputes in the United States almost always become legal disputes.)

Rate of Profits And Value Of Stock Independent Of Workers Saving

.

1.0 Introduction

This post presents elements of a model of a smoothly reproducing economy, that is, of an economy growing along at the warranted growth rate. I have previously presented a more detailed exposition of a variant of this model. One could add, say, Harrod-neutral technical change to that exposition. I would find it easier to add biased technical change by assuming fixed, not variable, coefficients of production. Perhaps this model reflects conventions and the balance of class forces prevalent in Anglo-American economies after World War II and before the collapse of the Bretton Woods system.

Anyways, I am revisiting this model because, recently, I have noticed another mathematical property of this model. Not only are the determinants of the rate of profits along a warranted growth path independent of the decisions of the workers to save. So is the average stock price of corporations.

2.0 The Model

This model abstracts from the existence of government spending and taxation. It also treats foreign trade as negligible. National income is comprised of wages, W, and profits, P. The rate of profits, r, is the ratio of profits to the value of capital goods, K, used in producing national income.

2.1 The Corporate Sector

I begin with corporations. The corporations own the capital goods and hire the workers to produce output with these capital goods. Corporate managers decided on the level of investment, I, to achieve a target growth rate, g.

Investment, in this model, is financed by some mixture of retained profits and the issuance of new stock (also known as shares) on the stock market. Corporate managers decide on this mix. Let s_c be the proportion of profits that are retained to finance new investment. And let f be the proportion of investment financed by issuing new shares:

I = s_c P + f I

Some algebra yields:

P/K = [(1 - f)/s_c] (I/K)

Or:

r = [(1 - f)/s_c] g

Thus, the rate of profits consistent with a warranted rate of growth is determined by parameters characterizing decisions made by corporate managers.

2.2 Finances and Households

In this model, households do not own capital goods. Rather, corporations own capital goods, and households own stock in these corporations. The ratio of the market value of stock to the value of the capital goods owned by the corporations is called the valuation ratio, v. The valuation ratio is assumed constant along a warranted growth path. Variations in the valuation ratio reflect short-term speculation. Generally, the valuation ratio is above unity.

Households are divided into two classes in this model, workers and capitalists. Workers receive part of their income in the form of wages. Given a positive savings rate on the part of workers, they also receive dividends and capital gains from their stock. Capitalists do not labor; their households receive all their income from dividends and capital gains. The variable j is used to denote the proportion of stocks owned by the workers.

Dividends consist of profits received and not retained by the corporations. By assumption, the value of dividends is then (1 - s_c)P. Net investment, I, is the increase in the value over a year of the capital goods owned by corporations, while the increase in the value of stocks is vI. But the value of new shares is only fI. The difference, (v - f)I, is the value of capital gains.

The interest rate is the ratio of the returns to financial capital (that is, dividends and capital gains) to the value of stock. With a valuation ratio above unity the interest rate, i, falls below the rate of profits. The valuation ratio then becomes:

v = (r - g)/(i - g)

I assume workers typically save at the rate s_w, and capitalists typically save at the greater rate s_r. Table 1 shows sources of savings, based on these definitions and behavioral assumptions.

Table 1: Sources of Economy-Wide Savings

Source	Amount
Retained Earnings:	sc P
Capitalist Savings Out of Dividends:	(1 - j)sr(1 - sc)P
Minus Capitalist Consumption Out of Capital Gains:	- (1 - j)(1 - sr)(v - f)I
Worker Savings Out of Wages:	swW
Worker Savings Out of Dividends	j sw(1 - sc)P
Minus Worker Consumption Out of Capital Gains:	- j(1 - sw)(v - f)I

In adding up savings, one must be sure not to double-count retained earnings. Corporations decide to save retained earnings, but households can undo this decision by consuming capital gains. Total savings for capitalists, S_r, are:

S_r = (1 - j) s_r[(1 - s_c)P + (v - f)I]

Total savings for workers, S_w, are:

S_w = s_wW + j s_w[(1 - s_c)P + (v - f)I]

Along a warranted growth path, investment is always equal to savings. The following equation is based on the components in Table 1:

I = s_c P + (1 - j)[s_r(1 - s_c)P - (1 - s_r)(v - f)I]

+ s_wW + j [s_w(1 - s_c)P - (1 - s_w)(v - f)I]

A bit of algebra allows the investment-savings equality to be restated:

I = s_c P + S_r + S_w - (v - f)I

The last term (that is, capital gains) is subtracted to avoid double-counting.

Another condition of a warranted growth path in this model is that the corporate sector, capitalist households, and workers continue to endure. This condition requires that the rate of growth of the book-value of the capital goods held by the corporations, the rate of growth of the value of the stock held by capitalists, and the rate of growth of the value of the stock held by the workers all be equal. Thus, the rate of growth of the value of the stock held by capitalists is:

g = S_r/[(1 - j)v K]

The rate of growth of the value of the stock held by workers is:

g = S_w/(j v K)

This completes the exposition of the equations I need for my point here.

2.3 Some Algebra

I now report on some algebraic manipulations of these equations. The condition that the value of the stock held by capitalists and workers grows at the same rate yields the following condition:

S_w = S_r [j/(1 - j)]

Substituting in the investment-savings equality, one can obtain:

I = s_c P + [S_r/(1 - j)] - (v - f)I

Or, by expanding the definition of capitalist savings:

I = s_c P + s_r[(1 - s_c)P + (v - f)I] - (v - f)I

Regrouping yields:

[1 + (1 - s_r)(v - f)]I = [s_c + s_r(1 - s_c)]P

Dividing through by the book value of the capital goods owned by the corporations, one obtains:

r = {[1 + (1 - s_r)(v - f)]/[s_c + s_r(1 - s_c)]} g

Equating for the value of the rate of profits previously found, one obtains an expression for the valuation ratio in terms of model parameters:

v = {[s_r(1 - s_c)]/[s_c(1 - s_r)]} - {s_r/[s_c(1 - s_r)]} f

Notice the parameters on the right-hand-side characterize either corporate decisions or the decisions of capitalist households. The saving propensities of the workers do not enter into it. The more that corporations finance investment by issuing shares, instead of using retained earnings, the lower the valuation ratio is along a warranted growth path. If the proportion of profits distributed in dividends lies below the proportion of investment financed by issuing new stock, a smaller capitalist savings propensity is associated with a higher valuation ratio. In some sense, capitalists get what they spend.

3.0 Conclusions

This post has outlined some necessary properties of a warranted growth path in a model containing:

• Corporations, a capitalist class, and a class of workers.
• A stock market, in which ownership shares in the corporations are bought and sold.
• A growth rate determined by decisions of the corporate managers.

In this model, the decisions of the corporate manager as to the growth rate, retained earnings, and finance obtained by issues of new stock determine the rate of profits consistent with a warranted growth path. These decisions of the corporate managers, along with the savings propensities of the capitalists, determine the ratio of the price of stock to the book value of the capital goods owned by the corporations. A fortiori, these decisions also determine the interest rate. Within the limits where a warranted growth path exists, the savings propensities of the workers have no effect on the growth rate, the rate of profits, the price of stock, the interest rate, or the functional distribution of income. The savings decisions of the workers do affect, however, the personal distribution of income and the proportion of stock owned by the workers.

Appendix: Variable Definitions

• K is the book value of the capital goods, in numeraire units, owned by the corporations.
• I is investment, in numeraire units.
• P is corporate profits, in numeraire units.
• S_r is capitalist savings, in numeraire units.
• S_w is worker savings, in numeraire units.
• f is the proportion of investment financed by issuing new stock (also known as shares).
• g is the warranted rate of growth.
• i is the interest rate.
• j is the proportion of stock owned by workers.
• r is the rate of profits earned by the corporations on the book value of their capital stock.
• s_c is the proportion of profits retained by corporations.
• s_r is the (average and marginal) to save of the capitalists.
• s_w is the (average and marginal) to save of the workers.
• v is the valuation ratio, that is, the ratio of the value of the stocks of the corporations to their book value.

Reference

• Scott J. Moss (Dec. 1978). The Post-Keynesian Theory of Income Distribution in the Corporate Economy, Australian Economic Papers, V. 17, N. 31: pp. 302-322.

Against Biotechnological Determinism

1.0 Introduction

Perhaps arguments lasting between groups for decades have some underlying issues that are not immediately apparent by looking at the details. I often attempt to explain technical details of the Cambridge Capital Controversy (CCC). Is there something central, but hardly articulated by the participants and on-lookers, that helps in understanding the positions taken by economists on the CCC? I take the concept and the phrase biotechnological determinism from Stephen Marglin (1984).

2.0 Neoclassical Economics As Embodying Biotechnological Determinism

A naive neoclassical economics embodies biotechnological determinism. The biology is to be seen in population demographics and in preferences, including over intertemporal consumption plans and over choices between labor and leisure. The technology is to be seen in production functions and endowments.

From about 1870 up to the 1930, neoclassical economists emphasized incoherent models of long-run equilibrium. To maintain biotechnological determinism after the transition to very short-run models of temporary and intertemporal equilibrium, neoclassical economists must adopt a theory of the short-run. The most congenial short run models to this determinism will assume all markets always clear.

3.0 Post Keynesianism Rejects Biotechnological Determinism

Post Keynesians, as I see it, reject biotechnological determinism. Here are some characteristic ideas of Post Keynesianism that, at least, are in tension with such determinism:

• An emphasis on open models.
• A view that appropriate models might vary among countries, sectors, and decades.
• An emphasis on historical time and the acceptance or development of models in which history matters.
• The adoption of models in which corporations are taken as having power to make decisions on the rate of growth and the markup of prices over costs.
• The rejection of the descriptive accuracy of the autonomous utility-maximizing consumers.
• The rejection of the natural rate of unemployment.
• The rejection of the Wicksellian concept of the natural rate of interest, in all runs.
• The acceptance of the idea that fiscal policy can be effective.

4.0 Can Mainstream Economists Reject Biotechnological Determinism?

Of course, markets do not always clear in neoclassical economics. For decades, economists have been talking about, for example, sticky prices, asymmetric information, and multiple equilibrium. Nevertheless, I am often surprised by how willing many economists who have studied such matters seem to be willing to talk as if the economy is always trending towards a unique, given long-run equilibrium. Forces that prevent the economy reaching equilibrium in the short run seem to have no effect on the long run theory. Maybe a tension exists in neoclassical economics between the formal properties of the theories that have been developed and the underlying vision of many economists.

Some argue that mainstream economics is no longer neoclassical and, at least at the research level is open to a wide variety of ideas. Some recent ideas, such as evolutionary game theory, seem compatible with outcomes emerging that cannot be calculated in a closed-form solution as uniquely determined by the givens of the model.

I think older trends, emphasizing perfect competition and instantaneous adjustment to equilibrium, are still widely prevalent among economists and how economists portray their ideas to the public. A skeptic might argue that newer trends will never replace such ideas because of their incompatibility with this underlying vision of biotechnological determinism.

5.0 Conclusion

Do different views on biotechnological determinism underlie the visions of various economists? Can contrasting views on this issue ever be settled by empirical evidence, and if so, how?

Bibliography

• Stephen A. Marglin (1984). Growth, Distribution, and Prices, Harvard University Press.

Sraffa Prices As A Linear System

Figure 1: Two Equivalent Block Diagrams for a Linear System

1.0 Introduction

I have previously gone on about complex, out-of-equilibrium phenomena arising in certain non-linear models for economics. This post provides a contrast, by defining linear. Sraffa's system of equations for prices of production, from a certain perspective¹, is an example of a linear system.

I regard the mathematical manipulations expressed in this post as fairly trivial. Nevertheless, it will not surprise me if some find it difficult to read. I do not think any such reading difficulties result solely from defects in my expository powers. Rather, I am trying to echo the sort of abstract reasoning typical of advanced mathematics courses taught at many universities. I think I only gesture here at the advantages provided by such abstractions.

2.0 Definition of "Linear"

Functions can be characterized as linear or non-linear. A function, f(), maps elements in some set to elements in another, possibly different, set. The set of possible arguments² for a function is known as the domain of the function. The set that elements of the domain are mapped into is known as the range of the function. One assumes that elements of the domain can be added together, in some sense, to obtain another element of the same set. Furthermore, each element of the domain can be multiplied by a scalar³. Last, one makes the same assumptions about the elements of the range.

The function f is linear if the following two conditions are met:

f(x₁ + x₂) = f(x₁) + f(x₂)

f(a x) = a f(x)

These equations are illustrated, respectively, by Figure 1 above and Figure 2 below. The first condition states that when a linear function is applied to the sum of two elements, the summation can equally well be calculated after applying the function to the elements being summed. The second condition states that the order of scalar multiplication and the application of the function can likewise be interchanged, with no effect on the output.

Figure 2: Two More Equivalent Block Diagrams for a Linear System

Maybe the simplest example of a linear system is the equation of a straight line going through the origin:

y = f(x) = m x,

where x and y are real numbers⁴.

3.0 Sraffa's Price Equations

The above definition would not be worth much if the only example of a linear function was a straight line through the origin in a two-dimensional Cartesian space. Accordingly, I will describe an example for a function whose argument is a vector.

Suppose an economy is observed at a point in time. And, in this economy, at the observed scale, firms have adopted n processes to produce n commodities. The j-th process is characterized by its inputs and outputs. Its inputs consist of a_0,j person-years of labor, a_1,j units of the first commodity, a_2,j units of the second commodity, and so on. Its outputs consist of b_1,j units of the first commodity, b_2,j units of the second commodity, and so on⁵. A common rate of profits, r, is also among the givens in this model. These givens allow one to set up the following system of equations for the wage, w, and prices of production⁶, p₁, p₂, ..., p_n:

(p₁ a_1,1 + ... + p_n a_n,1)(1 + r) + a_0,1 w = p₁ b_1,1 + ... + p_n b_n,1

(p₁ a_1,2 + ... + p_n a_n,2)(1 + r) + a_0,2 w = p₁ b_1,2 + ... + p_n b_n,2

.
.
.

(p₁ a_1,n + ... + p_n a_n,n)(1 + r) + a_0,n w = p₁ b_1,n + ... + p_n b_n,n

The above system of n equations in n + 1 unknowns can be conveniently expressed in matrix form:

p A(1 + r) + a₀w = p B,

where a₀ and p are row vectors and A and B are square vectors. Some manipulations yields the following matrix equation:

p [B - A(1 + r)] - a₀w = 0

These manipulations suggest the definition of a linear function.

3.1 A Linear Function

Accordingly, consider the following function:

f(p, w) = p [B - A(1 + r)] - a₀w

This function maps a vector space with the dimension n + 1 to an n-dimensional vector space. Figure 3 illustrates for the case where n is two. The components of the vector calculated by this function are the extra profits earned in each process in use. Two, almost one-line, proofs demonstrate the linearity of this function.

Figure 3: A Linear Function for a Two-Commodity Economy

3.1.1. Proof of the First Condition

By definition, the value of the function for the sum of two elements of its domain is:

f(p + q, u + v) = (p + q) [B - A(1 + r)] - a₀(u + v)

Or:

f(p + q, u + v) = p [B - A(1 + r)] - a₀u + q [B - A(1 + r)] - a₀v

Or, by the definition of the function:

f(p + q, u + v) = f(p, u) + f(q, v),

which was to be shown.

3.1.2. Proof of the Second Condition

By definition, the value of the function for an argument consisting of the product of a scalar and an element of the domain of the function is:

f(c p, c w) = (c p) [B - A(1 + r)] - a₀(c w)

Or:

f(c p, c w) = c { p [B - A(1 + r)] - a₀w}

Or, by definition,

f(c p, c w) = c f(p, w)

which, again, was to be shown.

3.2 Observations and Questions

Consider all the elements of the domain of a function that map into the zero element in the range. This subspace of the domain is called the null space⁷. Figure 4 illustrates a null space for a linear function that, generically, does not arise for the Sraffa model. The three dimensions in the figure represent the domain of the function. For a linear model, the origin is in the null space. In this case, two non-zero independent vectors, represented by the two heavy arrows not along any of the three axes, map to zero. So the plane in which these two vectors lie represents the subset of the domain which maps to zero.

Figure 4: The Subspace of Zeros of a Linear Function

Wages and prices of commodities are positive in an economically meaningful solution to Sraffa's model. Thus, the null space should contain a ray leading from the origin through the first quadrant. Furthermore, if the extension of such a ray is all of the null space, the solution of this model is unique, up to multiplication by a constant. Choosing a numeraire for measuring prices and the wage specifies a location on this ray.

The economic setting of this model suggests conditions⁸ that might lead to the desired properties of the null space:

• No coefficients of production are negative, while direct labor inputs are always positive.
• Every process requires some commodities as inputs, and produces at least some commodities.
• Every commodity is produced as an output by at least some process.
• The economy hangs together, in some sense. One cannot find two or more sets of commodities where, for instance, no commodities from the first set enter as inputs into the second set and vice versa.
• The production processes are all distinct, in some sense. Technically, no production process is a linear combination of the other processes.
• The economy produces a surplus. The quantities of commodities required as inputs can be replaced out of the outputs, with some commodity output left over.
• With a notional rescaling of processes, a set of commodities can be found that, in some sense, enter into the production of all commodities and that are being produced at a same rate of surplus production.
• The rate of profits does not exceed that maximum rate of surplus production.

More is going on here than a counting of equations and variables.

4.0 Conclusion

Sraffa, in his book, does not present his sequence of models in these abstract terms. But many comments and sections, such as the appendix on "beans", demonstrate that he was aware of the mathematical issues arising with his models. One can read Sraffa as having an interest in computability not shown in my exposition.

Finally, this post proves that the use of models in which the solution illustrates the mutual interdependence of a system of equations is simply insufficient to demonstrate that economists think of the economy as a complex, non-linear system.

Footnotes

1. If one took the wage, instead of the rate of profits, as the independent variable, Sraffa's equations would define a non-linear system. Furthermore, since Sraffa's model is open, it is consistent with non-linearities in economic relationships not in the model, such as provided by Increasing Returns to Scale.
2. In this section, arbitrary elements of the domain are represented by x, x₁, and x₂.
3. Technically, the domain and the range are each examples of a vector space, also known as a linear space. The scalars are from a field. The sets of real and complex numbers are canonical examples of a field.
4. Although the graph of an affine function, y = m x + b, is a straight line, an affine function is, technically, non-linear when the y-intercept is non-zero.
5. Since more than one commodity can be produced as output for each process, this is a model of joint production. See Chapter VII, Sections 50-52 of Production of Commodities By Means of Commodities.
6. Prices of production allow for the outputs to be redistributed among industries such that the economy can continue (re)production undisturbed.
7. For a linear function, the null space is a linear space.
8. Such conditions are more obvious for the special case of no single-product industries. I do not fully understand the issues for joint production, especially when the processes in use are chosen from a larger set of possible processes.

Warren Mosler On Front Business Page Of New York Times

Anne Lowrey provides a profile of Warren Mosler and Modern Monetary Theory. I am sitting in my favorite coffee shop, when I open my newspaper to this article. I say, "Hey, I know this guy. I once sold him a book on-line." But I did not go on about economics. I know the fellow next to me is a fan of Formula 1 racing. So I say, "He has his own car company. He makes race cars, I think." And I skim forward to the third to last paragraph, skipping over quotes from professors at the University of Missouri at Kansas City and such like, to read about Mosler Automotive, which apparently he is looking to sell.

Elsewhere

• Frances Woolley claims that, nowadays, economics is more empirically grounded and better than it used to be.
• Edward Fullbrook says that academic success in economics is furthered by publishing papers that serve best as manure and hindered by publishing serious work.
• Noah Smith describes what he calls four levels of science.

(It would be nice to have a catalog of responses to Greg Mankiw's latest vicious tomfoolery, to be published in the Journal of Economic Perspectives.)

Corporations And The Theory Of The Firm

I think the following are fairly typical aspects of a large corporation:

• Operation of more than one plant.
• Production of more than one product.
• Use of large amounts of capital goods with fixed costs.
• Production and sales in more than one country.
• Provision of stock (also known as shares) that are traded on a specified stock exchange.

I suggest the indicated work of the following economists¹ are useful to read² in attempting to understand such organizations:

• Joe Bain and Paolo Sylos Labini on Industrial Organization³.
• John Maurice Clark, especially Studies in the Economics of Overhead Costs⁴.
• John Kenneth Galbraith, especially his book The New Industrial State
• Michal Kalecki on mark-up pricing.
• Robin Marris' on managerial theories of the firm.
• Gardiner Means and Adolf Berle, especially their book The Modern Corporation and Private Property⁵
• Edith Penrose, especially her book The Theory of the Growth of the Firm.
• Herbert Simon on the theory of administration.
• Josef Steindl, who, as I understand it, was a follower of Michal Kalecki and did much work in Industrial Organization.

The theory of the firm, as taught to undergraduates, does not cover modern corporations and these economists. I do not claim that the theory cannot be expanded. Important issues include knowledge, organization, and competencies needed to expand into adjacent products and to expand the number of plants.

Footnotes

1. Some of these authors or their works I only know of through secondary literature.
2. Bruno Rizzi's 1939 book, La Bureaucratisation du Monde, occasioned an internal debate among followers of Trotsky and supposedly foretold some of the themes in some of the following works.
3. Franco Modigliani's 1958 paper, "New Developments on the Oligopoly Front", reviews an important book by each member of this pair of authors.
4. I do not want to claim Piero Sraffa showed how to correctly account for overhead costs; do corporations have sufficient data to set up his equations in their full generality? Do they not commonly adopt heuristics that sometimes, but not always, deviate from his equations?
5. As I understand it, this book deals with, among other issues, the separation of ownership and control.

Two Systems Thinking Models: Mind Your Ps and Qs

Figure 1: A Market Mediated By Quantity

1.0 Introduction

I have been examining John D. Sterman's textbook, Business Dynamics. Sterman is a chaired professor at the Sloan School of Management and director of the System Dynamics Group at the Massachusetts Institute of Technology (MIT). The System Dynamics Group was founded by Jay Forrester, and the group is continuing research in his tradition.

This systems thinking approach provides tools for visualizing the hypothetical causal relationships and structures of dynamical systems. They show models in which hypothetical causal relationships, the distinction between stocks and flows, and temporal lags can be postulated and displayed. Software for specifying model structures provides capabilities for simulating dynamical behavior. These tools are directed towards managers who may not fully understand complex dynamical systems. The diagrams are intended to package and facilitate informal discussions about models, including desired system states. Simulations for the resulting models give some understanding of possible dynamics.

Sterman's diagrams and associated tools are one approach. Researchers in related disciplines have proposed other visual languages, with varying degrees of formalism for the syntax and semantics of the elements of such diagrams. I think of system block diagrams and the Unified Modeling Language (UML), for instance. Likewise, a number of tools exist (for example, Steve Keen's Minsky system, MathWorks' Simulink, Berkeley's Ptolemy system, and tools supporting Model-Driven Architecture and Model-Driven Development) for processing corresponding system specifications for various purposes.

2.0 "Tell Me What the Wires Do"

I might as well explain a bit about selected components of what Sterman calls Causal Loop Diagram (CLD). CLDs contain curved arrows connecting variable names. The arrowheads in CLDs are annotated with either a plus or a minus sign. Arrowheads indicate causal relations. Suppose an arrowhead points from the variable X to the variable Y:

• Positive Link: If the arrowhead is labeled with a plus sign, Y increases when X increases, all else equal. In other words, ∂Y/∂X > 0.
• Negative Link: If the arrowhead is labeled with a minus sign, Y decreases when X increases, all else equal. In other words, ∂Y/∂X < 0.

A CLD may contain circles with arrows, where each circle contains either the letter B or R, indicating, respectively, either a negative (balancing) or positive (re-enforcing) loop. The dynamical behavior of a system containing a single balancing loop is to approach an equilibrium point. On the other hand, a system containing a single re-enforcing loop exhibits exponential growth. The dynamical behavior of a system containing a combination of interacting balancing and re-enforcing loops, especially if it is non-linear, is more difficult to predict without simulation.

3.0 Two of Three Models

Since Sterman's textbook is directed towards business managers, he provides some examples from economics. In Section 5.5, he presents three models of a single market:

• Demand and supply responding to price (Figure 5-26 in Sterman (2000), Figure 2 below)
• Orders and production respond to queues (Half of Figure 5-27 in Sterman(2000), Figure 1 above)
• Customer base and service quality interact (Other half of Figure 5-27 in Sterman (2000), not shown here)

Figure 2: A Market Mediated By Price

I think Sterman's model of demand and supply mediated by price mixes classical and neoclassical ideas. One should read "demand" and "supply" in Figure 2 as, by an abuse of language, actually referring to the quantity demanded and the quantity supplied. We see that this model postulates that firms increase the quantity supplied for industries in which profits are high, that is, when the price increases more above the cost of production. This is a classical idea, to be found in Adam Smith. The model also postulates that an increase in the quantity demanded puts upward pressure on price. I think how demand is conceptualized in this model, including the role of substitution in consumption, is close to how demand functions are presented in neoclassical textbooks.

Figure 1 shows a model in which firms respond more to increased demand by changes in the level of production, not by changes in price. If price were to be inserted into this model, price would be appropriately modeled by theories of administered, full-cost, or mark-up pricing.

I am not sure I agree with all of Sterman's economic examples. But the above picture of markets fits a Post Keynesian view, articulated by Michal Kalecki, that different microeconomic theories are needed to describe the prices and quantities for markets for raw materials, industrially-produced goods, and services. Do business schools provide a somewhat greater opening for non-neoclassical economics than supposedly leading economics departments?

References

• John D. Sterman (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World, Irwin McGraw-Hill

On "Substitutability"

"[The] validity [of the Cambridge Criticism of neoclassical theory] is unquestionable, but its importance is an empirical or an econometric matter that depends upon the amount of substitutability there is in the system. Until the econometricians have the answer for us, placing reliance upon neoclassical economic theory is a matter of faith. I personally have the faith; but at present the best I can do to convince others is to invoke the weight of Samuelson's authority." -- C. E. Ferguson (1969) [as quoted in Carter (2011)].

1.0 Introduction

In this post, I describe two different meanings of "substitutability", as used in the literature and economists' remarks on the Cambridge Capital Controversy¹.

2.0 Joan Robinson's Criticism

Imagine two island capitalist economies, Alpha and Beta, each in a steady state and with access to the same technology. Suppose for some reason, the distribution of income happens to be different in the two islands. Then the capitalists on the islands will, maybe, have adopted different techniques of production and be producing a different mixture of commodities for final output. Consequentially, the structure of capital goods, both in composition and in quantities, will differ between the two islands.

An (illegitimate) thought experiment is to imagine the distribution of income slowly changing from as it is on one island to the distribution on the other. One might mistakenly consider the capital equipment slowly changing through the composition appropriate to imaginary intermediate islands. This claim ignores the reality of what Joan Robinson called historical time. One is treating a process occurring in time as if it occurring in space, ignoring that past bygones are gone, and assuming no difficulties exist in getting into equilibrium.

Neoclassical² economists frequently ignore the structure of capital equipment and the plans of the entrepreneurs. One meaning of "substitutability" is the assumption that capital goods can be instantaneously taken apart and reassembled to be appropriate for whatever equilibrium is being considered. The tranverse from one equilibrium to another is abstracted from. Robinson satirized this meaning of substitutability by designating the capital good in, say, the Solow-Swan growth model with such names as "ectoplasm", "leets", and "mecanno sets". Post Keynesians, including Sraffians, are generally suspicious of this approach. (Any fans of Austrian school economists want to chime in in the comments?)

3.0 Substitutability and Smooth Microeconomic Production Functions

Another meaning relates to the smoothness of production functions. One might say substitutability exists when derivatives (including, second, third, etc. derivatives) exist for all production functions. That is, substitutability exists in these examples, but not in these ones. (But what would you say about this one, where the cost-minimizing technique varies continuously with the interest rate, and output and each capital good are produced with fixed-coefficients?)

As far as I know, capital-reversing, for example, is consistent with substitutability, in this sense of smooth production functions. I, too, will invoke the weight of Samuelson's authority, even though I reject it in the former case. I would like, however, to see an explicit numeric example.

4.0 Conclusion

I believe C. E. Ferguson was referring to my section 2 meaning of "substitutability". That is, when neoclassical economists claim that Sraffians rely on a lack of substitutability for their critique of neoclassical economics, they should not be objecting to a lack of differentiability of microeconomic production functions.

Footnotes

1. Other usages are ignored in this post. For example, J. R. Hicks' "elasticity of substitution", as used in his mistaken Theory of Wages (1932), is not treated here.
2. As far as I am concerned, "neoclassical" is a meaningful and appropriate word in this context.

References

• Scott Carter (July 2011). C. E. Ferguson and the Neoclassical Theory of Capital: A Matter of Faith, Review of Political Economy, V. 23, N. 3: pp. 339-356

Elsewhere, On Neoclassical Economics

• Noah Smith complains about the supposed overuse of the label.
• Alex Marsh comments.
• Matias Vernengo responds.
• Lars Syll responds, including in pictures. Also, see here.
• I wrote much of the wikipedia article, albeit not the introduction. And some stuff in it I now disagree with. I also wrote much of the Wikipedia article on Classical economics, and the subsection of that article is especially relevant to a Sraffian perspective on neoclassical economics.
• Daniel Kuehn shares some thoughts.
• David Ruccio comments.

Update: Added some links.

Haikus

These have been written by authors who have not acknowledged their authorship. (I have written many of them myself.)

John Maynard Keynes
Created Bretton Woods system
The theory works

Michal Kalecki
Macro with markup pricing
Empirical success

Nicholas Kaldor
Nonlinear business cycle
Generates chaos

Lorie Tarshis
Elements of Economics
Met McCarthyism

Richard Goodwin
Tenureless at Harvard
Among best of the best

John Kenneth Galbraith
The world listened
Not economists

Joan Robinson
Predicted stagflation
Bastard golden age

John Hicks
Renounced IS/LM
Post Keynesianism

Nicholas Kaldor
Defeated Milton Friedman
Endogenous money

Paul Davidson
Explains historical time
Nonergodicity

Post Keynesians
Kicked out of Rutgers
Alfred Eichner died

Wynne Godley
Invents Sectoral Balances
Predicts Crises

The genius of Keen
His splendid model
Remains unrecognized

Post Keynesianism
Destroyed Reinhardt and Rogoff
No surprises here

A Continuous Time System Block Diagram For Nicholas Kaldor

A System Block Diagram For A Business Cycle Model

In this model of business cycles, two state variables, Y(t) and K(t), represent national income and the value of the capital stock, respectively. These state variables are each specified by a differential equation. In the above block diagram, I have adopted a notation from Steve Keen. The triangles in the upper-right and lower right equate the integrals of their inputs, over time, to their outputs. In other words, the following differential equations obtain:

dY/dt = α[I(t) - S(t)]

dK/dt = I(t) - δK(t)

You can compare and contrast this continuous-time representation of a dynamical system with its analogous discrete-time version.

This is a multiplier-accelerator model that allows for the economy to normally be out of equilibrium. An economic interpretation¹ of the model is that entrepreneurs have some sort of common opinion about the level of economic activity they expect in this nation's economy. And they have an opinion about the total value of capital stock that they believe is needed to sustain that activity. When these expectations are realized, this dynamical system is in an equilibrium. The model shows that when the economy has more activity than expected, entrepreneurs tend to increase the capital stock more rapidly, and vice versa for when activity falls below the expected level. This tendency is a non-linear relationship. Maybe, the more extreme the difference between the actual level and the expected level is, the less likely entrepreneurs are to expect the actual level to continue.

Neither interest rates nor prices are modeled here. Such modeling might be justified by the claim that the income effects in the model overwhelm the effects of prices. At any rate, this model does not contain an aggregate production function. Capacity can be operated either above or below the rate that was desired when the capital equipment being evaluated was installed. If the value of the capital stock falls below the expected level, entrepreneurs tend to increase investment, and vice versa for when the value of the capital stock rises above the expected level. (I think of the depreciation of the capital stock shown in the model as an accounting heuristic, not a physical decay.)

I am not putting forth grand empirical claims. To me, this model is of mathematical interest. It illustrates how non-linear economic dynamics can be generated endogenously. A source of continuous external shocks is not needed².

Unlike in the discrete-time case, I do not see how the continuous-time model given here can generate chaos. Trajectories in the two-dimensional state space are smooth, with no gaps. They cannot intersect. So, I think, this continuous-time model can generate cycles, but not strange attractors³. Another difference between discrete-time and continuous-time systems revolves around the details of stability analysis⁴.

Anyways, the graphical specification of the Kaldor model, given in this post, is suitable for numerical exploration in Steve Keen's software, as I understand it.

Footnote

1. As I understand it, mainstream macroeconomists currently reject the rough-and-ready microfoundations I provide here. They insist on formal microfoundations, even though their preferred formal treatments are just nonsense.
2. Some more mainstream economists seem to be willing to make this points in Overlapping Generations (OLG) models. I am willing to explore the mathematics there, despite the absurdity of assuming investment is driven by intertemporal utility-maximization of consumption.
3. The logistic equation is an example of a one-dimensial, discrete-time, chaotic dynamical system. Off-hand, I cannot think of a continuous-time chaotic system with less than three dimensions.
4. In discrete-time systems, one analyzes the stability of a fixed point by analyzing whether the eigenvalues of the system, linearized around the fixed point, are inside or outside the unit circle in the complex plane. In a continuous-time system, one looks to see if the eigenvalues are to the left or the right of the complex axis, if I recall correctly.

Marx On Ricardo

Karl Marx wrote a lot about David Ricardo's economics. Here is some of what he had to say in Theories of Surplus Value:

Ricardo starts out from the determination of the relative va1ues (or exchangeable values) of commodities by “the quantity of labour”.  (We can examine later the various senses in which Ricardo uses the term value.  This is the basis of Bailey’s criticism and, at the same time, of Ricardo’s shortcomings.)   The character of this “labour” is not further examined, If two commodities are equivalents—or bear a definite proportion to each other or, which is the same thing, if their magnitude differs according to the ||524| quantity of “labour” which they contain—then it is obvious that regarded as exchange-values, their substance must be the same.  Their substance is labour.  That is why they are “values”.  Their magnitude varies, according to whether they contain more or less of this substance.  But Ricardo does not examine the form—the peculiar characteristic of labour that creates exchange-value or manifests itself in exchange-values—the nature of this labour.  Hence lie does not grasp the connection of this labour with money or that it must assume the form of money.  Hence he completely fails to grasp the connection between the determination of the exchange-value of the commodity by labour-time and the fact that the development of commodities necessarily leads to the formation of money.  Hence his erroneous theory of money.  Right from the start he is only concerned with the magnitude of value, i.e., the fact that the magnitudes of the va1ues of the commodities are proportionate to the quantities of labour which are required for their production.  Ricardo proceeds from here and he expressly names Adam Smith as his starting-point (Chapter I, Section I).

Ricardo’s method is as follows: He begins with the determination of the magnitude of the value of the commodity by labour-time and then examines whether the other economic relations and categories contradict this determination of value or to what extent they modify it.  The historical justification of this method of procedure, its scientific necessity in the history of economics, are evident at first sight, but so is, at the same time, its scientific inadequacy.  This inadequacy not only shows itself in the method of presentation (in a formal sense) but leads to erroneous results because it omits some essential links and directly seeks to prove the congruity of the economic categories with one another.

Historically, this method of investigation was justified and necessary.  Political economy had achieved a certain comprehensiveness with Adam Smith; to a certain extent he had covered the whole of its territory, so that Say was able to summarise it all in one textbook, superficially but quite systematically.  The only investigations that were made in the period between Smith and Ricardo were ones of detail, on productive and unproductive labour, finance, theory of population, landed property and taxes.  Smith himself moves with great naïveté in a perpetual contradiction.  On the one hand he traces the intrinsic connection existing between economic categories or the obscure structure of the bourgeois economic system.  On the other, he simultaneously sets forth the connection as it appears in the phenomena of competition and thus as it presents itself to the unscientific observer just as to him who is actually involved and interested in the process of bourgeois production.  One of these conceptions fathoms the inner connection, the physiology, so to speak, of the bourgeois system, whereas the other takes the external phenomena of life, as they seem and appear and merely describes, catalogues, recounts and arranges them under formal definitions.  With Smith both these methods of approach not only merrily run alongside one another, but also intermingle and constantly contradict one another.  With him this is justifiable (with the exception of a few special investigations, [such as] that into money) since his task was indeed a twofold one.  On the one hand he attempted to penetrate the inner physiology of bourgeois society but on the other, he partly tried to describe its externally apparent forms of life for the first time, to show its relations as they appear outwardly and partly he had even to find a nomenclature and corresponding mental concepts for these phenomena, i.e., to reproduce them for the first time in the language and [in the] thought process.  The one task interests him as much as the other and since both proceed independently of one another, this results in completely contradictory ways of presentation: the one expresses the intrinsic connections more or less correctly, the other, with the same justification—and without any connection to the first method of approach—expresses the apparent connections without any internal relation.  Adam Smith’s successors, in so far as they do not represent the reaction against him of older and obsolete methods of approach, can pursue their particular investigations and observations undisturbedly and can always regard Adam Smith as their base, whether they follow the esoteric or the exoteric part of his work or whether, as is almost always the case, they jumble up the two.  But at last Ricardo steps in and calls to science: Halt!  The basis, the starting-point for the physiology of the bourgeois system—for the understanding of its internal organic coherence and life process—is the determination of value by labour-time.  Ricardo starts with this and forces science to get out of the rut, to render an account of the extent to which the other categories—the relations of production and commerce—evolved and described by it, correspond to or contradict this basis, this starting-point; to elucidate how far a science which in fact only reflects and reproduces the manifest forms of the process, and therefore also how far these manifestations themselves, correspond to the basis on which the inner coherence, the actual physiology of bourgeois society rests or the basis which forms its starting-point; and in general, to examine how matters stand with the contradiction between the apparent and the actual movement of the system.  This then is Ricardo’s great historical significance for science.  This is why the inane Say, Ricardo having cut the ground from right under his feet, gave vent to his anger in the phrase that “under the pretext of expanding it” (science) “it had been pushed into a vacuum”.  Closely bound up with this scientific merit is the fact that Ricardo exposes and describes the economic contradiction between the classes—as shown by the intrinsic relations—and that consequently political economy perceives, discovers the root of the historical struggle and development.  Carey (the passage to be looked up later) therefore denounces him as the father of communism.

I find the following, at least, of interest in this long passage:

• Marx here writes about "the connection as it appears in the phenomena of competition", "the external phenomena of life, as they seem and appear", "externally apparent forms of life". I think these phrases echo what Marx elsewhere describes as "vulgar political economy", commodity "fetishism", and the "illusions" created by competition.
• Marx criticizes Ricardo for only being concerned with "the magnitudes of values of commodities", not with the "peculiar character of labour that ... manifests itself in exchange values". I think this supports those who do not see a (great) contradiction between volumes 1 and 3 of Capital.
• Marx talks about the connection of labor values with money. I like interpretations or solutions of Marx's transformation problem that relate value to some abstract measure of the value of the output of a capitalist economy, namely:
  • Those based on Sraffa's standard commodity
  • Foley and Duménil's new interpretation, which focuses on the Monetary Expression of Labor Time (MELT).
• I quite like that "Halt!" I think it fair to say that Marx saw himself following and transcending Ricardo in exploring "the obscure structure of the bourgeois economic system", "the intrinsic relations", "the inner coherence, the actual physiology of bourgeois society".