Friday, May 31, 2013

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".

Monday, May 27, 2013

Kalecki And Sraffa: Compatible?

Two Great Economists
1.0 Introduction

Michal Kalecki set out macroeconomic models in which markup pricing was common. Economists in this tradition rarely explore the effect of inter-industry flows on prices. Sraffians, on the other hand, usually specify prices, at least, to a first approximation, in a model of full competition. Can work in the traditions of Michal Kalecki and of Piero Sraffa be usefully combined?

2.0 A Model

Consider an economy in which n commodities are produced by n (single-product) industries. Inter-industry flows are described by a nxn matrix A, where ai, j is the amount of the ith commodity used as input per unit output in the jth industry, at the given level of output of the jth industry. Labor inputs are described by the row vector a0, where a0, j is the quantity of labored hired in the jth industry per unit output, at the given level of output of the jth industry.

The positive constants m1, m2, ..., mn represent barriers to entry among the different industries. The going rate of profits is earned in industries in which mj is unity. Industries in which mj exceeds unity have high barriers to entry. Perhaps a large scale of production is needed to operate profitably in such an industry. Industries with mj less than unity are backwards, in some sense. At any rate, they earn less than the going rate of profits. These constants lie along the principal diagonal of the diagonal matrix M. That is, mi, j is mj, for i equal to j. And mi, j is zero, for i unequal to j.

The row vector p represents prices, where pj is the price of a unit quantity of the output of the jth industry. Suppose w represents the wage, and r represents The rate of profits.

The matrix A, the row vector a0, the diagonal matrix M, and one of the distributive variables (say, the rate of profits r) are the given data for this model. The prices p and the remaining distributive variable (for example, wages w) are the unknowns to be found. One can set out the (modified) Sraffa equations for prices:

(p A M + a0 w)(1 + r) = p

(I think models of full cost prices typically show markups being earned on both labor and material costs.) A numeraire should be specified. For example, one can set out the following normalization:

p1 + p2 + ... + pn = 1

Likewise, the markups are only specified by the model, so far, up to a scalar multiple. I suggest the following normalization condition for markups:

m1 x m2 x ... x mn = 1

Presumably this model can be extended, as in Sraffa (1960) to embrace fixed capital, land, joint production in general, and an analysis of the choice of technique.

3.0 Conclusion

The above has set out a model of prices of production. This model provides a framework for analyzing both the effects of inter-industry flows on prices and of markup pricing, arising from barriers to entry and other hindrances to full competition. The compatibility of some such model with both Kaleckian macroeconomics and the larger research agenda of Sraffa remains to be argued. Likewise, I have not shown the usefulness of this sort of model in empirical explanations of actual capitalist economies. One important issue in such discussions would probably be the applicability of models of prices of production to industries in which the planned operating level is less than full capacity.

This post should really have a bibliography, since the question of the compatibility of the economics of Kalecki and of Sraffa has been raised before. I gather that Paolo Sylos Labini, in some unpublished work in the 1960s, set out and analyzed a model rather like the above.

Friday, May 24, 2013

A System Block Diagram For Nicholas Kaldor

A System Block Diagram For A Business Cycle Model

I have previously presented a (replication of an) analysis of a discrete-time formalization of Kaldor's Keynesian model of business cycles. The system block diagram, above, is another way of specifying the model. This diagram, I think, helps make certain characteristics of the system more readily apparent:

  • The non-linear component of the system, that is, the inverse tangent function, stands out.
  • Only two state variables, national income (Yt) and the value of the capital stock (Kt), need to be specified for this system.
  • The ordered pair (Yt, Kt) = (μ, σμ/δ) is a fixed point of the function specified by this system.

I am not sure about the use of one-step time lags to represent iteration for the Kaldor model. Presumably, Steve Keen has thought about this question for his software.

I think Keynes' General Theory can be read as leading towards systems thinking prior to its development in other disciplines.

Tuesday, May 21, 2013

Our Rulers Do Not Know Why They Dislike Government Debt

Table 3: The Perceived Importance of Problems Facing U.S.A.
Problem% Wealthy Saying
"Very Important"
Budget deficits87
International terrorism74
Energy supply70
Health care57
Child poverty56
Loss of traditional values52
Trade deficits36
Climate change16

A few weeks ago, Paul Krugman mentioned a recent paper by Page, Bartels, and Seawright. I believe it is this one:

This paper reports a pilot study on the political views of the wealthiest Americans. The authors gathered data in interviews with residents drawn from a sample of the very wealthy in Chicago. Page et al. motivate their interest in the policy preferences of wealthy Americans by noting recent research demonstrating that the vast majority of the country has little to no influence on policy decisions made in the Federal government. They hope to expand their research to a national sample in the future.

They report views on many areas of public policy. Generally, our rulers are reactionary and the opposite of benevolent. Business backgrounds in finance or industry, inherited wealth or "earned" wealth, were not correlated with differences in views. The sample size might be too small to provide enough power to distinguish, among the wealthy, effects of where they sit on where they stand. Professionals, mainly lawyers and doctors, tended to be slightly less reactionary.

Above, I reproduce Table 3 from this paper. Those surveyed "think" government budget deficits are the biggest problem facing the United States. One might suggest that lowering such deficits could be only an intermediate, instrumental goal. But towards what end? Page et al. note that they do not seem worried about deficits leading to high rates of inflation; notice how low inflation is as a worry. Page et al. suggest that the wealthy have bought into the "crowding out" argument. Of course, theoretically, supply and demand for savings does not determine interest rates. Empirically, the crowding out argument makes no sense in the current conjuncture either.

I have an old explanation of this puzzle. Paul Krugman recently cited Michal Kalecki's explanation of why capitalists dislike increased government spending in depressions, even though such fiscal policy successfully dampens downswings in business activity. Krugman is not just depending on the capability of Kalecki's explanation to make sense of history long post-dating Kalecki's contribution. Krugman is also aware of the quantitative survey data I cite above.

Sunday, May 12, 2013

Planning Empirically Superior To Markets: The Fixed Microwave Spectrum

This post notes the existence of the following article:

This article is about the microwave spectrum, in the range from 3 to 100 Gigahertz, with an emphasis on the commercial use of the low end of this range. From World War II until fairly recently, conflicts and potential interference in the use of the microwave spectrum were resolved by discussions among engineers working for the users of the conflicting resources. Nowadays, conflicts are resolved by auctioning off the spectrum. (Presumably, these auctions are inspired by the work for which the so-called Nobel prize in economics was awarded last year.) And, Lazarus argues, these auctions have failed to work as well as the previous regime did.

Lazarus provides a popular survey of some technical characteristics of microwave radiation. Microwave is used for point-to-point communication, not for broadcast. This use often parallels a physical infrastructure in an area. The auctions typically leave the frequencies put up for auction underused, or so Lazarus argues.

Friday, May 03, 2013

A Near-Term Goal

I would like to develop a numeric example with:

  • Smooth production functions, and
  • Properties analogous to the ones highlighted in this example.

One of the parameters of the utility functions in this example expresses the willingness of consumers to defer consumption. A greater willingness to defer consumption supposedly represents a greater supply of "capital", in some sense. In a "perverse" case, this greater supply, all else the same, is associated with a long run equilibrium with a higher equilibrium interest rate.

I do not think that the "perversity" I am trying to illustrate depends on the distinction between discrete technologies and smooth production functions. I am aware, however, of a theorem that applies to a technology with smooth production functions, but not to discrete technology:

Theorem: Consider an economy in which all produced commodities are basic, in the sense of Sraffa, for all feasible techniques. And suppose the production of one commodity can be described by a continuously differentiable production function. Then this economy cannot exhibit reswitching of techniques.

The relevance of this theorem to my goal is not clear. I am willing to consider examples with non-basic goods. So examples should be possible to construct with smooth production functions and reswitching. But I do not even need reswitching. I am merely looking for capital-reversing. And I do not even insist that real Wicksell effects be positive. I will be content with positive price-Wicksell effects swamping negative real Wicksell effects.

Maybe the kind of example I am seeking is set out in a end-of-the-chapter problem in Heinz D. Kurz and Neri Salvadori's 1997 book, Theory of Production: A Long-Period Analysis (Cambridge University Press).

By looking at the convexity of the wage-rate of profits curves on the frontier, one can read off the direction of price Wicksell effects. And I have already shown that an example can be created with Cobb-Douglas production functions and positive price Wicksell effects. I have yet to examine the relative sizes of price and real Wicksell effects in the example, derive conditions on their directions and sizes, or create a numeric example satisfying those conditions.

Eventually, I would like to explore the dynamics of non-stationary equilibrium paths in such a model built on unarguably neoclassical premises. The point is to continue an internal critique of neoclassical microeconomics, not to describe actually existing capitalist economies.