Wednesday, January 01, 2025


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

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

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

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

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

Wednesday, October 21, 2020

Sraffa's PoCbMoC At 60


I finally watched Production of Commodities at 60. Our host and moderator is Matias Vernengo. Seminar participants are Franklin Serrano, Antonella Palumbo, and Ed Nell, who present in that order. They take questions at the end.

I cannot recall who made these points; they generally agreed. But here are some I noted. Sraffa is not only about an internal critique of marginalist theory, but a setting out of an alternative theory. This is a rediscovery of the classical theory of value.

Sraffa's theory is not restricted to perfect competition. Paul Sweezy was wrong to think that the advent of monopoly capitalism meant that only qualitative assertions could be made about value.

Ed Nell talks about linear programming, as contrasted to prices that support the reproduction of the economy. He is probably thinking of an appendix in Pasinetti (1977). I take his point, but I and others have shown that a LP can be used to formalize prices of reproduction.

In the Q and A at the end, Vernengo reads a question about whether Sraffa was inspired by Marx's schemes of simple and expanded reproduction in his development of his first and second system of equations equations. Like the seminar participants, I do not have a strong opinion on this question. I wish the scholars debating this would look into Sraffa's reading of the french translation of Kautsky's edition of Theories of Surplus Value. What is different about the later more complete edition? Does Sraffa's copy have marginal notes?

Another question concerns the relevance of steady state growth paths. Come to think of it, Serrano's remarks about a more general, looser concept might draw on his work on the supermultiplier, which he otherwise does not talk about. I think it was Nell who raises the point that Robinson did not think much of the analysis of the choice of technique. When one technique replaces another over historical time, this is not a choice with given knowledge of alternative techniques. What would Robinson think of my merging the two by considering, say, perturbations of coefficients of production in logical time? Probably not much.

Anyways, this is just a selection of topics from a far-ranging discussion.

Thursday, October 15, 2020

Non-Uniform Rates Of Profits

This post presents a limited account of the history of analyzing prices of production with non-uniform rates of profits. I start from developments in post Sraffian price theory. D’Agata (2018) and Zambelli (2018b) have argued that Sraffian prices of production can still be defined when rates of profits have regular and persistent variations among industries. Barriers to entry or idiosyncratic properties of investment can result in such variations. Steedman (1981) presents the first formulation in post Sraffian price theory that I know of in English with systematic variations of the rate of profits among industries. Roemer (1981: 23-29) provides microfoundations for modeling imperfect competition in linear production models. He assumes different capitalists have different information sets; they only know of some of the production processes that are available. He argues that this can lead to specified ratios of rates of profits among industries. Cogliano et al. (2018) and Screpanti (2019) are some more Marxist contributions along the same lines.

Adam Smith (1776) called 'natural prices' what I, following Marx, am calling prices of production. He explained differences in rates of profits among industries as arising both in competitive conditions and as a result of barriers to entry. Book 1, Chapter X of The Wealth of Nations is titled 'Of wages and profits in the different employments of labour and stock'. According to Smith, the rate of profits is systematically higher in industries thought disagreeable or disgraceful. It is also higher in less risky investments, because capitalists overvalue their chance of gain and undervalue the chance of loss. (Smith also explained systematic differences in wages from these same causes. Typically, in my approach:

"We suppose labour to be uniform in quality or, what amounts to the same thing, we assume any differences in quality to have been previously reduced to equivalent differences in quantity so that each unit of labour receives the same wage" (Sraffa 1960: 11).))
Smith argues that for natural prices to obtain, employments must be well-known and long established in each neighborhood. Policy in European countries, according to Smith, restricted competition in some employments and encouraged excessive employments in others. Furthermore:

"It is to prevent this reduction of price, and consequently of wages and profit, by restraining that free competition..., that all corporations, and the greater part of corporation laws, have been established" (Smith 1776).

(This chapter contains another well-known quotation:

"People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices" (Smith 1776).)

David Ricardo and other classical economists accepted Smith’s account of the causes of non-uniform profits and wages.

Many groups of economists during the twentieth century developed theories of oligopoly and analyzed the effects on prices and the rate of profits of barriers to entry. Edward Chamberlin (1958) and Joan Robinson (1933) put forth almost simultaneously their theories of monopolistic and imperfect competition. Robinson drew on the earlier work of Sraffa (1926). These works clarified, to some extent, the assumptions needed for the neoclassical theory of perfect competition.

Some were inspired by empirical research. The Oxford Economists’ Research Group was set up in the 1930s. As part of the group’s research, Hall and Hitch (1939) found, in interviews with businessmen, that firms do not set prices based on marginal cost and marginal revenue. Michal Kalecki (1965) took these findings in stride and developed a theory of markup pricing as a microfoundation for his independently developed Keynesian macroeconomics. Perhaps some of my work can be seen as a partial answer to Steedman's questions for Kaleckians (Steedman 1992).

Old industrial organization, as developed by Joe Bain (1956) and Paolo Sylos Labini (1969), (Modigliani (1958) is a prescient survey.) rediscovered a classical notion of competition and a corresponding theory of oligopoly. Free competition is about the absence of barriers to entry, in contrast to the marginalist notion of perfect competition, in which managers of firms take prices as given.

Since I am interested in the labor theory of value, I want to mention the treatment of oligopoly and monopoly by economists associated with the Monthly Review. (For example, Sweezy (1942), Baran (1957), and Baran and Sweezy (1966).) As I read them, oligopolies and monopolies present a challenge to maintaining a quantitative theory of prices:

"Under conditions of monopoly, exchange ratios do not conform to labour-time ratios, nor do they stand in a theoretically demonstratable relation to labor-time ratios as is the case with prices of production." (Sweezy 1942: 270)

Baran (1957) is a Marxist who, as a consequence of his understanding of the importance of the role of monopoly, drops talk of 'surplus value' for the more qualitative concept of the 'surplus'. At the high level of abstraction of my work, however, this attitude seems unjustified.

Managerial theories of the firm (Marris (1964), Eichner (1973 and 1976), Harcourt and Kenyon (1976), and Wood (1975), for example. See also Penrose (1980).) were developed during the 1960s and 1970s. In these theories, firms set their markup over cost to generate internal funds to, in combination with external finance, fund investment plans to achieve a target rate of growth. They strive to achieve a normal rate of profits at a planned rate of capacity usage.

The research briefly summarized above has been quite influential, particularly among non-mainstream economists, to this day. For my purposes, I ignore distinctions among behavioral and managerial theories of the firm, administrated prices, full cost prices, normal cost prices, theories of the degree of monopoly, and markup pricing. (Lee (1999) emphasizes the distinctiveness of the theories of administered, normal cost, and markup price theories.) Rather, ratios of rates of profits among industries are taken as given parameters in defining prices of production.

This post is basically an abstract from something I may never publish.

Monday, October 12, 2020

Can We Hear Phil Mirowski In The Media Talk About Paul Milgrom And Robert Wilson?

The 2020 "Nobel Prize" in economics goes to Paul Milgrom and Robert Wilson. I suppose it is nice that economists acknowledge that markets are not natural entities but need to be constructed. For example, consider the Federal Communications Commission auction of the microwave spectrum.

The 2012 "Nobel Prize" went to Alvin Roth and Lloyd Shapley. The 1996 "Nobel Prize", to William Vickrey (a Post Keynesian, by the way) was also for acution theory. The 2002 prize went to Daniel Kahneman and Vernon Smith. Smith's work included experiments with markets constructed in the laboratory.

I do not know much about this field. But I am hoping some journalists know of Philip Mirowski, an expert on the history of information in economics, and get him to comment on the award this year.

Saturday, October 10, 2020

A Fluke Case For Requirements For Use

Figure 1: Prices of Production
1.0 Introduction

This post presents a new kind of fluke case in the analysis of the choice of technique, at least new to me. I call this a pattern for requirements for use, and it can arise only in a case of joint production. My graphs in this post have some incomprehensible notation, since I am currently exploring perturbing parameters, in line with my research agenda. I know that perturbing the requirements for use removes the indeterminancy in this example.

2.0 The Givens

For this example, the data consist of the available technology and the proportions in which the two produced commodities, corn and silk, enter into the commodity basket specified by the requirements for use. I also choose a numeraire. The example is a perturbation of problem 8.2 in Kurz and Salvadori (1995).

Table 1 specifies a constant returns-to-scale technology. In each of three processes known to managers of firms at a given time, laborers work with inputs of corn and silk to produce outputs of corn, silk, or both. The inputs are completely used up in producing the output, and all three processes are assumed to take a year to complete. Since two commodities are produced in this numerical example, a technique consists of at most two processes. Table 2 lists the techniques and the processes corresponding to each technique.

Table 1: Coefficients of Production for The Technology
Labor1 Person-Yr.1 Person-Yrs(e/16) Person-Yr.
Corn1 Bushel1 Bushel1 Bushel
Silk1 Sq. Meter1 Sq. Meter1 Sq. Meter
Corn3 Bushels5 Bushels0 Bushel
Silk3 Sq. Meters0 Sq. Meter5 Sq. Meters

Table 2: Techniques of Production
Alpha(I), (II)
Beta(I), (III)
Gamma(II), (III)

The requirements for use are such that equal quantities of corn and silk are required. The numeraire consists of a commodity basket of one bushel corn and one square meter of silk.

3.0 Quantity Flows

Which techniques can satisfy the requirements for use? Suppose, contrary to the specification, that requirements for use specified that more bushels of corn be supplied than square meters of silk. The Alpha technique technique could satisfy these requirements for use, with Process I and Process II both being operated at a positive level of operations. As the requirements for corn declined, the relative level of operation of Process II would decline. The Alpha technique satisfies the given requirements for use with Process II operated at a level of zero. This is a corner case in which Process II still contributes an equation to the price system.

By a symmetric argument, the Beta technique can also satisfy the requirements for use. Process III is operated at a level of zero in the Beta techniquye.

The Gamma technique can satisfy any composition of the requirements of use, as in the theory of single production. So it can satisfy the requirements for use in this case, too.

The Delta technique can satisfy any requirements for use, as well. However, when the requirements for use specify an unequal number of bushels corn and square meters of silk, one commodity is in excess supply and its price of production is zero.

Neither the Epsilon nor the Zeta technique can satisfy the requirements for use when the net output must contain a positive quantity of both commodities.

4.0 Prices of Production

But being feasible, in the sense that a technique can satisfy the requirements for use, is not sufficient for a technique to be cost-minimizing. Prices of production must be considered, as in models of the production of commodities with single production. Prices of production vary with distribution and the technique. Figure 1, at the top of this post, graphs the price of corn for the three techniques which contribute two equations, in addition to the equation specifying the numeraire, to determine the four price variables (price of corn, price of silk, the wage, and the rate of profits).

4.1 The Alpha Technique

Suppose the Alpha technique is in operation. The wage can range from zero to two numeraire units per person-year. Figure 2 shows that the Alpha technique is not cost-minimizing at low rates of profits, but is cost-minimizing at high rates of profits. If, at low rates of profits, Process III replaces I, the Gamma technique will be adopted. If it replaces Process II, the Beta technique is adopted. But the Beta technique is not cost-minimizing at low rates of profits. (In a model of single production, it is unambiguous which process is replaced when a new process is introduced into a technique.)

Figure 2: Extra Profits with Prices for the Alpha Technique

4.2 The Beta Technique

On the contrary, suppose the Beta technique is in operation. Figure 3 shows that this technique is cost-minimizing only at high rates of profits. At low rates of profits, firms will have an incentive to operate Process II. If they replace Process III by Process II, firms will be operating the Alpha technique. The above analysis has shown that the Alpha technique would not be cost-minimizing in this range of the rate of profits. If Process I is replaced by Process II, firms would be operating the Gamma technique.

Figure 3: Extra Profits with Prices for the Beta Technique

4.3 The Gamma Technique

The Gamma technique is cost-minimizing at low rates of profits. Figure 4 shows extra profits for prices for the Gamma technique. Both the Alpha and the Beta technique are cost-minimizing at high rates of profits. Extra profits can be made in operating Process I at Gamma prices for high rates of profits. Firms would find it profitable to replace either Process III or Process II, resulting in either the Alpha or the Beta technique, respectively.

Figure 4: Extra Profits with Prices for the Gamma Technique

4.4 The Delta Technique

I am going to present the Delta technique in more detail. For Process I to neither make extra profits nor to incur extra costs, the following equality must obtain.

(p1 + p2)(1 + r) + w = 3 p1 + 3 p2

The specification of the numeraire yields the following equation:

p1 + p2 = 1

For the Delta technique to be cost-minimizing, the two equations above must hold, extra profits must not be obtainable in operating Process II, and extra profits must not be obtainable in operating Process III.

Prices drop out of the equation arising out of the requirement that Process I neither obtains extra profits nor incurrs extra costs. The wage is an affine function of the rate of profits:

w = 2 - r

The above wage curve is identical with the wage curves for the Alpha and the Beta techniques.

For the Delta technique to be cost-minimizing, firms must not be able to obtain extra profits in operating Process II. This condition yields an inequality:

p1 ≤ 1 + r + w

Substituting the wage curve and re-arranging terms yields an upper bound on the price of corn:

p1 ≤ 3/5

That is, the price of corn cannot exceed the price of corn falling out of the Alpha technique. This inequality is shown by the upper bound of the shaded region in Figure 1 at the top of this post.

The condition that firms cannot obtain extra profits in operating Process III also yields an inequality:

p2 ≤ 1 + r + (e/16) w

Or the price of corn cannot fall below a lower bound:

(1/80)[64 - 2 e - (16 - e)rp1

This inequality is shown by the lower bound of the shaded region in Figure 1.

The Delta technique can be consistent with cost-minimizing for any price of corn in the shaded region, including the boundaries. The two constraints combined impose a lower bound of the rate of profits:

[2 (8 - e)]/(16 - e) ≤ r

The lower bound on the rate of profits is the rate of profits at the switch point.

As with the Alpha, Beta, and Gamma techniques, one can plot extra profits versus the rate of profits for all processes, given the price system for the Delta technique. Since the Delta technique has an extra degree of freedom, one must choose a price, as well as, say, the rate of profits for such an analysis. Figure 5 shows such a graph for a price of corn of 3/5 numeraire units per bushel. The switch point here is at the same rate of profits as for the switch point shown in Figures 2 and 3. For rates of profits below the switch point, firms will want to adopt the Gamma technique. For rates of profits above the switch point, the Delta technique is cost-minimizing, but not uniquely so. Firms would also be willing to adopt the Alpha technique.

Figure 5: Extra Profits with One Set of Prices for Delta

But suppose the price of corn happens to be 1/2 numeraire units per bushel. Figure 6 plots extra profits in the three processes against the rate of profits. Firms will no longer be willing to choose to operate Process II along side Process I for some distribution of income. Costs exceed revenues for Process II, whatever the rate of profits.

Figure 6: Extra Profits with Another Set of Prices for Delta

For low rates of profits, the Delta technique is not cost-minimizing; firms will want to adopt the Beta technique. The "switch point" in Figure 6 is to the right of the switch point shown in all the other graphs in this post. From Figure 3, we know the adoption of the Beta technique is not the end of the story if the rate of profits lies below the rate of profits in the original switch point. For rates of profits between the two "switch points", prices must adjust until no extra profits can be obtained by operating the Beta technique. For rates of profits above the new "switch point", the Delta technique is uniquely cost minimizing at these prices and distribution of income. The Beta and Delta techniques are both cost-minimizing only at the new "switch point".

4.5 Summary

I find the possibilities in joint production confusing. I am fairly convinced of the above analysis, but I would not be surprised if my exposition could be improved. Anyway, here is a summary of the analysis of the choice of technique for this numerical example:

  • When the rate of profits is smaller than the rate of profits at the switch point (or, equivalently, the wage is greater than the wage at the switch point), the Gamma technique is uniquely cost-minimizing. Prices are determined, given, say, the wage.
  • When the rate of profits is larger than the rate of profits at the switch point (or the wage is lower than the wage at the switch point), the Alpha, Beta, and Delta techniques can all be cost-minimizing. Prices are indeterminate, with the price of corn confined to lie in the limits shown in Figure 1 by the curves for the Alpha and Beta techniques. Processes II and III in the technology are each operated at a level of zero, whatever the technique.
  • When the rate of profits and the wage are as at the switch point, the Alpha, Beta, Gamma, or Delta technique are all cost-minimizing. Prices are determined, with a bushel corn priced at 3/5 numeraire units and a square meter of silk at 2/5 numeraire units.

5.0 Conclusion

This is a fluke case. If the proportions in which corn and silk enter into the commodity basket specified by requirements for use are varied at all, the indeterminancy of prices associated with a low wage vanishes. If bushels of corn exceeds square meters of silk in requirements for use, the Alpha and Gamma techniques are feasible. The Beta technique cannot satisfy the requirements for use. The Delta technique can satisfy the requirements for use, with an excess supply of silk at a price of zero. But then extra profits would be available by operating the second process. So only the Alpha or Gamma technique would be cost-minimizing, depending on income distribution.

Wednesday, October 07, 2020

Origins of Selection from the Prision Notebooks?

This is C27 in Sraffas archives.

97 Fortis Green
London N2
Tudor 0214

6th August 1966

Dear Piero,

I do not know whether you know Roger Simon, who is Secretary of the Labour Research Department. At all events he is a great admirer and enthusiast of Gramsci. Thanks to his initiative, plans are afoot (in which I too am collaborating) to publish a new volume of Gramsci's works translated into English and Lawrence & Wishart have agreed, in principle, to undertake publication.

We would very much welcome views and suggestions from you on how this should be done. The general idea at present is a bigger book than the L & W. 1957 translation (which is now out of print), including, if appropriate, passages already translated on that occasion. One line of thought that we are pursuing is that the volume should comprise mainly longer writings from the Notebooks and should be so presented that, if successful, it could be followed by further volumes, with the possible aim of ultimately translating all Gramsci's works. It would be good if the publication of this volume could sow the seeds of a growing interest in and knowledge of this outstanding political thinker, and so it is probably worth giving quite a bit of thought as to how this first step in that direction should be taken.

One problem is the choice of a translator; the ideal might be a young don specialising in twentieth century Italy and an admirer of Gramsci who would be keen to make a scholarly study of him, his times and his work. Do you know any such person?

Also do you by any chance know, or know anything of, Gwyn A. Williams who wrote a very interesting and scholarly article on Gramsci in the Journal of the History of Ideas, 1960, and who was at that time at the University College of Wales, Aberystwyth?

Are there other Gramsci scholars known to you?

I hope that we may have a chance of meeting some time in the Autumn.

With best wishes


Stephen Bodington

Piero Sraffa Esq., M. A.,
Trinity College,

  • Antonio Gramsci (1971) Selections from the Prison Notebooks (Quintin Hoare and Geoffrey Nowell Smith ed. and trans.), London: Lawrence & Wishart

Saturday, September 26, 2020

Keynes and Henderson Create A Qualitative Multiplier

In 1929, John Maynard Keynes and Hubert D. Henderson wrote, Can Lloyd George Do It? The Pledge Examined. This was published by The Nation and Athenaeum and is an examination of the pledge by the leader of the Liberal party, if elected, to dramatically reduce the amount of unemployment in Great Britain. (I was inspired to look up this work while reading Zachary Carter's new book.)

Chapter VI of Keynes and Henderson is concerned with "How Much Employment Will the Liberal Plan Provide?" The direct employment for each million pounds can be quantified. The authors divide the resulting indirect employment into two types. The first, in the industries that directly and indirectly supply road-building, housing, and so on, Keynes and Henderson think can be quantified:

VI.2 The Importance of Indirect Employment

"...There is nothing fanciful or fine-spun about the proposition that the construction of roads entails a demand for road materials, which entails a demand for labour and also for other commodities, which, in their turn, entail a demand for labour. Such reactions are of the very essence of the industrial process. Why, the first step towards a right understanding of the economic world is to realise how far-reaching such reactions are, to appreciate how vast is the range of trades and occupations which contribute to the production of the commonest commodities. That a demand for a suit of clothes implies a demand for yarns and tops, and so for wool; that the services of farmers, merchants, engineers, miners, transport workers, clerks, are all involved - this is the A B C of economic science...

Generally speaking, the indirect employment which schemes of capital expenditure would entail is far larger than the direct employment. This fact is one of the strongest arguments for pressing forward with such schemes; for it means that the greater part of the employment they would provide would be spread far and wide over the industries of the country. But the fact that the indirect employment would be spread far and wide does not mean that it is in the least doubtful or illusory. On the contrary, it is calculable within fairly precise limits..."

The second type of indirect employment results from the multiplier effects on aggregate demand of an increase in government spending. At this time, Keynes did not think these indirect effects could be estimated ahead of time, even though he considered them of immense importance:

VI.3 The Cumulative Force of Trade Activity

"But this is not the whole of the story. In addition to the indirect employment with which we have been dealing, a policy of development would promote employment in other ways. The fact that many workpeople who are now unemployed would be receiving wages instead of unemployment pay would mean an increase in effective purchasing power which would give a general stimulus to trade. Moreover, the greater trade activity would make for further trade activity; for the forces of prosperity, like those of trade depression, work with a cumulative effect. When trade is slack there is a tendency to postpone placing orders, a reluctance to lay in stocks, a general hesitation to go forward or to take risks. When, on the other hand, the wheels of trade begin to move briskly the opposite set of forces comes into play, a mood favourable to enterprise and capital spreads through the business community, and the expansion of trade gains accordingly a gathering momentum.

It is not possible to measure effects of this character with any sort of precision, and little or no account of them is, therefore, taken in 'We Can Conquer Unemployment." But, in our opinion, these effects are of immense importance. For this reason we believe that the effects on employment of a given capital expenditure would be far larger than the Liberal pamphlet assumes. These considerations have a bearing, it should be observed, on the time factor in Mr. Lloyd George's pledge. It is a mistake to suppose that a long interval would elapse after, let us say, the work of road construction had been commenced before the full effect on employment would be produced. In the the economic world, 'coming events cast their shadows before,' and the knowledge that large schemes of work were being undertaken would give an immediat fillip to the whole trade and industry of the country."

It would take the work, a few years later, of Richard Kahn and James Meade to formalize these indirect effects and show how to quantify them, in terms of the marginal propensity to consume.