Wednesday, August 30, 2023

Correspondence Among Marxists

I have been (re?-)transcribing various letters in which various points of Marxism are elaborated. This post is an index of what I have so far. I do not know that I will go on much.

  • Marx to Engels, 2 August 1862, sets out the transformation problem and Marx's solution.
  • Marx to Engels, 18 June 1867, on the order of presentation in Capital.
  • Marx to Engels, 24 August 1867, on the two best points in volume 1 of Capital.
  • Marx to Engels, 8 January 1868, on three original points in volume 1 of Capital.
  • Marx to Engels, 30 April 1868, outlines the three volumes of Capital, especially the transformation problem.
  • Marx to Vera Zasulich, 8 March 1881, on how Russia might not go through the same modes of production as western Europe.
  • Engels to J. Bloch, 21 September, 1890, about historical materialism and the relation of the superstructure to the base.
  • Engels to Conrad Schmidt, 27 October, 1890, about historical materialism and the relation of the superstructure to the base.
  • Engels to Franz Mehring, 14 July 1893, which initiates the concept of false consciousness.
  • Engels to Werner Sombart, 11 Marx 1895, on the law of value.
  • Antonio Labriola to Georges Sorel, 14 May 1897, in which he describes historical materialism as the philosophy of praxis.

You can see that I am interested in the political economy, and a bit in historical materialism.

Thursday, August 24, 2023

On My Research Program With Fluke Switch Points

I have a research program that I have been pursuning for several years. And I seem to be able to go on for several more years.

I have been looking at the analysis of the choice of technique in models of the production of commodities by means of commodities. Fluke cases are characterized as losing their qualitative properties with almost any perturbation of the parameters of the model. The parameter spaces in these models are partitioned by these fluke cases. Within a region formed by the partitions, qualitative behavior is invariant. I have been looking for regions in which such phenomena as reswitching, capital-reversing, the reverse substitution of labor, or the recurrence of processes occur. These models are open, with the functional distribution of income taken as exogenous to the model.

I think of my reseach as in agreement with Ian Steedman. The critique of marginalism coming out of the Cambridge Capital Controversy was too gentle. Prices of production are not to be explained by supply and demand. My hope is that if others take into account my sort of fluke cases, they will see that so-called 'perverse' cases are not strange at all. One can find statements in the literature about some cases being non-generic and other examples allowing for continuous variation in parameters to some extent. I suppose I ought to note such statements next time I come across them.

I have already achieved some publications from this research program:

In addition, I have a forthcoming article in the Bulletin of Policial Economy presenting examples of both the reswitching of the order of fertility and the reswitching of the order of rentability

I wonder if this approach can be used to continue to generate papers for some time. I have decided that describing a single fluke case, such as a real Wicksell effect of zero, is not interesting. Nor is a comprehensive partitioning of a part of a parameter space of interest. Some connection needs to be drawn to some propositions of interest for economic theory. I have a sort of survey article of perturbing fluke switch points. This article has been desk-rejected once, and I have yet to submit it elsewhere. I have a draft article demonstrating that extending the economic life of a machine has no necessary connection with increased capital-intensity.

I have more models in which to try to identify fluke cases. I am continuing to think about a model that combines intensive and extensive rent. A further extension could consider cases in which more than one process is known for producing the industrial commodity or in which more than one agricultural commodity can be produced. Kurz and Salvadori (1995) have a chapter on the joint utilization of machines, and one could perturb parameters in numerical examples in that chapter. I think pure fixed capital models with machines of constant efficiency can be combined with extensive rent and still retain simple properties of circulating capital. Of course, I would want to look for fluke switch points in models with machines of non-constant efficiency. And, one can look at models of pure joint production. All of these can be extended to include a kind of markup pricing.

My blog archives probably have fluke cases I have forgotton about. Some I vaguely remember, but probably will not do anything with. For example, I once considered a preturbation of an example in which two techniques have the same wage curve, that is, a continuum of switch points. I considered a case in which a continuum of wage curves are tangent at a switch point. Another case is indeterminacy arising with perturbing parameters for requirements for use in a model of joint production.

There are some directions one could take this research program that I probably will not pursue:

  • Define a taxonomy of fluke cases: At first, I thought that all of the fluke switch points created by varying coefficients of production would be a matter of combining four normal forms, in some sense. This was a failure of imagination.
  • Partition a multidimensional parameter space: I have been confining myself to two-dimensional diagrams. But if one looks at the whole parameter space, one should talk about manifolds in higher-dimensional spaces.
  • Generic structures in parameter spaces: I have at least a couple of suggestive examples. For the above two and this extension, it might be helpful to know more algebraic geometry or tropical geometry than I know.
  • Relate partitions to defined biases in technical change: I am thinking about Harrod-neutral and Marx-biased technical change, for example. Perhaps this sort of research should deal with vertically integrated models rather than how I have typically addressed structural economic dynamics.
  • Relate partitions to short run dynamics of market prices: I would like to see some connections drawn to bifurcation theory and explicit dynamic models. I am not sure the normal forms drawn in such a theory will correspond to my fluke cases.

I have tried to write overviews of my research program before:

Saturday, August 19, 2023

Intensive Rent, Extensive Rent, And Absolute Rent

1.0 Introduction

I have decided that this previous post is inadequate. If intensive rent exists on some type of land, the system of equations for prices of production cannot include a process that only partially cultivates some other type of land producing the agricultural commodity.

So to form an example with both intensive and extensive rent, I need the technology to specify the possibility of cultivating at least three types of land. I might as well include markup pricing so as to maybe create an example with intensive, extensive, and absolute rent all existing. If this example works out, it would provide a refutation, in some sense, of this paper.

2.0 Technology, Endowments, Requirements for Use, and Relative Markups

Table 1 presents coefficients of production defining technology. Three types of land exist, and four processes are known for producing corn on land. Each corn-producing process is operated on one type of land. A negligible amount of land is used in producing iron, the industrial commodity.

Table 1: The Coefficients of Production
Type I Land0c1,2000
Type II Land00c2,300
Type II Land000c3,4c3,5

The givens include the amount of each type of land available. Let t1 be the acres of type 1 land available, t2 acres of type 2 land, and t3 acres of type 3 land.

Following Sraffa, I take requirements for use as parameters. In my understanding, requirements for use specify the net product. Let d1 be the tons iron and d2 the bushels corn required for net output.

Finally, I want to allow for industry or agriculture to have some sort of market power. So let s1 r be the rate of profits obtained in operating the first (industrial) process. Let s2 r be the rate of profits obtained in operating any of the agricultural processes. (I am actually going to solve this model, if I do, with parameters for the markups of each type of land.)

The above has set out the givens for what I think is a minimal model with heterogenous capital goods and the possibility of intensive, extensive, and absolute rent arising.

3.0 Techniques

I can define various techniques (Table 2) with this technology. This is an example of the Sraffian combinatorial explosion. (Omega is the only greek letter not listed.) Not all techniques are feasible, given technology, endowments, and requirements for use. Which technique(s) are cost-minimizing varies with, say, the wage. The cost-minimizing technique need not be unique, even away from switch points. Land is not scarce for the Alpha, Beta, Gamma, and Delta techniques, and ownership of land pays no rent. The Epsilon through Upsilon techniques are examples of extensive rent. Phi is an example of intensive rent. Chi and Psi are examples of the combination of intensive and extensive rent.

Table 2: Techniques of Production
Type 1Type 2Type 3
AlphaI, IIPartially farmedFallowFallow
BetaI, IIIFallowPartially farmedFallow
GammaI, IVFallowFallowPartially farmed
DeltaI, IVFallowFallowPartially farmed
EpsilonI, II, IIIPartially farmedFully FarmedFallow
ZetaI, II, IVPartially farmedFallowFully Farmed
EtaI, II, VPartially farmedFallowFully Farmed
ThetaI, II, IIIFully FarmedPartially farmedFallow
IotaI, III, IVFallowPartially farmedFully Farmed
KappaI, III, IVFallowPartially farmedFully Farmed
LambdaI, II, IVFully FarmedFallowPartially farmed
MuI, III, IVFallowFully FarmedPartially farmed
NuI, II, VFully FarmedFallowPartially farmed
XiI, III, IVFallowFully FarmedPartially farmed
OmnicronI, II, III, IVPartially farmedFully FarmedFully Farmed
PiI, II, III, VPartially farmedFully FarmedFully Farmed
RhoI, II, III, IVFully FarmedPartially farmedFully Farmed
SigmaI, II, III, VFully FarmedPartially farmedFully Farmed
TauI, II, III, IVFully FarmedFully FarmedPartially farmed
UpsilonI, II, III, VFully FarmedFully FarmedPartially farmed
PhiI, IV, VFallowFallowFully Farmed
ChiI, III, IV, VFallowFully FarmedFully Farmed
PsiI, II, IV, VFully FarmedFallowFully Farmed

4.0 To Do

The above sets out a model to solve. Thw first step is to find levels of operation needed to satisfy requirements for use, given the technique. One should then identify which techniques are feasible. An infeasible technique is one in which some processes must be operated at a negative level or in which more of a type of land must be cultivated than exists. Then one can, given the wage w or the scale factor r for the rate of profits, find prices of production, including rent, for each feasible technique. Finally, one can determine the cost-minimizing technique(s) at each wage.

I do not necessarily expect to find examples in which more than one cost-minimizing technique exists at a given wage. Nor do I expect to find a case with the non-existence of a cost-minimizing technique. Even if one cannot find such examples, one should discuss their possibility in any write up of this model. One should discuss the orders of efficiency and rentability. The Chi and Psi techniques are examples in which no cultivated land pays no rent. When either is cost-minimizing, it is not a fluke case. I have some interesting graphs, I think, that can show how the dependence of the cost-minimizing technique on the wage varies with the ratio of markups in industry and agriculture. The point is to identify the variation in rent with that ratio as variation in Marx's absolute rent.

This post is an example of my attempt to find something interesting hitherto not clearly explained between models of circulating capital and fully general models of joint production.

Friday, August 18, 2023


Randall Wray on MMT. (About 40:55: Most economics is "fraud". Lots of ads.)

Friday, August 11, 2023

Some Assertions Of Marx And Some Remarks On The Labor Theory Of Value

1.0 Introduction

I have been reading fools in other parts of the Internet. Hence this post.

2.0 Assertions

Marx says the following (I am least sure of 6):

  1. Both sides to an exchange gain. (Capital, volume 1, chapter 5)
  2. Nobody, neither consumers, nor workers, nor investors, nor the managers of firms, make decisions on the grounds of the labor time embodied in commodities. (Capital, volume 1, chapter 1, section4)
  3. Surplus value (dividends, interest, rent, etc.), in an ideal competitive capitalist economy, is not stolen from the worker. (Capital, volume 1, chapter 7, section 2)
  4. Relative prices do not tend towards relative surplus values. (Capital, volume 1, chapter 5, last footnote; Capital, volume 3, part II)
  5. After the revolution, workers will not receive equal wages. (Critique of the Gotha Program)
  6. After the revolution, the planning authority should not necessarily set prices equal to labor values. (Critique of the Gotha Program, Poverty of Philosophy)?
  7. Labor is not the source of all wealth.
3.0 On The Labor Theory Of Value

Consider a capitalist economy. At the start of a year, say, firms own certain plants and goods in process in their inventories. During the year, laborers working with this plant and inputs for energy, lubricants, semi-finished goods, and so on, work up these goods to produce an immense quantity of commodities, the gross product for the year. Firms, who own this gross product, buy and sell some of these commodities among themselves or retain some to replace used up plant and inventories. The renainder is the net product. This net product consist of goods in the form that can be used to expand the plant, including the capital goods needed to work with this plant, and the necessaries and conveniencies of life.

This net product, at a certain level of abstraction, can be seen as divided into wages and income for the owners. The overall rate of profits is the ratio of the net product to the sum of the capital goods used up in production and wages, if one treats wages as advanced.

The above is the perspective of classical political economists such as Adam Smith and David Ricardo. But the above summary is of an approach that needs better definition. I have defined the rate of profits as a ratio between heterogenous quantities, a nonsense quantity. One needs prices or some other way of forming a single number out of the large mish mashes of commodities.

Following Sraffa, assume that a uniform rate of profits is made in each line of production. Then, still at a very abstract level, one can set up a system of equations for prices of production. "...the distribution of the surplus must be determined through the same mechanism and at the same time as are the price the price of commodities" (Sraffa). And this system of equations can be solved.

Ricardo and Marx did not have available the concept of an eigenvalue. They had a conjecture. The ratio defining the rate of profits can be found by evaluating large aggregates of commodities with the labor embodied in each commodity. They knew and said that there was some error here. Nevertheless, this approach attempts "to penetrate the inner physiology of bourgeois society," as Marx put it. Ricardo correctly identified the trade-off between proportional wages and the rate of profits, a trade-off later rediscovered by Nicholas Georgescu-Roegen and taken up by Paul Samuelson under the moniker of the 'factor price frontier'.

Ricardo and Marx both focused on a good of average capital-intensity, in some sense. Ricardo sought a measure of value that somehow did not vary with distribution or improvements in technology. If the ratio of a price of production to the price of such a commodity varied with distribution, that variation was supposed to be caused by the invidual commodity, not by stretching or shrinking of the yardstick. One of Ricardo's insight was that a higher wage could be accompanied by a lower price of production of some commodities.

Sraffa identified a 'standard economy' built into the quantity flows for his system of equations. In the standard system, which has the same level of employment as the actual system, capital goods, gross output, and net output are all composed of commodity baskets in which the quantities of commodities enter in the same proportion. Suppose the net product of the standard system is adopted as the numeraire for the wage, which, therefore, ranges from zero to unity. Then one can calculate the rate of profits as a ratio of homogeneous quantities, without ever evaluating commodities at prices.

This rate of profits is not a price phenomenon insofar as it does not depend of relative prices. The general rate of profits is unchanged by evaluating commodities at market prices, at prices of production with a uniform rate of profits, at prices of production with varying markups among industies refracting market power, at labor values, or at energy values. It just does not matter.

This perspective on the labor theory of value, which I mainly take from Pierangelo Garegnani, presents it as a technical solution to a technical problem in trying to understand capitalist economies. Fratini and Ravagnani has some interesting work on the standard system. Whatever socialogical insights one may take from Marx's early writings on alienation or Lukacs writings on reification does not seem to have much to do with the matter.

Garegnani notes how little understanding some critics of Marx had of what they were attempting and failing to criticize:

"We find instead no mention whatsoever, in Böhm-Bawerk, of the correct proposition that the rate of profit is determined when the real wage is specified, or of the ensuing inverse relation between the wage and the profit rate which the labour theory of value had allowed Ricardo and Marx to establish, overcoming the deficiencies of Smith’s determination of profits..." (Garegnani 2018)


Two observations seem sufficient to indicate how Böhm-Bawerk coped with Marx’s Volume III prices of production, without essentially changing his conclusions about Marx’s work. The first is that Marx’s idea that the rate of profit and, therefore, the prices of production originate from a redistribution of aggregate surplus value is broken down by Böhm-Bawerk into a 'premise' and no less than four distinct 'arguments', thus rendering Marx's reasoning practically incomprehensible. The second observation is that the crux of Böhm-Bawerk's argument, contained in ten out of the essay's 110 pages, shows some awareness of the true difficulties besetting Marx's theory of prices of production, centring around the use of 'values' rather than 'prices of production' in the price equations themselves. [footnote:] See Böhm-Bawerk’s criticism of what he reconstructs as Marx's 'fourth argument' on labour values in Böhm Bawerk (1896). In the course of his criticism, Böhm-Bawerk notices that the determination of aggregate surplus value cannot ignore the fact that wage goods can be sold at 'prices' of production which deviate from 'values', the same point, we may recall, made by Marx in his sketch of a theory of prices." (Garegnani 2018)

  • Saverio M. Fratini and Fabio Ravagnani, Sraffa and the 'slogans not used'.
  • Pierangelo Garegnani. 2018. On the labour theory of value in Marx and in the Marxist tradition Review of Political Economy

Wednesday, August 09, 2023

Marx: Labor Is NOT The Source Of All Wealth

I think most quote the first page of the Critique of the Gotha Program for Marx asserting this:

"First part of the paragraph: 'Labor is the source of all wealth and all culture.'

Labor is not the source of all wealth. Nature is just as much the source of use values (and it is surely of such that material wealth consists!) as labor, which itself is only the manifestation of a force of nature, human labor power. The above phrase is to be found in all children's primers and is correct insofar as it is implied that labor is performed with the appurtenant subjects and instruments. But a socialist program cannot allow such bourgeois phrases to pass over in silence the conditions that alone give them meaning. And insofar as man from the beginning behaves toward nature, the primary source of all instruments and subjects of labor, as an owner, treats her as belonging to him, his labor becomes the source of use values, therefore also of wealth. The bourgeois have very good grounds for falsely ascribing supernatural creative power to labor; since precisely from the fact that labor depends on nature it follows that the man who possesses no other property than his labor power must, in all conditions of society and culture, be the slave of other men who have made themselves the owners of the material conditions of labor. He can only work with their permission, hence live only with their permission."

But the same proposition is in the first chapter of the first volume of Capital:

"The use values, coat, linen, etc., i.e., the bodies of commodities, are combinations of two elements – matter and labour. If we take away the useful labour expended upon them, a material substratum is always left, which is furnished by Nature without the help of man. The latter can work only as Nature does, that is by changing the form of matter. Nay more, in this work of changing the form he is constantly helped by natural forces. We see, then, that labour is not the only source of material wealth, of use values produced by labour. As William Petty puts it, labour is its father and the earth its mother."

Wealth, for Marx, is not value. It is use values.

You can find many supposed critiques of Marx claiming that he is wrong for denying p. Yet Marx asserts p, and not in some obscure part of his writing. I suppose I also find socialists irritating who advocate for socialism on the basis of Marx by means of propositions that he explicitly denies or argues he transcends. Socialists who explicitly state that they base their arguments on pre-Marxian notions of, say, the labor theory of value are better.

Saturday, August 05, 2023

A Fluke Case And The Disappearance Of Intensive Rent

Figure 1: Wage Curves For A Fluke Case
1.0 Introduction

This post examines perturbations around a fluke case in a model of intensive rent. The model illustrates an analysis of prices and the choice of technique in which the quantity of commodites produced matters. Yet the level and composition of net output are taken as given, independent of any variation, for example, from their dependence on distribution and relative prices. The model also illustrates a case in which prices of production are not uniquely determined by the level of wages.

In the fluke case considered, the requirements for use necessitate, for one technique, that the single type of land available be just fully culitivated with a single process being operated. For an infintesimal lower level of output with that technique, the land would be in excess supply, and no rent would be paid. On the other hand, for any increased output, a linear combination of some processes would need to be operated if the given process would be used. The fluke case can be viewed in which two processes are operated on the land, with one process operated at a level of operation of zero. The rent is an additional variable in the equations characterizing prices of production, but, for a given wage, the solution is such that the rent is zero.

The example has a second fluke property. The wage curves for three techniques intersect at a switch point on the wage axis, at a rate of profits of zero.

Perhaps the complexity of this example overwhelms any insight it provides. I expect to continue to explore other areas of the parameter space.

2.0 Technology, Land Endowments, and Requirements for Use

The example varies the parameters from an example by Antonio D'Agata.

Table 1 presents coefficients of production, a perturbation of an example from D'Agata (1983). Only one type of land exists, and three processes are known for producing corn on it. The scarcity of land is shown by the possibility of two corn-producing processes being operated side-by-side in the cost-minimizing technique.

Table 1: The Coefficients of Production

Following D'Agata, assume that one hundred acres of land are available and that net output consists of 90 tons iron, 60 tons steel, and 19 bushels corn. The net output is also the numeraire. All three commodities must be produced for any composition of net output. Table 2 lists the available techniques. Delta is never feasible for the parameter ranges considered. Not all land is farmed and only one corn-producing process is operated under Alpha and Beta. Under Gamma also, only one corn-producing process is operated. Two corn-producing processes are operated together under Epsilon and Zeta.

Table 2: Techniques
AlphaI, II, III
BetaI, II, IV
GammaI, II, V
DeltaI, II, III, IV
EpsilonI, II, III, V
ZetaI, II, IV, V

3.0 A Fluke Case

A set of equations for prices of production can be set out for each technique. Each process in the technique provides one equation. The systems of equations for Alpha, Beta, and Gamma each consist of three equations, and no rent enters into them. The systems for Epsilon and Zeta consist of four equations, with rent as an additional variable. I assume both rent, when it exists, and wages are paid out of the surplus product at the end of the year. The numeraire adds a fourth or fifth equation, depending on the technique.

Given the wage or the rate of profits, these equations can be solved. In the parameter ranges considered, only one solution exists for each technique. Figure 1, at the top of the post, plots wage curves and rent, as a function of the rate of profits, for each feasible technique. In the parameter ranges considered in this post, the wage varies monotonically with the rate of profits for each technique.

Consider the parameters for the fluke case illustrated in Figure 1. For a low wage or a rate of profits higher than the rate of profits at the switch point with the highest rate of profits, the Beta technique is cost-minimizing. The wage curve for Beta contributes to the frontier. Since under Beta, land is in excess supply when the requirements for use are satisfied, no rent is paid if the Beta technique is adopted.

For a higher wage or any non-negative rate of profits up to where the Beta technique is cost-minimizing, the Gamma technique is cost-minimizing. The wage curve for Gamma also contributes to the wage frontier. No rent is paid when the Gamma technique is adopted.

At the maximum wage or a rate of profits of zero, the Alpha technique is cost-minimizing. The wage curve for Alpha contributes to the wage frontier only at the switch point on the wage axis. Land is in excess supply under Alpha, and no rent is paid.

The construction of the wage frontier out of the outer envelope of the wage curves for Alpha, Beta, and Gamma follows the well-known logic of simple (non-joint) production. But this outer envelope is not the entire wage frontier here. The wage curve for Epsilon contributes to the wage frontier between the wage at the switch point between the wage curves for Epsilon and Zeta and the maximum wage. And when Epsilon is adopted, rent is paid, as illustrated on the right pane in Figure 1.

Furthermore, the Zeta technique is also cost-minimizing for a certain range of distribution. Consider the wage at the switch point between Epsilon and Zeta and at the switch point between the wage curves for Beta, Gamma, and Zeta. The wage curve for Zeta contributes to the wage frontier in this range of wages. And rent is paid here too.

So I claim that the choice of technique is not unique for certain ranges of the wage in this fluke case. In an intermediate range of wages, the Beta, Epsilon, and Zeta techniques are each cost-minimizing. Depending on which technique is adopted, a different rate of profits and different prices of production for iron, steel, and corn will prevail. For wages in a range from the upper limit of the previously described range to the maximum wage, the Gamma and Epsilon techniques are cost-minimizing. The rate of profits and prices of production are non-unique here too. If a market algorithm can be defined for this example, what technique and prices of production it would converge to would depend on initial conditions here.

4.0 A Local Partition of the Parameter Space

I now consider perturbations of the two unspecified coefficients of production in Table 1, around the fluke case illustrated in Figure 1. Further partitions of the parameter space exist outside the borders of Figure 2. But within this plot, the analysis of the choice of technique does not qualitatively vary within each of the four regions.

Figure 2: A Slice of the Parameter Space around the Fluke Case

The regions to the northwest and southwest illustrate the analysis of prices of production under simple production. Any of the three corn-producing processes, when combined with the first two processes, can satisfy requirements for use, with some land left over. Land is not scarce, and no technique in which two corn-producing processes operate side-by-side on fully-cultivated land can satisfy requirements for use. The wage frontier, in such a case, is the outer frontier of the wage curves for Alpha, Beta, and Gamma. To the southwest, Beta is cost-minimizing at a low wage, and Gamma is cost-minimizing up to the maximum wage. To the northwest, Alpha is cost-minimizing towards the highest wage.

The Alpha, Beta, Epsilon, and Zeta techniques are feasible in the regions to the northeast and southeast. In the region to the southeast, Beta is cost-minimizing at a low wage. At intermediate wages, Epsilon, Zeta, and Beta are all cost-minimizing. The cost-minimizing technique, the rate of profits, rent, and prices of production are not a unique function of the wage. At a higher wage, up to the maximum wage, Epsilon is uniquely cost-minimizing.

The region to the northeast resembles the region to the southeaqst, except at higher wages. For a range of wages up to the maximum wage, Alpha is uniquely cost-minimizing. No rent is paid on land for a range of low and high wages. But rent can be paid in a range of intermediate wages. In some of this range, where Epsilon is uniquely cost-minimizing, rent must be paid.

5.0 The Choice of Technique

Above, I have made many statements about the choice of the cost-minimizing technique. I here briefly describe how you can check these claims.

For each technique and a wage up the maximum wage for that technique, one can find the rate of profits; rent per acre, if any; and prices of production. For each process in Table 1, consider the revenues obtained when producing one ton iron, one ton steel, or one bushel corn, depending on the process. Find the difference between these revenues and costs, where capital goods are costed up at the going rate of profits. This difference, which can be negative, is the extra profits obtained for a given process operated at the unit level, with the prices of production for the given technique at the given wage. These extra profits are always zero for the iron and steel-producing process since equations for these processes enter into the system of equations for prices of production for each technique in the example.

Figure 3 graphs extra profits for the three corn-producing processes for prices of production for the Alpha and Beta techniques. Coefficients of production are as in the fluke case graphed in Figure 1, at the top of this post. You cannot see on the left pane a curve for the third process, that is, the first corn-producing process. This corn-producing process is operated under the Alpha technique, and its extra profits are zero for the full range of possible wages under Alpha. For any wage less than the maximum wage, extra profits can be made by operating the last corn-producing process, and for some range of lower wages, by operating the second corn-producing process. Thus, Alpha is only cost-minizing at the maximum wage, which is a switch point.

Figure 3: Extra Profits at Alpha and Beta Prices

The right-pane demonstrates that Beta is cost-minimizing over of range of wages bounded below by zero. If prices of production for Beta prevail and wage exceeds that at the switch point, managers of cost-minimizing farms will want to adopt the last corn-producing processes, sometimes.

Figure 4 shows extra profits for corn-producing processes when prices of production for Gamma prevail. For the coefficients of production for the fluke case, Alpha, Beta, and Gamma are feasible, and no rent is paid when these techniques are adopted You can see from the graph that Gamma is cost-minimizing over a range of high wages. The maximum wage is at a switch point. Adopting the first corn-producing process at the highest wage will neither incur excess costs or make extra profits.

Figure 4: Extra Profits at Gamma Prices

Figure 5 shows extra profits for prices of production for Epsilon and Zeta, respectively. These are the two feasible techniques which pay a rent. Since two corn-producing processes are operated for each of these techniques, a curve showing extra profits is only apparent for one process in each pane. In each case, this is the corn-producing process not operated under the technique for which prices of production are found. Epsilon is only cost-minimizing for a range of the wage up to the maximum wage.

Figure 5: Extra Profits at Epsilon and Zeta Prices

Extra profits are only shown in Figure 5 for an intermediate range of wages for Zeta. Below this range, a non-negtive rate of profits cannot be obtained. Above this range, rent must be negative. Zeta is cost-minimizing only in a subrange of high wages for the range of wages in which it makes sense to calculate extra profits for Zeta.

The above has justified the claims in Section 3 about the cost-minimizing technique for the fluke case explored in this post. Parts of the wage curves for the Gamma, Epsilon, Zeta, and Beta techniques lie on the wage frontier for this case. The wage curve for Alpha contributes to the wage frontier only at the switch point at the maximum wage.

6.0 Conclusion

One can think of a movement from the northeast to the southwest in Figure 2 as an example of technical progress. The two coefficients of production I have chosen to explore decrease. As a result of the decline in the acres of land needed to produce corn in one process, land becomes non-scarce for a given net output. Intensive rent disappears.

I think those who have made it this far will grant that the fluke case in Figure 1 is different than any graph of a wage frontier ever seen in the literature. Kurz and Salvadori (1995), for completeness, do consider a case in which requirements for use are satisfied by just cultivating all of a certain type of land. I do not know that any numeric example has ever been put forth where the cost-minimizing technique does not depend uniquely on the wage away from a switch point. But this possibility is known, I guess, to Bidard, Kurz, Salvadori, Schefold, and others. I expect that I may generate further examples in this parameter space.

  • D'Agata, Antonio. 1983. The existence and unicity of cost-minimizing systems in intensive rent theory. Metroeconomica 35: 147-158.
  • Kurz, Heinz D. and Neri Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge: Cambridge University Press.

Tuesday, August 01, 2023

Engels To Conrad Schmidt In 1890

This is another example of Engels explaining the theory of historical materialism. I know of this letter from Mills and Goldstick (1989). They also point out this letter from Engels. Here we see the metaphor of ideas "standing on their head", not in relation to Hegel's idealism, but as real economic relations reflected in finance. I like the emphasis on the interdependence of industries that could be expressed in Leontief matrices. Does this letter express a deterministic, strict dependence of the superstructure on the base? Or does Engels explain historical materialism as a mutual interaction of base and superstructure?

London, 27 October 1890

Dear Schmidt,

I am taking advantage of this, the first free time I have had, to answer you letter. I think you would be very well advised to accept the post in Zurich. At any rate you'll be able to learn a good deal about economics there, especially if you bear in mind that Zurich is, after all, only a third-rate financial and speculative market and hence that the impressions to be gained there will be dulled, if not deliberately distorted, these being but reflections seen at second or third remove. But you will learn how the machinery works in practice and will be obliged to follow at first hand the stock market reports from London, New York, Paris, Berlin and Vienna, and thus the world market - in its reflection as a money and stock market - will be revealed to you. Economics, politics, etc., are reflected as objects are in the human eye - they pass through a converging lens and are therefore seen the wrong way up, standing on their heads. Except that there is no nervous apparatus to set them on their feet again for the benefit of the imagination. Your money market man sees the trend of industry and of the world market merely in the inverted reflection of the money and stock markets and thus for him effect becomes cause. I observed this back in the 40s in Manchester; as a guide to industrial progress and its periodical peaks and troughs, the London stock market reports were absolutely useless, since the gentlemen sought to explain everything in terms of money market crises, though these were themselves for the most part little more than symptoms. At that time they were concerned to explain away industrial crises by attributing them to temporary overproduction and thus the thing also had a tendentious aspect which invited distortion. This is a point which has now ceased to apply - once and for all, at any rate so far as we are concerned, and it is, moreover, a fact that the money market may also have its own crises in which actual industrial disturbances play only a subordinate role, if any at all, and in this sphere there is much to be ascertained and investigated, particularly in regard to the history of the last 20 years.

Where there is division of labour on a social scale, the various sections become mutually independent. Production is, in the final analysis, the decisive factor. But as soon as trade in products becomes independent of actual production, the former follows a trend of its own which is, by and large, undoubtedly dictated by production but, in specific cases and within the framework of that general dependence, does in turn obey laws of its own, laws inherent in the nature of this new factor; it is a trend having its own phases and reacting in turn on the trend of production. The discovery of America was due to the gold famine which had already driven the Portuguese to Africa (cf. Soetbeer's Edelmetall-Produktion), because the vast expansion of European industry and the corresponding growth in trade in the 14th and 15th centuries called for more means of exchange than Germany - the main source of silver from 1450 to 1550 - was able to provide. The conquest of India by the Portuguese, Dutch and British between 1500 and 1800 had as its aim import from India and no one thought of sending exports there. And yet how tremendous were the repercussions upon industry of these discoveries and conquests carried out solely in the interests of trade - it was only the need to export to those countries which created and developed large-scale industry.

It is the same with the money market. Once trade in money becomes divorced from trade in commodities, it will - under certain circumstances determined by production and by the trade in commodities and within those limits — develop in its own way subject to the special laws and distinctive phases determined by its own nature. If, in addition and in the course of this further development, the trade in money expands to comprise trade in securities, the said securities being not simply government paper, but also the shares of industrial and commercial concerns, i.e. if the trade in money gains direct control of a section of the production by which it is largely dominated, then the reaction of the trade in money on production will be even stronger and more complex. The traders in money own railways, mines, foundries, etc. These means of production assume a twofold aspect: They must be run, now in accordance with the immediate interests of production, now in accordance with the needs of the shareholders in so far as these are traders in money. The most striking example of this is the North American railroads, the running of which is entirely dependent on the day-to-day stock market operations of a Jay Gould, Vanderbilt, etc., which have nothing whatever to do with any particular railroad or its interests quaa means of transport. And even here in England the railway companies have for decades been fighting over the boundary areas separating this concern or that - struggles in which a vast amount of money has been squandered, not in the interests of production and transport, but solely out of a rivalry which for the most part had but one purpose, namely to facilitate the stock market operations of the traders in money who held the shares.

With these few remarks about my view of the relationship of production to the trade in commodities and of both to the trade in money, I have already dealt in the main with your questions about historical materialism generally. The subject is best approached from the standpoint of the division of labour. Society engenders certain common functions which it cannot do without. Those nominated for this purpose form a new branch of the division of labour within society. They thereby acquire interests of their own vis-à-vis, amongst others, their mandatories and become independent of them - and so you have the state. From then on the process is much the same as in the trade in commodities and, later, the trade in money - while the new independent power must, it is true, generally follow the trend of production, it will also, by virtue of its inherent independence, i.e. a relative independence formerly conferred upon it and which it has gradually enlarged, react in turn upon the conditions and the course of production. It is the interaction of two unequal forces, of the economic trend on the one hand and the new political power which is striving for the greatest possible independence and which, having once been installed, assumes a trend of its own, on the other. By and large, the economic trend will predominate but it must also be reacted upon by the political trend which it has itself induced and which has been endowed with relative independence - the trend of, on the one hand, state power and, on the other, of the simultaneously engendered opposition. Just as the trend of the industrial market is largely reflected in the money market, given the provisos set out above, but, of course, the wrong way up, the struggle between the already extant and warring classes is reflected in the struggle between government and opposition, and again the wrong way up; it is no longer reflected directly but indirectly, not as a class struggle but as a struggle over political principles, and in so distorted a form that it has taken us a thousand years to sort it out again.

The government may react to economic developments in three ways: it can take the same direction, in which case things go faster; it may take a contrary one, in which case, as conditions are today and in any of the larger nations, it will eventually come to grief, or it may block certain lines of economic development and lay down others - which will ultimately amount to the same as one of the two foregoing instances. But it is obvious that, in instances 2 and 3, political power can wreak havoc with economic development and cause energy and materials to be squandered on a vast scale.

Then again there is the instance of the seizure and brutal destruction of economic resources which, in earlier days and in certain circumstances, could ruin economic development both locally and nationally. Today, this would mostly have the opposite effect, at least where the larger nations are concerned. In the long run the vanquished may have more to gain economically, politically and morally than, on occasion, the victor.

It is much the same in the case of the law: As soon as the new division of labour becomes necessary and creates professional lawyers, yet another new, independent field is opened up which, for all its general dependence on production and trade, is nevertheless capable of reacting in its own way to those spheres. In a modern state not only must the law correspond to the general economic situation and be its expression, it must of itself constitute a coherent expression that does not, by reason of internal contradictions, give itself the lie. And to achieve this, the fidelity with which economic conditions are reflected is increasingly thrown to the winds. All the more so for the rarity with which a statute book is the harsh, unmitigated, unadulterated expression of the domination of one class: this of itself would be contrary to the 'concept of law'. The pure, logical concept of law of the revolutionary bourgeoisie of 1792-96 had already been adulterated in many respects even in the Code Napoléon and, in so far as it was embodied therein, has had to be constantly subjected to all manner of modifications as a result of the growing power of the proletariat. Not that this has prevented the Code Napoléon from being the statute book on which all new codifications in every part of the world are based. Thus the course of the 'law's development' has largely consisted simply in this: Firstly, the attempt to eliminate the contradictions arising from the direct translation of economic conditions into legal principles and to establish an harmonious legal system and, secondly, the fact that the influence and pressure of further economic developments repeatedly disrupt that system, involving it in fresh contradictions (at this stage I am speaking only of civil law).

The reflection of economic conditions as legal principles is likewise necessarily one that presents the image the wrong way up; it does so without the beholder being aware of it; the lawyer imagines he is dealing in a priori principles whereas they are, in fact, no more than economic reflections - and thus the whole thing is the wrong way up. And it seems to me self-evident that this inversion which, in as much as it is not recognised, constitutes what we call an ideological view, reacts in its turn on the economic base and may, within certain limits, modify the same. The basis of the law of inheritance, assuming the family to have attained the same stage of development, is an economic one. Nevertheless, it would be difficult to prove that, for instance, absolute testamentary freedom in England and the strict limits imposed thereon in France are in every respect of economic origin. But both, in a very significant way, react on the economy in that they influence the distribution of wealth.

Now as regards the more rarefied ideological fields such as religion, philosophy, etc.; these have a prehistorical fund of what today would be termed rubbish which was taken over lock, stock and barrel by the historical period. In so far as these various false conceptions of nature, of the nature of man, of spirits, magic forces, etc., are economically based, it is only in a negative sense; false conceptions of nature are the corollary of the low level of economic development in the prehistorical period, but also on occasion its precondition if not its actual cause. And even if economic necessity may have provided the main incentive for progress in natural science and done so to an increasing extent, it would be pedantic to seek economic causes for all this primitive rubbish. The history of science is the history of the gradual elimination of that rubbish and/or its replacement by new, if progressively less ridiculous, rubbish. The people responsible for this in turn belong to special spheres of the division of labour and see themselves as working in an independent field. And to the extent that they constitute an independent group within the social division of labour, what they produce, including their errors, exerts a reciprocal influence on social development as a whole and even on economic development. But for all that, they are themselves in their turn subject to the dominant influence of economic development. In philosophy, for example, this is most easily demonstrated in respect of the bourgeois period. Hobbes was the first modern materialist (in the 18th-century sense), but an absolutist at a time when, throughout Europe, absolute monarchy was in its heyday and, in England, was embarking on a struggle with the populace. In religion as in politics, Locke was the product of the class compromise of 1688. The English deists and their more logical successors, the French materialists, were the true philosophers of the bourgeoisie - and, in the case of the French, even of the bourgeois revolution. German philosophy, from Kant to Hegel, is permeated by the German philistine - now in a positive, now in a negative, sense. But in every epoch philosophy, as a definite sphere of the division of labour, presupposes a definite fund of ideas inherited from its predecessors and from which it takes its departure. And that is why economically backward countries can nevertheless play first fiddle where philosophy is concerned - France in the 18th century as compared with England, upon whose philosophy the French based themselves and, later on, Germany as compared with both. But in France as in Germany, philosophy, like the general flowering of literature at that time, was also the result of growing economic prosperity. I am in no doubt about the ultimate supremacy of economic development over these fields also, but it will come about within the terms laid down by each individual field; in philosophy, for instance, by the operation of economic influences (which again for the most part operate only in their political, etc., guise) on extant philosophical material handed down by predecessors. Here, political economy creates nothing a novo [from scratch], but determines the way in which the existing fund of ideas changes and develops, and this too is done for the most part indirectly, since it is its political, legal and moral reflections which exert the greatest immediate influence on philosophy.

As for religion, I have said all that is necessary in the last chapter of Feuerbach.

So if Barth opines that we deny that the political, etc., reflections of the economic trend have any effect whatsoever on that trend itself, he is simply tilting at windmills. After all, he only has to look at Marx's Eighteenth Brumaire which is devoted almost exclusively to the particular role played by political struggles and events - needless to say within the framework of their general dependence on economic conditions. Or again at Capital, e. g. the section on the working day where legislation, which is, after all, a political act, appears in such an uncompromising light. Or at the section on the history of the bourgeoisie (Chapter 24). Otherwise why should we be fighting for the political dictatorship of the proletariat if political power is economically powerless? Might (i.e. state power) is also an economic force!

But I have no time at present to criticise the book. The third volume has got to come out first and in any case I believe that e.g. Bernstein is also perfectly capable of attending to it.

What all these gentlemen lack is dialectics. All they ever see is cause on the one hand and effect on the other. But what they fail to see is that this is an empty abstraction, that in the real world such metaphysically polar opposites exist only in a crisis, that instead the whole great process takes place solely and entirely in the form of interplay - if of very unequal forces of which the economic trend is by far the strongest, the oldest and the most vital - and that here nothing is absolute and everything relative. So far as they are concerned, Hegel might never have existed.

As regards the rumpus in the party, I was forcibly dragged into it by the gentlemen of the opposition and thus had no choice. Mr Ernst's conduct vis-à-vis myself is quite indescribable unless I call it that of a schoolboy. I am sorry if he's a sick man and forced to write for his living. But if someone has an imagination so vivid that he can't read a line without inferring the opposite of what it says, he should apply his imagination to spheres other than socialism which is no figment. He should write novels, plays, art criticism and the like, when all he will harm is bourgeois culture, benefiting us in the process. He might then acquire sufficient maturity to be able to achieve something in our field also. Never before have I seen such a rigmarole of half-baked material and utter rubbish as has been dished out by the said opposition. And these callow lads, who are blind to everything but their own boundless egotism, propose to dictate party tactics. I have learnt more from a single one of Bebel's articles in the Vienna Arbeiter-Zeitung than from all the rigmarole these chaps have produced. And they imagine they are worth more than that clear-sighted man who has such an admirably correct grasp of circumstances and depicts them so graphically and succinctly. They are all of them failed belletrists, and even a successful belletrist is a pretty obnoxious animal.

I should be sorry were the Volks-Tribüne to succumb. Under your editorship it has shown that something might well be achieved by a weekly which devotes more space to theory than to news - and I am well aware what sort of contributors you have! But I must say that, now that the Neue Zeit has become a weekly, it's somewhat doubtful whether yours can be kept going. At all events, you will be glad to cast off the joys and sorrows of editorship and have time for something other than purely journalistic tasks. And even in Berlin the immediate future will be dominated by all the various reverberations of the late rumpus, and there'll be nothing to gain for anyone by being mixed up in it.

Your printing the passage from my letter did no harm, but that sort of thing is best avoided. In a letter, one writes from memory and at speed, without looking anything up, etc., and is thus always liable to let slip some expression which may well be seized on by one of those people we Rhinelanders describe as a Korinthenscheisser [someone who trivializes everything], and God knows what rubbish might not come of it.

Many thanks for your anticipatory congratulations on my 70th birthday which is still a month ahead. So far I am still very well except that I still have to spare my eyes and am not allowed to write by gaslight. Let's hope I remain so.

Now I must close.

With warm regards,


F. Engels

  • Charles W. Mills and Danny Goldstick. 1989. A new old meaning of 'ideology'. Dialogue 28: 417-432.