Communism Worked In Central New York Around 1500

A Beach On The East End Of Oneida Lake

The Iroquois are an example of primitive communism. This post includes lots of anachronisms, and I use current place names. I had never heard of the Haudenosaunee before, which apparently is the preferred term. I find I do not know much about my neighbors, the Oneidas. The Oneidas were one of the five nations in the Iroquois confederacy.

I am confused whether primitive capitalism is tied exclusively to hunter-gatherer societies, without a surplus product. Given the role of the three sisters, that is, corn, beans, and squash, in, say, the Oneida society, I guess they must have been an agricultural society. I gather that anthropologists have found the concept of a surplus product useful. Useful questions include who gets the surplus? What do they do with the surplus? Clark (1992) is an example of an institutionalist economist who questions whether a surplus can be conceptualized independently of its use and distribution. If primitive communism prevailed among many for much of prehistory, Marx and Engels are wrong in saying, "The history of all hitherto existing societies is the history of class struggles". Apparently, in later editions of the Communist Manifesto, Engels wanted to replace 'history' with 'recorded history'.

Anyways, as I understand it, extended families of Oneidas lived collectively in longhouses. Society was relatively egalitarian and matriarchal. They had a concept of personal property, but not of private property. In particular, land could not be owned. I gather land was periodically reallocated among families, as needed. Luxemburg, in the framents of her textbook on political economy, says that land was likewise reallocated in the German mark, where a mark is a village in ancient times. I guess some villages raided others, but, as a whole, the Iroquois lived under the great law of peace. Memorial day weekend is almost the only time one can see NCAA lacrosse on national television in the USA.

Lewis Henry Morgan was a nineteenth century anthropologist. I do not know much about him, how Marx and Engels built upon his studies, or current views by anthropologists of these ideas. I was surprised to find he was from New York State and extensively used the Iroquois as an example for his claims.

What happened to these working communist societies? My answer is very selective. The Sullivan expedition was a genocidal campaign ordered by George Washington during the U.S. revolution. The question of Oneida land claims in New York are a matter of recent current events.

References

• Charles M. A. Clark. 1992. An institutionalist critique of Sraffian economics. Journal of Economic Issues 16(2): 457-468.
• Rosa Luxemburg. 2013. The Complete Works of Rosa Luxemburg: Volume I, Economic Writings 1, Verso.
• Brian Moore. 1985. Black Robe
• Lewis Henry Morgan. 1877. Ancient Society or Researches in the Lines of Human Progress from Savagery through Barbarism to Civilization

David Champernowne

No book-length biography of D. G. Champernowne exists, as far as I can see. Even his Wikipedia page is quite terse. Yet he advised and participated in important twentieth-century intellectual developments.

From Hodges biography of Alan Turing, I learned that 'Champ' was a friend of his. Champernowne did early work in programming chess-playing algorithms, along with Turing and Claude Shannon. Game-playing is one of those disappointing applications of Artifical Intelligence. What seems to work best, like ChatGPT, uses lots of processing power, while ignoring what experts in the subject matter say. Anyways, Champernowne was in on the invention of the computer.

Champernowne (1953-1954) published an appreciation and explanation of the English translation of von Neumann's article on economic 'equilibrium'. This was in the same journal issue. Von Neumann's model is classical in inspiration. No agents are maximizing utility. The composition of capital goods is found as a solution of the model. Champernowne acknowledges conversations with Kaldor and Sraffa. in writing this article.

I had not previously known about Chamernowne's (1952, 1953, 1973, 1988) work on the Pareto distribution, in the context of income distribution. I find the Pareto distribution useful in the context of extreme events.

His commentary on Joan Robinson's article kicking off the Cambridge Capital Controversy (CCC) was published in the same journal issue as Robinson's article. He explicitly notes the possibility of capital-reversing and, if I understand correctly, provides a numerical example. And he develops chain-index measure of capital to enter in an aggregate production function when no such 'perverse' case exists.

Bibliography

• D. G. Champernowne. 1945-1946. A note on J. v. Neumann's article on 'A model of economic equilibrium'. The Review of Economic Studies 13(1): 10-18.
• D. G. Champernowne. 1952. The graduation of income distribution. Econometrica 20(4): 591-615.
• D. G. Champernowne. 1953. A model of income distribution. Economic Journal 63(250): 318-351.
• D. G. Champernowne. 1953-1954. The production function and the theory of capital: a comment. The Review of Economic Studies 21(2): 112-135.
• D. G. Champernowne. 1973. The Distribution of Income between Persons.
• D. G. Champernowne and Frank A. Cowell. 1998. Economic Inequality and Income Distribution.
• Andrew Hodges. 2015. Alan Turing: The Enigma, updated edition. Princeton University Press.

Future Papers For My Research Program?

I have sometimes written retrospectives about my research program. I have been exploring the results of perturbing parameters in models of the choice of technique. This is a bit more prospective.

• Illustrations of One-Dimension Pattern Diagrams: I have a selection of these written up.
• Independence of Economic Life of Machines and Capital-Intensity: I have the analytical results I want. I am being slow to read what I need to connect results up to Austrian capital theory. I have had a much different earlier version rejected by Metroeconomica.
• Illustrations of Partitions of Parameter Spaces by Fluke Switch Points: I have had a draft paper like this rejected by the Cambridge Journal of Economics.
• Extensive rent with perturbations of markups: I have had a paper based on this rejected by the Review of Radical Political Economics. I need to reach a more definite conclusion. I probably will not go further.
• Intensive rent with perturbations of markups: This is somewhat beyond me, and I probably will not develop this further.
• Extensive rent, intensive rent, and markup pricing: This, too, is somewhat beyond me, and I do not see that I will pursue it soon.
• The Choice of Technique with Harrod-Neutral Technical Progress: This is somewhat beyond me. I probably will not develop this.

I do not see if organizing my starts will inspire me to be more productive. Since I am working on my reading for the second suggestion above, maybe I should expect to be slow at this point.

Hayek In The Pure Theory Of Capital

This is more of my commonplace book, based on reading some of Hayek's The Pure Theory of Capital. Hayek rejects Böhm Bawerk's average period of production, a single number summarizing the capital intensity of a structure of production. He still strives to say that more capital-intensive techniques are longer in some non-aggregate sense. I probably will not finish this book. To compare and contrast this book with J. R. Hicks' Value and Capital would be of interest.

Hayek correctly takes issue with the treatment of capital as a homogeneous quantity and the explanation of interest by the supply and demand of capital:

"the attempts to explain interest, by analogy with wages and rent, as the price of the services of some definitely given 'factor' of production, has nearly always led to a tendency to regard capital as a homogeneous substance the 'quantity' of which could be regarded as a 'datum', and which, once it had been properly defined, could be substituted, for purposes of economic analysis, for the fuller description of the concrete elements of which it consisted." (Hayek 1941, p. 5)

and:

"As we shall see, it is more than doubtful whether the discussion of 'capital' in terms of some single magnitude, however defined, was fortunate even for its immediate purpose, i.e. the explanation of interest. And there can be no doubt that for the understanding of the dynamic processes it was disastrous. The problems that are raised by any attempt to analyse the dynamics of production are mainly problems connected with the interrelationships between the different parts of the elaborate structure of productive equipment which man has built to serve his needs." (Hayek 1941, p. 6)

Sraffa, of course, analyzes the structure of productive equipment in a different way.

Hayek is one of the originators of the notion of intertemporal general equilibrium

"An effective discussion of the problems of capital theory must, however, move precisely in that neglected field which deals with general equilibria that are not at the same time stationary states." (Hayek 1941, p. 6)

Hayek goes on to a discussion later built on by Lachmann and paralleling Robinson. At any point, the complex of capital equipment is unsuitable, inherited from the past in which the present was not completely foreseen. In equilibrium, the plans of all agents are adjusted. Equilibrium is not a state that an economy can get into in historical time. Nevertheless, equilibrium analysis has a logical use in a preliminary analysis. Hayek does not want to consider a temporary partial equilibrium, instead of a general intertemporal equilibrium. Furthermore, Hayek puts money aside, including the lending and borrowing of money in most of this preliminary study.

Hayek distinguishes between permanent and non-permanent resources and between producible and non-producible resources.

"The term capital itself, in so far as it is required to describe a particular part of the productive resources, will accordingly be used here to designate the aggregate of those non-permanent resources which can be used only in this indirect manner to contribute to the permanent maintenance of the income at a particular leve1." (Hayek 1941, p. 54, italics in original)

Both producible and non-producible resources can be capital. The latter include something like oil, which can be exhausted by drilling.

In his non-homogeneous concept to capital, Hayek still thinks a connection exists between capital-intensity and time:

"There are two main ways in which the productivity of investment shows itself ... the investment of any group of services of the permanent resources can be combined into one single 'process' of production in two ways. In the one case it is the duration of the actual process of production where the time factor enters, and in the other case is the durability of the product (or of the non-permanent resources used in production)." (Hayek 1941, Ch. 6, p. 65, italics in original)

Hayek was an early adopter of the distinction and terminology of point input, flow input, point output, and flow output:

"it is useful to construct ideal limiting cases which show their peculiarities in the purest form. The first case is best represented if we conceive of a continuous application of input through a period of time, leading to an output all of which matures at a moment of time at the end of the period. This has been described as the 'continuous input – point output' case. The second case is ideally represented if we imagine durable good which is produced at a moment of time and then rendes services continuously over a period of time. This case has correspondingly been described as the 'point input – continuous output' case." (Hayek 1941, p. 66-67, italics in original)

Hayek distinguishes the investment period from the length of the process and the period of production:

"The fundamental fact with which we are concerned is the change in the periods for which particular units of input are invested, that is, the interval between the application of a unit of input and the maturing of the quantity of output due to that input. This interval of time we shall describe as the investment period of that unit of input.” (Hayek 1941, p. 69, italics in original)

Hayek recognizes that an investment period requires a high degree of abstraction to identify and may not always exist.

Hayek is considering the choice of technique, in which many techniques are known for producing a given final output:

"The considerations advanced above - and it is important to remember this throughout the discussion - have nothing to do with technological progress in this sense. On the contrary, they refer to changes under conditions where knowledge is stationary. All that is assumed is that at any moment there are known possible ways of using the available resources which would yield a greater return than those actually adopted, but would not yield this return until a later date, and for this reason are not actually used.

Among the wide range of possible methods of production known at any one time there will be some which will yield their product after shorter periods of time and some which will not yield it until after longer periods. From among each group of methods involving the same 'amount of waiting' - if we may make provisional use of this vague term - the one that will be chosen will be the one which yields the greatest return from a given investment of factors. But so long as there is any limitation on the 'amount of waiting' for which people are prepared, processes that take more time will evidently not be adopted unless they yield a greater return than those that take less time. (Hayek 1941, p. 72-73)

Hayek uses 'process' synomously with what I usually call a technique. Hayek thinks longer processes, in some sense, support a greater division of labor and often the use of resources that were not used before. Perhaps the consumer good is different but satisfies the same needs.

Here Hayek is once again rejecting an average period of production:

"Before we can pass on to this problem it is necessary to return for a moment to the, difficulty of talking about changes in the length of the process of production. It will probably be fairly obvious by now that as the complete processes of production with which we have to deal become increasingly complex it becomes more and more difficult, and may in some cases be impossible, to say in any general way which of several, alternative processes under consideration is as a whole the shortest or the longest. The total length of time which elapses between the very beginning of the process and the completion of the product may be shorter in one process than in another, and yet by far the greater part of the input used may be applied very early in the first process and very late in the second process. Which of these two processes is to be regarded as the longer? It is impossible to answer this question at the present stage, and there is in fact no general answer to it. It is only mentioned at this point in order to warn the reader against any attempt to provide himself with an answer by introducing some concept of an 'average period' of production. Such a concept, as we shall see, is not only unnecessary but is also highly misleading." (Hayek 1941, p. 76)

The above does not get at reswitching, I do not think. He wants a process in which resources are applied at the start and the end, in contrast to when they are used mostly in the middle.

Somewhere around here, Hayek defines stages of production, much like in his triangles.

I think the following gets at the possibility of reswitching:

"... when we compare two different investment structures, it will not always be possible even to say, on purely technical grounds, which of them involves the greater amount of waiting. At one set of relative values for the different kinds of input and at one rate of interest, the one structure, and at a different set of values or a different rate of interest, the other structure will represent the greater amount of waiting, or will be 'longer' in the sense in which this term has commonly been used." (Hayek 1941, Ch. 11, p. 144)

There is also something suggestive of capital-reversing in Chapter XXI.

"We shall not follow up this point in detail. For the method adopted to give a general picture of the considerations involved is really not adequate for an exhaustive analysis. The reason for this is, of course, as in all other cases where productivity or demand curves for individual factors are regarded as given, that these curves cannot be regarded as simultaneously and independently valid. But to take account of the complicated relations of technological (and psychological) complementarity which are involved, requires another technique which has been evolved quite recently in closely related fields, and which will also have to be used in a more exhaustive investigation of our problems. Here all that we shall mention is that if we were to start from a complete statement of the substitution relationships between all the different resources concerned, all kinds of peculiarities and apparent anomalies in the behaviour of individual factors would appear to be quite consistent with the general tendencies which can be deduced from the cruder type of analysis. It is, for instance, quite possible that while a fall in the rate of interest will create a tendency for the services of most of the permanent factors to be invested for longer periods and for their prices to rise, in the case of some individual factor the effect may well be that it will be invested for shorter periods, or that its price will be lowered, or both." (Hayek 1941, Ch. 21, p. 191-192)

The earliest description of something like reswitching is due to Irving Fisher.

Hayek and other Austrian-school economists are, of course, wrong. In what sense, whether assessed by value measures or physical properties, do more well-chosen, roundabout techniques raise net output? Samuelson (1966) noted that reswitching is not consistent with "the simple tale told by Jevons, Bohm-Bawerk, Wicksell, and other neoclassical writers". Fratini (2019a, 2019b) shows that the adoption of techniques with an increased average period of production, as assessed by financial measures, is compatible with decreased net output per worker. Steedman (2020), in considering techniques associated with the operation of different types of machines, demonstrates that more durable machines can also yield less net output per worker. I know that the economic life of machines do not support Hayek's idea.

Technical Terms: Continuous (flow) input or point input, continuous (flow) output or point output, Intertemporal general equilibrium, Investment period, Period of production, Permanent and non-permanent resources, Producible and non-prodicable resources, Stages of production, Structure of production

Wages, Employment Not Determined By Supply And Demand

1.0 Introduction

I do not think I have presented an introductory example in a while in which an increased wage is associated with firms wanting to employ more labor, given the level of net output. This example is presented as a matter of accounting for a vertically integrated firm.

Exact calculations with rational numbers are tedious in this example. I expect that if anybody bothers to check this, they would use a spreadsheet. As far as I can tell, Microsoft Excel uses double precision floats.

2.0 Technology

The managers of a competitive, vertically-integrated firm for producing corn know of the four production processes listed in Table 1. Corn is a consumption good and also a capital good, that is, a produced commodity used in the production of other commodities. In fact, iron, steel, and corn are capital goods in this example. The first process produces iron, the second process produces steel, and the last two processes produce corn. Each process exhibits Constant Returns to Scale (CRS) and is characterized by coefficients of production. Coefficients of production (Table 1) specify the physical quantities of inputs required to produce the specified unit output in the specified industry. All processes require a year to complete, and the inputs of iron, steel, and corn are all consumed over the year in providing their services so as to yield output at the end of the year. The data on technology are taken from a larger example.

Table 1: Technology

Input	Process
	a	d	e	f
Labor	1/3 person-year	7/20 person-year	1 person-year	3/2 person-year
Iron	1/6 ton	1/100 ton	1 ton	0 tons
Steel	1/200 ton	3/10 ton	0 tons	1/4 ton
Corn	1/300 bushel	0 bushel	0 bushels	0 bushels
Output	1 ton iron	1 ton steel	1 bushel corn	1 bushel corn

The managers of the firm have available two techniques for producing corn from inputs of labor, with intermediate inputs being constantly replaced. The iron-producing, steel-producing, and first corn-producing processes are operated in the Gamma technique. The second corn-producing process, as well as the iron and steel-producing processes, are operated in the Delta technique. Iron, steel, and corn all enter, either directly or indirectly, into the production of corn in both techniques. Vertically-integrated firms can also operate a linear combination of the Gamma and Delta technique.

3.0 Quantity Flows

One can consider various levels of operations in each of the processes for each of the technique. I consider two examples of snychronized production, in which inputs of labor simultaneously produce a net output of corn for consumption. A structure of production, consisting of specific capital goods, intervenes between the inputs and output. The labor input reproduces that structure, as well as producing the output.

3.1 Gamma Quantity Flows

Suppose 14,000/11,619 ≈ 1.205 tons iron are produced with the first process, 100/11,619 ≈ 0.0086 tons steel are produced with the second process, and 34,997/34,857 ≈ 1.004 bushels corn are produced with the third process. Then the quantity flows illustrated in Table 2 result. 14,000/11,619 tons iron are used as inputs among the three industries. These inputs are replaced by the output of the iron-producing process. 100/11,619 tons of steel are used as inputs among the three industries, and these inputs are replaced by the output of the steel-producing process. 140/34,857 bushels of corn are used as inputs among the three industries, leaving a net output of one bushel corn. In short, these quantity flows are such that 49,102/34,857 ≈ 1.409 person-years produce one bushel corn net. Obviously, I did not pick a very good set of coefficients for this example to support exact calculations in rational numbers.

Table 2: Vertically-Integrated Production with the Gamma Technique

Input	Process
	a	d	e
Labor	14,000/34,857 person-year	35/11,619 person-year	34,997/34,857 person-year
Iron	7000/34,857 ton	1/11,619 ton	34,997/34,857 ton
Steel	70/11,619 ton	30/11,619 ton	0 tons
Corn	140/34,857 bushel	0 bushel	0 bushels
Output	14,000/11,619 ton iron	100/11,619 ton steel	34,997/34,857 bushel corn

3.2 Delta Quantity Flows

Suppose 100/23,331 ≈ 0.00429 tons iron are produced with the first process, 25,000/69,993 ≈ 0.3572 tons steel are produced with the second process, and 69,994/69,993 ≈ 1.00001 bushels corn are produced with the fourth process. By the same logic as above, these quantity flows are such that 1807/1111 ≈ 1.626 person-years produce one bushel corn net.

Table 3: Vertically-Integrated Production with the Delta Technique

Input	Process
	a	d	f
Labor	100/69,993 person-year	1,250/9,999 person-year	34,997/23,331 person-year
Iron	50/69,993 ton	250/69,993 ton	0 ton
Steel	1/46,662 ton	7,500/69,993 ton	34,997/139,986 tons
Corn	1/69,993 bushel	0 bushel	0 bushels
Output	100/23,331 ton iron	25,000/69,993 ton steel	69,994/69,993 bushel corn

4.0 Prices

Which technique will the managers of the firm choose to adopt? By assumption, they take the price of corn and the wage as given on the consumer and labor markets. For simplicity, assume that price of a bushel corn is unity. That is firms treat the price of the consumer good as numeraire. At the end of the year, firms own a stock of iron, steel, and corn. They sell some of the corn to consumers. They retain the iron, steel, and enough corn to continue production the next year.

In a consistent accounting scheme, the price of iron and steel are such that:

• The same (accounting) rate of profits is obtained in all operated processes.
• The cost of the inputs, per bushel corn produced gross, for the corn-producing process not operated for a technique does not fall below that for the operated process.

The first condition specifies prices of intermediate goods and the rate of profits the accountants register. The second condition states that no pure economic profits can be obtained. Under these conditions, the managers of the firm can price their capital stock at the end of any year.

4.1 Prices at a Low Wage

Suppose the wage is w = 19,296/352,547 ≈ 0.05473 bushels per person-year. The accountants set the price of iron at p₁ = 6,860/27,119 ≈ 0.2530 bushels per ton iron and the price of steel at p₂ = 76,454/27,119 ≈ 2.819 bushels per ton steel. Table 4 shows the cost per unit output for each process and the resulting rate of profits obtained by operating each process. In constructing the tables for price systems, wages are assumed to be advanced. Under these assumptions, the rate of profits is 9/4, that is 225 percent, in each process comprising the Gamma technique. A lower rate of profits is obtained in the remaining corn-producing process, and it will not be operated. This is a consistent accounting system for the vertically-integrated firm, given the wage.

Table 4: Costs and the Rate of Profits at a Low Wage

Process	Cost	Rate of Profits
a	(1/6)p1 + (1/200)p2 + (1/300) + (1/3)w = 27,440/352,547	225 percent
d	(1/100)p1 + (3/10)p2 + (7/20)w = 305,816/352,547	225 percent
e	p1 + w = 2,308/7,501	225 percent
f	(1/4)p2 + (3/2)w = 554,839/705,094	≈ 27.1 percent

4.2 Prices at a Higher Wage with the Original Technique

Now suppose the wage is higher, namely w = 1,332/5,197 ≈ 0.2563 bushels per person-year. Consider prices of p₁ ≈ 0.2622 bushels per ton iron and p₂ ≈ 0.4167 bushels per ton steel. Table 5 shows cost accounting for these prices.

Table 5: Costs and the Rate of Profits at a High Wage (Incomplete)

Process	Cost	Rate of Profits
a	0.141 Bushels per ton iron	85.9 percent
d	0.2241 Bushels per ton steel	85.9 percent
e	0.5379 Bushels per bushel	85.9 percent
f	0.5178 Bushels per bushel	93.1 percent

Notice the same rate of profits is obtained in operating the first three processes. But the cost of producing a bushel corn with the last process is lower than in producing corn with process e. A larger rate of profits is obtained in operating that process. The managers of the firm will realize that their accounting implies that the Delta technique should be operated. If this firm were not vertically integrated and iron and steel were purchased on the market, a market algorithm would also lead to the Delta technique being adopted at this wage.

4.3 Prices at the Higher Wage with the Cost-Minimizing Technique

Continue to consider a wage of w = 1,332/5,197 ≈ 0.2563 bushels per person-year. The accountants report prices of p₁ = 1,420/5,197 ≈ 0.2732 bushels per ton iron and p₂ = 2,402/5,197 ≈ 0.4622 bushels per ton steel. Table 6 shows costs per unit output for the five processes under these prices.

Table 6: Costs and the Rate of Profits at a High Wage

Process	Cost	Rate of Profits
a	710/5,197	100 percent
d	1,201/5,197	100 percent
e	2,752/5,197	≈ 88.8 percent
f	1/2	100 percent

With this set of prices, the Delta technique is operated, and a rate of profits of 100 percent is obtained. The cost of operating the first corn-producing process exceeds the cost of operating the corn-producing process in the Delta technique. With a higher wage, the managers of a cost-minimizing firm will choose to operate a corn-producing process that requires more labor per bushel corn produced gross. (3/2 person-years is greater than 1 person-year.) More labor will also be hired per bushel corn produced net.

5.0 Conclusion

Table 7 summarizes these calculations. The ultimate result of a higher wage in the range considered is the adoption of a more labor-intensive technique. If this firm continues to produce the same level of net output and maximizes profits, its managers will want to employ more workers at the higher of the two wages considered. So much for the theory that, given competitive markets, wages and employment are determined by the interaction of well-behaved supply and demand curves on the labor market.

Table 7: A More Labor-Intensive Technique at a Higher Wage

Wage	Technique	Labor Intensity
0.05473 bushels per person-year	Gamma	1.409 person-years per bushel
0.2563 bushels per person-year	Delta	1.626 person-years per bushel

This example can be generalized in many ways. Different types of labor can be introduced. More intermediate produced capital goods can be included. Any number of processes can be available for producing each good, including an uncountable infinity. The use of fixed capital introduces more complications. The introductory marginalist textbook story about wages and employment in competitive markets is without foundation.

Why do so many economists teach nonsense?

Alienation And Commodity Fetishism

Marx, in Theories of Surplus Value, quotes James Stuart writing about 'profit upon alienation'. When one sells a good one owns, one has alienated it from oneself. In the typical work relation under capitalism, the managers of firms, that is, the representatives of capitalists, sell the product or services that workers produce. Workers do not own the goods they produce, for they have previously sold their labor-power. That is, they have agreed that their product is not owned by themselves, and neither is their labor.

But alienation means something more in Marx's Paris Manuscripts. The work of Ludwig Feuerbach is important background here. (By the way, this post is based mostly on secondary and tertiary literature, I forget which. I have not read most of the Marx and Engels' works cited here in some time.)

Feuerbach's criticism of Christianity is of some importance for Marx's concept of alienation. According to Feurbach, God's human-like qualities of knowledge, wisdom, and power are projections of extensions of human qualities. We impose them on God. This result of the projection of human qualities is then taken as ruling over us.

Capital goods are themselves the result of human labor. But, in capitalism, the alienated worker is then ruled by these products of human labor. In both cases, human do not usually understand that they are ruled by an entity created collectively by themselves.

The word 'alienation' never appears in the three volumes of Capital as I understand it. Instead, Marx writes about commodity fetishism. I guess the continuity I am claiming is debated among scholars of Marx. But the following sounds like alienation, as developed from the ideas of Feuerbach, to me:

"A commodity is therefore a mysterious thing, simply because in it the social character of men's labour appears to them as an objective character stamped upon the product of that labour; because the relation of the producers to the sum total of their own labour is presented to them as a social relation, existing not between themselves, but between the products of their labour. This is the reason why the products of labour become commodities, social things whose qualities are at the same time perceptible and imperceptible by the senses... with commodities... existence of the things qua commodities, and the value relation between the products of labour which stamps them as commodities, have absolutely no connection with their physical properties and with the material relations arising therefrom. There it is a definite social relation between men, that assumes, in their eyes, the fantastic form of a relation between things. In order, therefore, to find an analogy, we must have recourse to the mist-enveloped regions of the religious world. In that world the productions of the human brain appear as independent beings endowed with life, and entering into relation both with one another and the human race. So it is in the world of commodities with the products of men's hands. This I call the Fetishism which attaches itself to the products of labour, so soon as they are produced as commodities, and which is therefore inseparable from the production of commodities.

The religious analogy suggests, perhaps, that this supposed relation between things appears as a independent being. That is, capital is an entity with seeming agency and its own logic. Marx uses such metaphors as zombies, vampires, and table-turning for this spectral creature. "Capital comes dripping from head to foot, from every pore, with blood and dirt." In a longer exposition, I would also want to go the formal and real subsumption to capital.

It may seem odd to talk about capital as a creature with agency. Many human beings, following certain protocols, can implement a Turing machine, unbeknowest to themselves. The analogy of markets to a computer is harly novel. More prosaically, every manager or firm owner who justifies layoffs; the closure of factories, stores, and offices; or the abandoment of one line of business and the start up of another is appealing to some such logics of capital. Whatever you may think of such people, they are not wrong in claiming to be ruled by an overarching entity.

Capital is not the only supra-personel entity, discussed among Marxists, that seems to have agency. Hardt and Negri's Empire also seems to be such an entity.

I think that Marx condemns capitalism, inasmuch as he does, because he objects to the rule of capital as a supra-personel entity. This creature is constructed by human beings, and we should be able to rule ourselves without such illusions. The rule of this creature hardly seems consistent with a society in which "the free development of each is the condition for the free development of all."

Precursors Of The Modern Revival Of Classical Political Economy

A revolution occurred in price theory about two-thirds of a century ago. Several scholars independently developed components of this revolution. This post merely lists selected literature. I have previously tried to briefly describe why some of these authors are precursors.

• Ladislaus von Bortkiewicz (1907) On the correction of Marx's fundamental theoretical construction i the third volume of Capital. Translated and reprinted by Sweezy.
• David G. Champernowne (1945-1946) A note on J. V. Neumann's article on "A model of economic equilibrium". Review of Economic Studies 13 (1): 10-18.
• Georg von Charasoff (2010) Das System des Marxismus: Darstellung und Kritik. Berlin: H. Bondy.
• V. K. Dmitriev (1974) Economic Essays on Value, Competition, Utility. English Trans.
• Walter Isard (1951) Interregional and regional input-output analysis: A model of a space economy. Review of Economics and Statistics 33 (4): 318-328.
• Wassily Leontief (1928). The economy as a circluar flow.
• Maurice Potron (2010) The Analysis of Linear Economic Systems: Father Maurice Potron’s Pioneering Works (ed. by Christian Bidard and Guido Erreygers). Routledge.
• Jacob Schwartz (1961). Lectures on the Mathematical Method in Economics. New York: Gordon & Breach.
• Piero Sraffa (1960) Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory Cambridge
• John Von Neumann (1945-1946) A model of economic equilibrium. Review of Economic Studies 13 (1): 1-9.

Elsewhere

• Prof. Rowena Ball teaches a course on indigenous mathematics at Australian National University.
• Prof. Caroline Fohlin, an economics professor at Emory University, is arrested for being assaulted by rioting police.
• Prof. Tim Garrett questions the units of measurement in aggregate production functions. Aggregate production functions are not laws of nature, and those not in a broken discipline should not be thrown by questions about units of measurement. Maybe some production functions make sense as limit cases of linear combinations of Leontief production functions.
• Daniel Kahneman has died.
• Deirde McCloskey asserts, without cogent argument, that the labor theory of value is wrong. In what units do you imagine the marginal product of capital is measured?
• Andy Merrifield has an article, "Gramsci and his friend 'S'", in Monthly Review.
• Branko Milanović reminisce about a neo-Ricardian study group in communist Yugoslavia.

Update on 1 May: Added link to Andy Merrifield essay,

Marxian Political Economy As Forward-Looking

Every child knows a nation which ceased to work, I will not say for a year, but even for a few weeks, would perish. Every child knows, too, that the masses of products corresponding to the different needs required different and quantitatively determined masses of the total labor of society. That this necessity of the distribution of social labor in definite proportions cannot possibly be done away with by a particular form of social production but can only change the mode of its appearance , is self-evident. No natural laws can be done away with. What can change in historically different circumstances is only the form in which these laws assert themselves. And the form in which this proportional distribution of labor asserts itself, in the state of society where the interconnection of social labor is manifested in the private exchange of the individual products of labor, is precisely the exchange value of these products. -- Karl Marx to Dr. Kugelmann, 11 July 1868

The above quotation is a pithy statement of a pre-analytical vision. The ideas underlying this vision are interesting, independently of what you may think about the details of Marx's theory of value.

One can start to explicate these ideas with a one-commodity model. Accordingly, consider an economy in which one commodity, corn, is produced. Suppose production takes one year. Let a₀ be person-years of labor needed to produce a bushel corn. Let a be the bushels of seed corn needed to produce a bushel corn. Assume labor is necessary to produce corn:

a₀ > 0

Assume that a surplus product is produced, in that more than a bushel corn is produced for every bushel of seed that is planted:

0 < a < 1

The table below shows how each person-year of workers hired by the capitalists are allocated.

Distribution of a Work in the Current Year

Labor Time	Purpose
1 - a	To produce (1 - a)/a0 commodities to consume at the end of the current year.
a (1 - a)	To produce capital-goods to be used to produce (1 - a)/a0 commodities to consume at the end of the next year.
a2 (1 - a)	To produce capital-goods to be used to produce capital goods to produce (1 - a)/a0 commodities to consume at the end of two years hence.
a3 (1 - a)	To produce ... (1 - a)/a0 commodities to consume at the end of three years hence.
. . .	. . .

Recall the sum of a geometric series:

1 + a + a² + a³ + . . . = 1/(1 - a)

So some algebra shows that the labor expended at a moment of time for the purposes shown in the table is indeed one person-year.

This is very simple, of course. The heterogenous nature of capital goods is not shown, even though such heterogeneity is essential for the full articulation of these ideas. In a capitalist economy, nobody is in charge of ensuring that the labor force is allocated so as to produce commodities for consuming now and in the future. The social division of labor comes about through participants responding to prices, orders, contracts, and so on, as they perceive them. A structure of production exist at any moment of time, refracting (not necessarily consistent) plans and expectations about what can be sold in the future.

Even in this simple example, variations can be introduced. Suppose the economy is expected to grow. And suppose that one expects technical progress to reduce one or both coefficients of production at some rate. Then the allocation of labor would not be as in the table. Pasinetti's vertically hyper-integrated sectors help in the analysis here.

Another question is if the plans implicit in the allocation of labor at a moment in time will be realized in the years to come. This realization depends on the mix of decisions to consume and save, now and in time to come. But those decisions are constrained by income, which depends on the decisions to hire workers for wages today. An independent equilibrium does not exist that is just being followed by agents in the economy. Instead, possible and actual future paths are being laid down, tile by tile, plank by plank. Thus, as Paul Davidson has argued, Post Keynesians have an appreciation of the distinction between uncertainty and risk that economists of the Austrian school lack.

Austrian School Claims About The Period Of Production And Capital

1.0 Introduction

Economists of the Austrian school generally retain some concept that lower interest rates incentivize capitalists or entrepreneurs to adopt more lengthy production processes, in some sense, while still rejecting aggregate physical measures of roundaboutness or capital intensity. This post collects some quotations of economists of the Austrian school or Austrian-adjacent saying such or saying something confused about the Cambridge Capital Controversy. I want to recall this post.

2.0 Hayek on the Mythology of Capital

Hayek's 1936 paper is, I think, often cited by Austrian economists. I can agree with the following:

"The basic mistake – if the substitution of a meaningless statement for the solution of a problem can be called a mistake – is the idea of capital as a fund which maintains itself automatically, and that, in consequence, once an amount of capital has been brought into existence the necessity of reproducing it presents no economic problem. According to Professor Knight, 'all capital is normally conceptually, perpetual,' 'its replacement has to be taken for granted as a technological detail,' and in consequence 'there is no production process of determinate length, other than zero' or 'all history,' but 'in the only sense of timing in terms of which economic analysis is possible, production and consumption are simultaneous.'" Hayek 1936: 201-202.

I think Bohm-Bawerk has a metaphor of capital as like a lake, with a stream flowing in and another one out. The streams may have the same volume of water flowing at the same rate, but the depth of the lake still matters.

Here is a less well-posed objection Hayek has to Knight:

"it is asserted that 'making an item of wealth more durable' or 'using a longer period of construction,' i.e. lengthening the time-dimension of investment in either of the two possible ways, is only one among an 'accurately speaking, infinite number' of possible ways of investing more capital, which are later even described as 'really an infinite number of infinities.'" Hayek 1936: 202

And here Hayek clearly makes a mistake:

"An increase of capital will always mean an extension of the time dimension of investment, that capital will be required to bring about an increase of output only in so far as the time dimension of investment is increased." Hayek 1936, p. 204

Hayek is considering the analysis of the choice of technique in a given state of technical knowledge:

"It should be quite clear that the technical changes involved, when changes in the time structure of production are contemplated, are not changes in technical knowledge." Hayek 1936: 205

And here Hayek rejects Böhm Bawerk's measure of the period of production:

"It is not proposed, and is in fact inadmissible, to reduce the description of the range of periods for which the different factors are invested to an expression of a single time dimension such as the average period of production." Hayek 1936: 206

3.0 de Soto on Reswitching

I skip ahead to this century. Here is a deeply confused quotation:

"growth in voluntary saving always causes, in prospective terms, a ‘lengthening’ of the productive structure, irrespective of whether techniques which were only profitable at higher interest rates are readopted in certain new investment processes - all initial factors (land, labor, and existing capital goods) are subjectively deemed to be 'original means of production' which merely determine the starting point of the production process. It is therefore irrelevant whether or not the new investment process incorporates techniques which, considered individually, may have been profitable at higher rates of interest." de Soto (2006)

Considering which techniques are cost minimizing at different rates of interest is an analysis conducted in a comparision of long period positions. It is questionable if it even makes sense to talk about an interest rate on money in an intertemporal equilibrium, that being the model in which initial quantities of capital goods are given. Some fans of Austrian economics have recently injected confusion into the entry on the Cambridge Capital Controversy. De Soto is certainly a 'reliable source', though, in Wikipedia terms.

4.0 Yeager on the CCC

Leland Yeager was, at least, sympathetic to the Austrian school. He re-introduced something like a period or production, where that period depends on prices:

"The paradoxes dissolve when we recognize that the amount of that factor required in a physically specified production process does indeed depend on its own price." (Yeager 1976)

I do not think his definition is clear. He calls this measure 'waiting':

"We have to recognize waiting as a factor of production—the tying-up of value over time." (Yeager 1976)

And he is clear about how it is dependent on prices:

"the amount of waiting required in accomplishing a physically specified purpose does depend on its own price." (Yeager 1976)

In their response to comments on their retrospective, Cohen and Harcourt say, as I recall, that Yeager misunderstood the issues. Traditional marginalist theory is about the allocation of given resources. Those given resources are land, labor, and capital. What does it mean to talk about a given quantity of capital in the theory? Yeager's waiting does not help answer this question.

At any rate, Yeager recognizes consumption-reversal remains a challenge:

"One paradox not cleared up to my full satisfaction concerns consumption... It seems inadequate to reply that labor is not the only factor of production and that the higher output per man in [a] technique ... does not, at all interest rates, mean higher output in relation to labor and waiting together." (Yeager 1976)

Yeager claims that not fully specifying a traverse limits the CCC:

"Standard theory need not be embarrassed by stories that do not even say how the interest rate is determined and changed, why one economy might be in a steady state employing one technique and an otherwise similar economy in a steady state employing another, or how an economy might make a transition between such states." (Yeager 1976)

I conclude with one more quotation:

"the concept of an aggregate of physical capital is inherently fuzzy. Some capital goods are always being worn out and scrapped, and new ones are always being constructed. Whether the aggregate is growing or shrinking or staying unchanged may be hard to say, especially since unforeseen changes in technology and tastes are always occurring and raising or lowering the market values and the genuine usefulness of particular capital goods." (Yeager 1976)

5.0 Cachanosky and Lewin

Cachanosky and Lewin champion an old measure of the period or production:

"It is the (present-) value-weighted amount of time involved in the investment. As such, it is a money-value of time measure. It can be easily show that it is also the elasticity of the NPV with respect to the discount factor f. Therefore, Duration (D) can be interpreted as a measure of 'roundaboutness' and also of the sensitivity of the value of the investment to changes in the interest rate." (Lewin and Cachanosky 2019b)

I know this measure from Hicks' Value and Capital. They also cite Macaulay, a researcher in finance about contemporary with Hicks' work. Duration depends on prices. Fratini recalls that this measure requires a division of zero in an equilibrium. I have noticed a lack of appreciation of the wage-rate of profits frontier in some literature from Austrian school economists.

Anyways, they present Duration in the context of Austrian business cycle theory:

"In its most generic form, the ABCT posits a scenario in which, because of an unsustainably low discount rate, many investors mistakenly invest in unsustainable (ultimately unprofitable) ventures. A surge of investments characterized by higher Durations as a result of the lower rate of discount, is followed eventually by a surge of business failures reversing this trend, bouncing back to lower Duration, safer, investments. Regardless of whether the Duration of some investments rise more or less than others, thus changing the ranking of ventures in terms of their Durations, investors are in general choosing higher duration investments." (Lewin and Cachanosky 2019b)

I am not sure quite what is being claimed in that last sentence, especially with the phrase, "in general".

Anyways, they resist explicitly equating Duration to a measure of the quantity of capital, although I thought that was the point:

"our definition of capital does not suggest that more capital and less labor is implied by an increase in Duration. These are the very aggregate concepts that are rejected by our approach." (Lewin and Cachanosky 2019b)

Consumption reversal might still be an issue for Cachanosky and Lewin.

6.0 Conclusion

I do not know how much more literature I want to look at. Above, I have nothing to say about Hayek's triangles or Hayek (1941). I skip over Roger Garrison's more recent book, too, and much more. Apparently, Cachanosky and Lewin have an even more recent book where they might have a response to Fratini.

References

• Cachanosky, N and P. Lewin. (2018). The role of capital structure in Austrian business cycle theory. Journal of Private Enterprise, 8(2): 268–280.
• de Soto, J. H. (2006). Money, Bank Credit, and Economic Cycles, 1st English ed. (trans. by M. A. Stroup) Auburn: Ludwig von Mises Institute.
• Fratini, S.M. (2019a) A note on re-switching, the average period of production and the Austrian business-cycle theory. Review of Austrian Economics. 32 (4): 363-374
• Fratini, S.M. (2019b) Re-switching and the Austrian business-cycle theory: A rejoinder. Review of Austrian Economics. 32 (4): 368-389.
• Hayek, Friedrich A. (1936). The mythology of capital. Quarterly Journal of Economics 50: 199-228.
• Hayek, Friedrich A. (1941). The Pure Theory of Capital. Chicago: University of Chicago Press.
• Lewin, P. and Cachanosky, N. (2019a) Austrian capital theory: A modern survey of the essentials. Cambridge: Cambridge University Press.
• Lewin, P. and Cachanosky, N. (2019b) Re-switching, the average period of production and the Austrian business-cycle theory: A comment on Fratini. Review of Austrian Economics. 32 (4):375-382.
• Yeager, Leland B. (1976). Capital paradoxes and the concept of waiting. In Time, Uncertainty, and Disequilibrium: Exploration of Austrian Themes (Ed. by Mario Rizzo). Lexington: D. C. Heath.

A Perverse Switch Point For Neoclassical Economics, Non-Perverse For Austrians

Figure 1: The Wage-Rate of Profits Frontier

1.0 Introduction

This post completes a demonstration that the economic life of a machine is independent of the capital-intensity of a technique. I here fill in the upper right of a two-by-two table. I have previously filled in the upper-left and lower right entries. And I also have an example for the lower left.

2.0 Technology

Tables 1 and 2 present coefficients of production for processes which can be combined to produce a new output of corn. The example has the structure of one from Salvatore Baldone. Corn is assumed to be the sole consumer good and the numeraire. In the first process, labor works with corn input to produce a machine with a physical life of three years. Labor works with seed corn and machines of the specified age, in each of the remaining processes, to produce a unit of corn and machines a year older. The machine is discarded after being operated in the last process.

Table 1: Inputs for The Technology

Input	Process
	(I)	(II)	(III)	(IV)
Labor	21/50	39/200	117/200	39/100
Corn	12/125	39/100	141/250	117/200
New Machines	0	1	0	0
One-Year Old Machines	0	0	1	0
Two-Year Old Machines	0	0	0	1

Table 2: Outputs for The Technology

Output	Process
	(I)	(II)	(III)	(IV)
Corn	0	1	1	1
New Machines	1	0	0	0
One-Year Old Machines	0	1	0	0
Two-Year Old Machines	0	0	1	0

3.0 Choice of Technique

Three techniques exist for producing a net output for corn. The Alpha, Beta, and Gamma technique differ in the economic life of the machine. In Alpha, the economic life of the machine continues to be one-year, while it remains its full physical life of three years in Gamma. Figure 1, at the top of this post, displays the wage curves for the three techniques. Gamma is cost-minimizing at a low rate of profits. Beta is cost-minimizing at an intermediate rate of profits, and Alpha is cost-minimizing at a high rate of profits. The wage curves for the Alpha and Beta techniques intersect at a low rate of profits within the frontier.

Perhaps this example is clarified by looking at prices. As shown in Figure 2, the price of a new machine is positive for the whole range of feasible rate of profits in the system of equations for each technique. Figure 3 graphs the prices of old machine of each age as a function of the rate of profits. Suppose the machine is operated for its physical life of three years, as under Gamma. The price of a two-year old machine is positive for rates of profits up to a switch point with Beta, at approximately 61 percent. The price of a one-year old machine is positive even for rates of profits slightly higher. Thus, the analysis of the choice of production based on prices confirms that Gamma is cost-minimizing at low rates of profits.

Figure 2: The Price Of A One-Year Old Machine

Figure 2: The Prices Of Old Machines

The price of a two-year old machine under Beta is zero. The price of a one-year old machine, when it is operated for two years, is positive between a rate of profits of approximately 24 and of 73 percent. That is, in a range of high rates of profits where Gamma is no longer cost-minimizing, Beta is cost-minimizing in the indicated range. Finally, Alpha is cost-minimizing in the highest range of profits, when the prices of one-year old and two-year old machines is negative under both Beta and Gamma.

If the physical life of a machine were two years, this example would be one of a reswitching. Around the switch point between Alpha and Beta at approximately 73 percent, a lower rate of profits is associated with a decreased value of capital per worker and an increased net output of corn per worker. On the other hand, around this switch point, a lower rate of profits is associated with an increased economic life of the machine.

4.0 Conclusion

This example fills in the upper right of this table. Table 1. The economic life of a machine is independent of the capital intensity of the techniques in which the machine is operated.

A Letter From Marx To Engels In 1858 Outlining His Critique Of Political Economy

I have previously repeated some transcriptions from the correspondence Marx and Engels. I tried to concentrate on some formulations from Engels of ideas important in Marxism, Marx stating what is important and novel in Capital, or outlines of the project, particularly concentrating on the so-called transformation problem. This long letter certainly belongs in this collection.

Marx's ideas were fairly well-developed in 1858. Here he has promised Duncker, a publisher, to write what eventually became A Contribution to the Critique of Political Economy. After delay, he only delivered to the publisher the first part of what he was aiming for. I have always found this short book less inspiring, as compared with Capital. Capital does not contain anything on advocates of labor notes, though. The introduction is notable for a short statement of historical materialism, with various aphorism. It went through German (Prussian?) censorship, but I have never seen anybody comment on that. Marx thought his work was scientific, I guess, and thus the censors could not object.

Anyways, we see that Marx only published the first of six parts that he had planned, and only the first subpart of that. Volume 3 of Capital has something on land and rent. And one could argue that he incorporated some of his theory of wages into volume 1. But his developed publications do not contain anything explicit on the state, international trade, and the world market. I think, with his work habits, if Marx promised a few pages, you can expect a long chapter. If he promised a chapter, you can expect a book. Or maybe you will never get anything.

I include the start of this letter for completeness. I did not look up what the first two paragraphs are about, other than to see that the battle of Alma was part of the Crimean war.

2 April 1858

Dear Frederick

The Guardian stories highly AMUSING. A correspondent of the Daily Telegraph (DIRECTLY UNDER PAM'S AUSPICES) writes of the great danger of being 'DEAF' in Paris, and says that all 'DEAF ENGLISHMEN' were being hounded by the police as Allsops. Also that ENGLISHMEN were leaving Paris en masse, partly because of police chicanery, partly for fear of an outbreak. For if the latter were to happen and the Bonapartists be victorious, the John Bulls feared they might be massacred by the MADDENED SOLDIERS, whereat the correspondent himself naively comments that IN SUCH A CASE [HE] SHOULD LIKE TO BE ANYWHERE ELSE BUT IN PARIS. This DESERTION by the Bulls AT THIS MOMENT OF COMMERCIAL DEPRESSION is queering the pitch of the Parisian épicier and householdr, whores, etc. Have you seen that 300 million francs have AVOWEDLY 'DISAPPEARED' FROM THE BUDGET, AND NOBODY KNOWS WHAT HAS BECOME OF THEM? There will, BY AND BY, be further REVELATIONS about Bonapartist FINANCE, and then the asses on the Tribune will realise the wisdom of not having published the very ELABORATED ARTICLES I sent them on the subject six months ago.219 The fellows are asses and anything which is not, in the crudest sense, a 'question of the day' they tend to cast aside as UNINTERESTING, only to go and compile the most egregious rubbish about the selfsame subject as soon as it does become à l'ordre du jour.

Nota bene: in the military clubs here it is being rumoured that EVIDENCE has been discovered among the papers left by Raglan that, 1. at the battle of the Alma he rightly suggested to attack the Russians, not from the direction of the coast, but from the opposite flank, and drive them into the sea; 2. that he proposed to advance on Simferopol after the batde of the Alma; 3. that at Inkerman it was only by dint of the most urgent pleas and MENACES that he extorted from Canrobert the order for Bosquet to hasten to his [Raglan's] assistance. It is further said that, if the boasting on the other side of the Channel were to continue, these PAPERS would be published, providing proof that the French were ever ready TO BETRAY THEIR DEAR ALUES. Indeed, a few HINTS which de Lacy Evans dropped in the HOUSE OF COMMONS seem to indicate something of the kind.

I've been so ill with my bilious complaint this week that I am incapable of thinking, reading, writing or, indeed, of anything SAVE the ARTICLES for the Tribune. These, of course, cannot be allowed to lapse since I must draw on the curs as soon as possible. But my indisposition is disastrous, for I can't begin working on the thing for Duncker until I'm better and my fingers regain their VIGOUR and GRASP.

The following is a SHORT OUTLINE OF THE FIRST PART. The whole thing is to be divided into 6 books: 1. On Capital. 2. Landed Property. 3. Wage Labour. 4. State. 5. International Trade. 6. World Market.

1. Capital falls into 4 sections, a) Capital en général. (This is the substance of the first instalment.) b) Competition, or the interaction of many capitals, c) Credit, where capital, as against individual capitals, is shown to be a universal element, d) Share capital as the most perfected form (turning into communism) together with all its contradictions. The transition from capital to landed property is also historical, since landed property in its modern form is a product of the action of capital on feudal, etc., landed property. In the same way, the transition of landed property to wage labour is not only dialectical but historical, since the last product of modern landed property is the general introduction of wage labour, which then appears as the basis of the whole business.

WELL (IT IS DIFFICULT FOR ME TO-DAY TO WRITE), let us now come to the corpus delicti.

I. Capital. First section: Capital in general. (Throughout this section wages are invariably assumed to be at their minimum. Movements in wages themselves and the rise and fall of that minimum will be considered under wage labour. Further, landed property is assumed to be zero, i. e. landed property as a special economic relation is of no relevance as yet. Only by this procedure is it possible to discuss one relation without discussing all the rest.)

1. Value. Simply reduced to the quantity of labour; time as a measure of labour. Use-value—whether regarded subjectively as the USEFULNESS of labour, or objectively as the UTILITY of the product—is shown here simply as the material prerequisite of value, and one which for the present is entirely irrelevant to the formal economic definition. Value as such has no 'substance' other than actual labour. This definition of value, first outlined by Petty and neatly elaborated by Ricardo, is simply bourgeois wealth in its most abstract form. As such, it already presupposes 1. the transcending of indigenous communism (India, etc.), 2. of all undeveloped, pre-bourgeois modes of production which are not in every respect governed by exchange. Although an abstraction, it is an historical abstraction and hence feasible only when grounded on a specific economic development of society. All objections to this definition of value derive either from less developed relations of production or else are based on confused thinking, whereby the more concrete economic definitions from which value has been abstracted (and which may therefore also be seen, on the other hand, as a further development of the same) are upheld as against value in this its abstract, undeveloped form. In view of the uncertainty of messieurs les économistes themselves about the precise relation of this abstraction to later, more concrete forms of bourgeois wealth, these objections were plus ou moins justified.

The contradiction between the general characteristics of value and its material existence in a particular commodity, etc.—these general characteristics being the same as those later appearing in money—gives rise to the category of money.

2. Money.

Some discussion of precious metals as vehicles of the money relation.

a) Money as a measure. A few comments on the ideal measure in Steuart, Attwood, Urquhart; in more comprehensible form among the advocates of labour money (Gray, Bray, etc. An occasional swipe at the Proudhonists). The value of a commodity translated into money is its price. For the moment price appears only in this purely formal distinction between it and value. Thus, in accordance with the general law of value, a specific amount of money merely expresses a specific amount of objectified labour. In so far as money is a measure, the variability of its own value is of no importance.

b) Money as a means of exchange, or simple circulation.

Here we need only consider the simple form of circulation as such. All the other conditions by which it is determined are external to it, and hence will not be considered till later (presuppose more highly developed relations). If the commodity be C and money M then, although simple circulation evinces the two circuits or final points: C—M—M—C and M—C—C—M (this latter constituting the transition to c), the point of departure and the point of return in no way coincide, save by chance. Most of the so-called laws put forward by economists do not consider money circulation within its own confines, but as subsumed under, and determined by, higher movements. All this must be set aside. (Belongs in part to the theory of credit; but also calls for consideration where money appears again, but further defined.) Here, then, money as means of circulation (coin). But likewise as realisation (not simply evanescent) of price. From the simple statement that a commodity, in terms of price, has already been exchanged for money in theory before it is so exchanged in fact, there naturally follows the important economic law that the volume of the circulating medium is determined by prices, not vice versa. (Here, some historical stuff on the polemic concerning this point.) Again it follows that velocity may be a substitute for volume, but that a certain volume is essential to simultaneous acts of exchange in so far as the relation of these themselves is not that of + and —, an equalisation and consideration which will only be touched on at this juncture by way of anticipation. At this point I shall not go further into the development of this section and would only add that the lack of congruence of C—M and M—C is the most abstract and superficial form in which the possibility of crises is expressed. If the law concerning the determination of circulating volume by prices be developed, it will be found that the assumptions made here are by no means applicable to all states of society; hence the fatuity of comparing e.g. the influx of money from Asia into Rome and its effect on prices there tout bonnement with modern commercial relations. On closer examination, the most abstract definitions invariably point to a broader, definite, concrete, historical basis. (OF COURSE, since to the extent that they are definite they have been abstracted therefrom.)

c) Money qua money. This is a development of the formula M—C—C—M. Money, the independent existence of value as opposed to circulation; material existence of abstract wealth. Already manifested in circulation in so far as it appears, not only as a means of circulation, but as realising price. In this capacity c), in which a) and b) appear to be no more than functions, money is the universal commodity of contracts (here the variability of its value acquires importance: value being determined by labour time); it becomes an object of HOARDING. (This would still seem to be an important function in Asia, as formerly in the ancient world and in the Middle Ages GENERALLY. Now persists only in a subordinate capacity within the banking system. In times of crisis money in this form again acquires importance. In this form money considered along with the world-historical DELUSIONS which it engenders, etc. Destructive properties, etc.) As the realisation of all higher forms in which value will appear; definitive forms in which all relations of value are externally concluded. Money, however, once fixed in this form, ceases to be an economic relation which is lost in its material medium, gold and silver. On the other hand, in so far as money comes into circulation and is again exchanged for C, the final process, the consumption of the commodity, again falls outside the economic relation. The principle of self-reproduction is not intrinsic to simple money circulation, which therefore implies something extrinsic to itself. Implicit in money—as the elaboration of its definitions shows—is the postulate capital, i.e. value entering into and maintaining itself in circulation, of which it is at the same time the prerequisite. This transition also historical. The antediluvian form of capital is commercial capital, which always generates money. At the same time the emergence of real capital, either from money or merchant capital, which gains control of production

d) This simple circulation, considered as such—and it constitutes the surface of bourgeois society in which the underlying operations which gave rise to it are obliterated—evinces no distinction between the objects of exchange, save formal and evanescent ones. Here we have the realm of liberty, equality and of property based on 'labour'. Accumulation, as it appears here in the form of HOARDING, is merely greater thrift, etc. On the one hand then, the fatuity of the economic harmonists, modern free traders (Bastiat, Carey, etc.), in upholding this most superficial and most abstract relation of production as their truth, as against the more advanced relations and their antagonisms. Fatuity of the Proudhonists and suchlike socialists, in contrasting the ideas of equality, etc., corresponding to this exchange of equivalents (or presumed AS SUCH), to the inequalities, etc., to which this exchange reverts and from which it emanates. In this sphere, appropriation by labour, the exchange of equivalents, appears as the law of appropriation so that exchange simply returns the same value in another material form. In short, while everything may be 'lovely' here, it will soon come to a sticky end and this as a result of the law of equivalence. For now we come to

3. Capital.

This is really the most important part of the first instalment and one on which I particularly need your opinion. But today I can't go on writing. My bilious trouble makes it difficult for me to ply my pen, and keeping my head bent over the paper makes me dizzy. So FOR NEXT TIME.

Salut.

Your

K. M.

There is a lot in this letter. In much of Capital, Marx takes wages as at a given level, but not always. The given level does not have to be a physical subsistence. We see the order of exposition is value, money, capital. The simple circulation of commodities, with money as an intermediary, provides the possibility of crises. Marx asserts the theory of endogenous money. Much is given here about presenting his ideas as in opposition to the Ricardian socialists. Marx gestures that his account of exploitation is consistent with justice in exchange.

The Fundamental Sraffian Theorem

1.0 Introduction

I have been reading Robin Hahnel. Hahnel argues even more strongly than Steedman did that labor values are redundant. And he argues for the importance of the fundamental Sraffian theorem. I think this may be Hahnel's coinage. Anyways' this is my working my way through some of what I think he is saying.

Hahnel has some interesting things to say, not discussed here, about analyzing environmental concerns in a Sraffian framework. I ignore the chapter in Hahnel (2017) on the moral critique of capitalism. Following Eatwell (2019) and others, I hold that mainstream economists do not have a theory of value and distribution, anyways.

2.0 The Setting

Suppose a capitalist economy is observed at a given point in time. n commodities are being produced, each by a separate industry. Suppose the technique in use can be characterized by a row vector a₀ and a n x n square matrix A. Let the column vector d denote the quantities of each commodity paid to the workers for a unit of labor.

The jth element of a₀ is the amount of labor directly employed in the jth industry in producing one unit of a commodity output from that industry. "We suppose labour to be uniform in quality or, what amounts to the same thing, we assume any differences in quality to have previously been reduced to equivalent differences in quantity so that each unit of labour receives the same wage…" - Piero Sraffa (1960).

The jth column of A is the goods used up in producing one unit of a commodity output. For example, suppose iron is produced by the first industry and steel is produced by the second industry. a_1,2 is then the kilotons of iron needed to produce a kiloton of steel. Assume that every good enters directly or indirectly into the production of each commodity. Iron enters indirectly into the production of tractors if steel enters directly into the tractor industry. Assume a surplus product, also known as a net output, exists. That is:

0 < λ_PF(A) < 1

where λ_PF(A) is the dominant eigenvalue of the matrix A. The dominant eigenvalue is also known as the Perron-Frobenius root.

3.0 Prices of Production

Suppose the wage purchases the specified bundle of commodities. And also assume the wage is advanced. One can define the input-output matrix with wage goods included:

A⁺ = A + d a₀

I think that Sraffa treats the input-output matrix as A⁺ in chapter 1 of his book.

The system of equations for prices of production is:

p A⁺ (1 + r) = p

where p is a row vector, and r is the rate of profits. One can show that, given a surplus product, not including wage goods, a solution exists.

Fundamental Sraffian Theorem: The rate of profits, r, in the system of prices of production is positive if and only if:

0 < λ_PF(A⁺) < 1

In fact, the rate of profits is:

r = 1/λ_PF(A⁺) - 1

Under these assumptions, the price of each produced commodity is positive with the above rate of profits. And this economically meaningful solution is unique, up to the specification of a numeraire.

4.0 Increased Surplus Product

Suppose one or more of the elements of A⁺ decrease. Then 1 - λ_PF(A⁺), which is strictly positive, increases. The surplus product that capitalists capture is increased by decreased components of the real wage and by decreased commodity inputs into production.

Suppose that the real wage is given and that an innovation results in a new technique, B, being available. This technique might have increased coefficients and decreases in other coefficients, as compared to A. It might even have a new column or delete a column for an industry that is not used to directly produce a wage good. This new technique is adopted at the given wage if and only if:

1 - λ_PF(B⁺) > 1 - λ_PF(A⁺)

Suppose further that:

1 - λ_PF(B) < 1 - λ_PF(A)

Then the maximum rate of profits, at a wage of zero, decreases. Suppose no reswitching exists. I think this is what is meant by Capital-Using, Labor-Saving technical change. This is also known as Marx-biased technical change. Marx's law of the tendency of the rate of profits to fall, presented in volue 3 of Capital, is not justified by this analysis.

5.0 Quantity Flows

This framework can also be used to examine the rate of growth. Suppose employment, at an instant of time, is unity:

L = a₀ q = 1

where q isthe column vector of gross outputs. In this formulation, employment increases at the rate of growth.

Let consumption out of the surplus product be in the composition of the column vector e, and let c be the level of such consumption. It is most coherent to take this consumption as not made by the workers:

We could hardly imagine that, when the workers had a surplus to spend on beef. their physical need for wheat was unchanged. -- Robinson (1961)

So prices of production associated with this treatment of qunatity flows are as above.

Let the column vector j represent investment goods. These are part of the surplus product. Then the column vector q of gross outputs satisfies the following equation:

q = A⁺ q + c e + j

The above is extremely general. I now consider a steady-state rate of growth. Assume constant returns to scale in every industry. The vector of investment goods is in the same proportion as existing capital goods:

j = g A⁺ q

Here I present a derivation, since I typed this out to check myself. Substituting the specification of investment goods and after some algebraic manipulations, one has:

c e = [I - (1 + g)A⁺] q

Assuming the rate of growth is less than the maximum, one has:

c [I - (1 + g)A⁺]^-1e = q

Premultiplying by the row vector of labor coefficients, one has:

c a₀ [I - (1 + g)A⁺]^-1e = a₀ q = 1

The solution of the system of equations for quantity flows is:

c = 1/{a₀ [I - (1 + g)A⁺]^-1e}

The maximum rate of growth is:

g_max = 1/λ_PF(A⁺) - 1

The level of consumption out of the surplus product is lower, the higher the rate of growth and vice versa. One can also consider the impact on the rate of growth of changes in the elements of the matrix A⁺. I believe one can prove the following:

Theorem: The steady state rate of growth, g is higher if:

• Consumption out of the surplus product, where the surplus product does not include wages, is lower.
• Necessary wages are lower.
• The dominant eigenvalue, λ_PF(A), of the input-output matrix is lower.

The theorem highlights dilemmas in development economics. One does not want to obtain a higher rate of growth by lowering wages for those who are already pressed. It does not help for foreign aid to end up in luxury consumption either. In chosing the technique out of a range of possibilities, one would like the one that maximizes the rate of growth. Unless the rate of growth equals the rate of profits, that is, consumption out of the surplus product does not occur, the cost-minimizing technique is unlikely to be efficient in this sense.

6.0 Conclusion

The theory of value and distribution has a family resemblance to modern formulations of classical and Marxian political economy. Labor values are not discussed. It is focused on prices of production. Yet, with its consideration of dynamic changes in dominant eigenvalues, it seems to be consistent with an analysis of the formal and real subsumption of labor to capital. The formulation in this post can easily be generalized in various ways, Hahnel emphasizes inputs from nature and mentions the theory's consistency with homogeneous labor inputs. The analysis of growth should include technical change. I am interested in fixed capital. Some issues arise with general joint production, but the model is open in any case.

References

• John Eatwell. 2019. 'Cost of production' and the theory of the rate of profit. Contributions to Political Economy.
• Robin Hahnel. 2017. Radical Political Economy: Sraffa Versus Marx. Routledge.
• Joan Robinson. 1961. Prelude to a critique of economic theory. Oxford Economic Papers, New Series. 13 (1): 53-58.