Jevons Versus Marshal On Ricardo

I have been pointing out that much teaching in most universities and high schools in economics is propaganda. Mistakes that were exposed more than half a century ago continue to be taught. Alternatives have been available, at varying levels, in textbooks for decades.

Does an alternative, building on classical political economy and Marx, exist? Assertions on this topic go back more than a century.

A (bad) way of reading classical political economy is that its proponents were struggling towards developing the one true system, that of marginalist economists. With this incorrect view of continuity, you might say incorrectly that they overemphasized supply. Their theories were corrected by developing theories of utility and demand.

A better reading recognizes that they had their own approach. Jevons held this view, although he was wrong about which approach was better:

"When at length a true system of Economics comes to be established, it will be seen that that able but wrong-headed man, David Ricardo, shunted the car of Economic science on to a wrong line - a line, however, on which it was further urged towards confusion by his equally able and, wrong-headed admirer, John Stuart Mill." -- William Stanley Jevons, The Theory of Political Economy, Preface to the Second Edition, p. li.

Marshall, on the other hand, was an early progenitor of a supposedly generous reading that blurs the distinctiveness of the classical theory of value and distribution:

"1... [Ricardo's] book makes no pretence to be systematic. He was with difficulty induced to publish it; and if in writing it he had in view any readers at all, they were chiefly those statesmen and business men with whom he associated. So he purposely omitted many things which were necessary for the logical completeness of his argument, but which they would regard as obvious. And further, as he told Malthus in the following October, he was 'but a poor master of language.' His exposition is as confused as his thought is profound; he uses words in artificial senses which he does not explain, and to which he does not adhere; and he changes from one hypothesis to another without giving notice.

If then we seek to understand him rightly, we must interpret him generously, more generously than he himself interpreted Adam Smith. When his words are ambiguous, we must give them that interpretation which other passages in his writings indicate that he would have wished us to give them. If we do this with the desire to ascertain what he really meant, his doctrines, though very far from complete, are free from many of the errors that are commonly attributed to them...

...Again, in a profound, though very incomplete, discussion of the difference between 'Value and Riches' he seems to be feeling his way towards the distinction between marginal and total utility. For by Riches he means total utility, and he seems to be always on the point of stating that value corresponds to the increment of riches which results from that part of the commodity which it is only just worth the while of purchasers to buy; and that when the supply runs short, whether temporarily in consequence of a passing accident, or permanently in consequence of an increase in cost of production, there is a rise in that marginal increment of riches which is measured by value, at the same time that there is a diminution in the aggregate riches, the total utility, derived from the commodity. Throughout the whole discussion he is trying to say, though (being ignorant of the terse language of the differential calculus) he did not get hold of the right words in which to say it neatly, that marginal utility is raised and total utility is lessened by any check to supply.

2. But while not thinking that he had much to say that was of great importance on the subject of utility, he believed that the connection between cost of production and value was imperfectly understood; and that erroneous views on this subject were likely to lead the country astray in practical problems of taxation and finance; and so he addressed himself specially to this subject. But here also he made short cuts." -- Alfred Marshall, Principles of Economics, Appendix I

Marshall is wrong here. For example, Ricardo describes riches as a collection of commodities. They were not measured along a single scale, whatever measurement level you might think that scale obtains. Even less could his labor values be said to have been marginal utilities.

Samuel Hollander is the greatest exponent in my lifetime of the view of continuity in the development of theories of value and distribution. Even he, though, recognizes that Marx had reasons for his reading of Ricardo, but I forget where.

On The Failure Of So-Called Neoclassical Economics

I want to contrast the theories of classical political economists and marginalists up to, say, the 1920s. I take David Ricardo as representative of classical political economy. For purposes of this post, I consider Karl Marx to also be a classical political economist.

For marginalists, I think of Eugen Bohm Bawerk, John Bates Clark, William Stanley Jevons, Alfred Marshall, Leon Walras, Knut Wicksell, and Philip Wicksteed among a host of others. Obviously, I am, at this level of abstraction, ignoring differences among both groups.

Modern economists have established that the classical political economists were broadly correct. And that the marginalists around the time of their intellectual revolution were ultimately incorrect.

Both groups tried to explain roughly the same object with their theories. That is, they proposed theories of long run equilibrium. (Some argue that, like other technical terms used by marginalists, applying the term 'equilibrium' to David Ricardo's theories is not quite correct.) Prices that exist in markets at any time vary. Even the same commodity may be sold at different prices by different buyers and sellers that are located nearby in time and space. Both goups thought, even so, that some sort of center of gravity was attracting these market prices, that they were fluctuating about this center. Anyways, they developed theories about this position. And in these theories, the law of one price would prevail. In competitive markets, the same rate of profits would prevail in all markets.

They did not theorize that a long run equilibrium would ever be reached. Walras, for example, compared his equilibrium to the flat surface of a lake that was always being disturbed by winds and waves.

But the groups differed on what data they took as given in that part of their theories that explained equilibrium prices. For the classical political economists, the givens in this part of the theory consist of:

• Technology
• The real wage
• How much of each commodity is produced.

As a matter of mathematics, these givens are sufficient to explain the prices prevailing in a long run position.

The marginalists have another set of data. These givens consist of:

• Technology
• Tastes
• The endowments of land, labor, and capital, including the initial distribution of these givens among the agents in the model.

As a matter of mathematics, a consistent model of a long run equilibrium cannot be constructed with these givens How to take the endowment of capital is one of those matters that differed among the marginalists. All of their approaches were incoherent.

This post merely echos conclusions that academics came to about half a century ago and have been repeating. I think of Leontief's input-output analysis and of some applications of mathematical programming as empirical work building on a renewed classical political economy.

John Stuart Mill Further Demonstrates The Marx Follows From Ricardo

I want to here consider further evidence that Ricardo's views lead to something like Marx's theory of surplus value. My argument is that John Stuart Mill read Ricardo in a way that supports this thesis. And that he correctly had Ricardo's value as an absolute value. In particular, he had Ricardo's labor value to be much like Marx’s. (I do not want to argue that distinctions exist between Marx and Ricardo's theories of value.)

I previously noticed that Mill's had, in his Principles of Political Economy, an account of the source of profits as what Marx described as the exploitation of labor. Here I turn to his earlier work, "On Profits, And Interest," in his 1844 Essays on some unsettled questions of political economy. This is in volume IV of The Collected Works of John Stuart Mill.

Mill says that Ricardo had a notion of labor values distinct from exchangeable value. According to Terry Peach, this was not Mill's later position. As far as Mill's own theories, Joseph Schumpeter, for one, has him halfway between classical political economy and neoclassical economics.

Anyways, Mill explains that Ricardo saw that the rate of profits could only rise as wages fall:

"Profits, then (meaning not gross profits, but the rate of profit), depend (not upon the price of labour, tools, and materials - but) upon the ratio between the price of labour, tools, and materials, and the produce of them: upon the proportionate share of the produce of industry which it is necessary to offer, in order to purchase that industry and the means of setting it in motion." -- J. S. Mill, p. 262

"And thus we arrive at Mr. Ricardo's principle, that profits depend upon wages; rising as wages fall, and falling as wages rise." -- J. S. Mill, p. 262

And then Mill explains what Ricardo meant by value:

"The rate of profits depends not upon absolute or real wages, but upon the value of wages.

If, however, by value, Mr. Ricardo had meant exchangeable value, his proposition would still have been remote from the truth. Profits depend no more upon the exchangeable value of the labourer's remuneration, than upon its quantity. The truth is, that by the exchangeable value is meant the quantity of commodities which the labourer can purchase with his wages; so that when we say the exchangeable value of wages, we say their quantity, under another name.

Mr. Ricardo, however, did not use the word value in the sense of exchangeable value.

Occasionally, in his writings, he could not avoid using the word as other people use it, to denote value in exchange. But he more frequently employed it in a sense peculiar to himself, to denote cost of production; in other words, the quantity of labour required to produce the article; that being his criterion of cost of production. Thus, if a hat could be made with ten days' labour in France and with five days' labour in England, he said that the value of a hat was double in France of what it was in England. If a quarter of corn could be produced a century ago with half as much labour as is necessary at present, Mr. Ricardo said that the value of a quarter of corn had doubled." -- J. S. Mill, p. 263

Mill goes on to reject Ricardo's claims, without modification. He has something like his version of the transformation problem. Mill argues that the rate of profits falls as the cost of production of wages rises, where Mill now includes profits on dated labor inputs in cost of production. He has something like Sraffa's more rigorous distinction between basic and non-basic commodities

Mill argues that the trend in the rate of profits varies with decreasing returns in agriculture and with improvements in production. The rate of profits declines if the former dominates. Marx wanted to avoid this explanation.

John Stuart Mill Explains Profits As The Result Of The Exploitation Of Labor

I find this passage based on guidance from Samuel Hollander:

"The cause of profit is, that labour produces more than is required for its support. The reason why agricultural capital yields a profit, is because human beings can grow more food, than is necessary to feed them while it is being grown, including the time occupied in constructing the tools, and making all other needful preparations: from which it is a consequence, that ff a capitalist undertakes to feed the labourers on condition of receiving the produce, he has some of it remaining for himself after replacing his advances. To vary the form of the theorem: the reason why capital yields a profit, is because food, clothing, materials, and tools, last longer than the time which was required to produce them; so that if a capitalist supplies a party of labourers with these things, on condition of receiving all they produce, they will, in addition to reproducing their own necessaries and instruments, have a portion of their time remaining, to work for the capitalist. We thus see that profit arises, not from the incident of exchange, but from the productive power of labour; and the general profit of the country is always what the productive power of labour makes it, whether any exchange takes place or not. If there were no division of employments, there would be no buying or selling, but there would still be profit. If the labourers of the country collectively produce twenty per cent more than their wages, profits will be twenty per cent, whatever prices may or may not be. The accidents of price may for a time make one set of producers get more than the twenty per cent, and another less, the one commodity being rated above its natural value in relation to other commodities, and the other below, until prices have again adjusted themselves; but there will always be just twenty per cent divided among them all." -- John Stuart Mill, Principles of Political Economy, Book II, Chapter XV, Of Profits, Section 5.

I find the above close to Marx. At the start of the chapter, Mill says that profits are the sum of interest as a payment for abstinence, "indemnity for risk", and "remuneration for the labour and skill required for superintendence". Apparently, Mill regarded this disaggregation as consistent with describring profit as the result of laborers working for more time than needed to reproduce their own necessaries and instruments. For purposes of this post, I do not go into what is wrong with the account of interest as the sum of these components.

I do not draw a connection to Mill's avowal of socialism. But then, I do not read Marx's account of exploitation as an ethical argument for socialism either.

The above quotation is evidence for those who want to argue that Marx has a certain continuity with Ricardo's theory. I do not mean to assert that differences do not exist, as well.

Three Cases In Which The Labor Theory of Value Is A Simple Theory Of Price

1.0 Introduction

This post should be mostly uncontroversial. The labor theory of value (LTV) explains prices in certain special cases.

2.0 An Economy of Self-Employed Artisans

First, consider a pre-capitalist economy with no employer and employees. Commodities are manufactured for the market by self-employed artisans. They might have titles like carpenters, weavers, or blacksmiths. In this case, market prices tend to be (proportional to) labor values.

Adam Smith described this case. Karl Marx can be read as presenting this case in chapter 1 of volume 1 of Capital. In that chapter, he has independent producers. He introduces concepts in a certain order. Can you find anything in that chapter about workers being paid wages?

3.0 When the Rate of Profits is Zero

I now turn my attention to a sort of capitalist economy. Employers hire workers for wages. The workers produce commodities for the employers to obtain the revenues from selling them on the markets.

But here the capitalists do not have the ability to generally obtain a profits. Market prices tend towards labor values.

Joseph Schumpeter wrote about this case in The Theory of Economic Development. He has profits being temporary, as innovating entrepreneurs destroy the smooth reproduction of a capitalist economy, until it tends to settle down again.

4.0 When Capital-Intensity Does Not Vary Among Industries

I now consider a capitalist economy in which the capitalists are generally able to obtain a rate of profits. Suppose capital-intensity does not vary among industries. The ratio of the total value of the capital goods used up in production to the labor directly used in producing each commodity is the same, whatever commodity is being produced. You might as well use labor values when adding up capital goods.

Then market prices tend towards labor values.

Karl Marx wrote about this case in much of the first volume of Capital. Obviously, he does not write about eigenvalues and Leontief input-output matrices.

5.0 Conclusion

Modern reformulations of classical political economy, of course, are not confined to the above special cases. I find of particular interest the mathematical dual of the last case. David Ricardo and Karl Marx discuss this dual case - not with that jargon. Ricardo's last essay, unpublished in his lifetime, was about that. Marx discussed this dual case towards the start of the third volume of Capital.

But really their interest was not in a theory of prices. Ricardo and Marx both investigated labor values in their explanations of profits, of the ability of capitalists to obtain returns on their investments.

John Stuart Mill, Avowed Socialist

I have been reading some secondary literature on John Stuart Mill. He was explicitly against meritocracy, although that term was not available until Young's satirical novel. Here is Mill:

"If some Nero or Domitian were to require a hundred persons to run a race for their lives, on condition that the fifty or twenty who came in hindmost should be put to death, it would not be any diminution of the injustice that the strongest or nimblest would, except through some untoward accident, be certain to escape. The misery and the crime would be that any were put to death at all. So in the economy of society; if there be any who suffer physical privation or moral degradation, whose bodily necessities are either not satisfied or satisfied in a manner which only brutish creatures can be content with, this, though not necessarily the crime of society, is pro tanto a failure of the social arrangements. And to assert as a mitigation of the evil that those who thus suffer are the weaker members of the community, morally or physically, is to add insult to misfortune. Is weakness a justification of suffering? Is it not, on the contrary, an irresistible claim upon every human being for protection against suffering?" – J. S. Mill

The above is not necessarily an argument for socialism. It is consistent with Mill's investigation of what a society organized around private property might be.

In his autobiography, Mill explicitly says that he became a socialist:

"Our [Mill and Harriet Taylor] ideal of ultimate improvement went far beyond Democracy, and would class us decidedly under the general designation of Socialists. While we repudiated with the greatest energy that tyranny of society over the individual which most Socialistic systems are supposed to involve. we yet looked forward to a time when society will no longer be divided into the idle and the industrious; when the rule that they who do not work shall not eat, will be applied not to paupers only, but impartially to all; when the division of the produce of labour, instead of depending, as in so great a degree it now does, on the accident of birth, will be made by concert, on an acknowledged principle of justice; and when it will no longer either be. or be thought to be. impossible for human beings to exert themselves strenuously in procuring benefits which are not to be exclusively their own, but to be shared with the society they belong to." -- J. S. Mill

Mill is the canonical example of a classical liberal. His short book On Liberty is still read. How can he also be a socialist?

Reference

• Helen McCabe. 2021. John Stuart Mill, Socialist. McGill-Queen's University Press.
• Matthew McManus. 2024. The Political Theory of Liberal Socialism. Routledge.
• Michael Young. 1958. The Rise Of The Meritocracy: 1870-2033.. Pelican.

Some Literature On The Compatibility Of Exhaustible Resources With Classical Political Economy

I have been writing about natural resources that emerge unchanged from the production processes. In contrast, Bidard & Erreygers (2001, 2020) developed the corn-guano model to examine the compatibility of classical political economy with exhaustible natural resources. They argue that a royalty for an exhaustible natural resource will vary over time, in accordance with the Hotelling rule. Parrinello (2004) and Kurz & Salvadori (2011, 2015) argue that when the resource will be exhausted is not well-enough known for the Hotelling rule to apply. The price system, under their assumptions, has enough equations to determine the royalty, without prices varying over time. For Ravagnani (2008), the royalty for an exhaustible resource provides another degree of freedom and is set as a percentage of production by conventions and social norms, much like the natural wage in Ricardo and Marx. Hahnel (2017) emphasizes throughput efficiency, which is related to the rates at which the natural environment’s stock of natural resources and environmental sinks are used by human economic activity. These applications of classical political economy to environmental concerns are outside the scope of of my treatment of absolute, extensive, and intensive rent.

References

• Bidard, Christian, and Guido Erreygers. 2001. The corn-guano model. Metroeconomica, 52(3): 243-253.
• Bidard, C. and G. Erreygers. 2020. Exhaustible resources and classical theory. Oeconomia: History, Methodology, Philosophy, 10 (3): 419-446.
• Hahnel, Robin. 2017. Radical Political Economy: Sraffa versus Marx. New York: Routledge.
• Kurz, Heinz D. and Neri Salvadori. 2011. Exhaustible resources: Rents, profits, royalties and prices. In Volker Caspari (ed.), The Evolution of Economic Theory: Essays in Honour of Bertram Schefold. London: Routledge, 39-52.
• Kurz, Heinz D., and Neri Salvadori. 2015. The ‘Classical’ approach to exhaustible resources: Parrinello and the others. In Heinz D. Kurz and Neri Salvadori, Revisiting Classical Economics. Studies in Long Period Analysis, 304-316. London: Routledge.
• Parrinello, Sergio. 2004. The notion of effectual supply and the theory of normal prices with exhaustible resources. Economic Systems Research, 16(3): 311-322.
• Ravagnani, Fabio. 2008. Classical theory and exhaustible natural resources: notes on the current debate. Review of Political Economy, 20(1).

Extensive Rent And Labor Values

1.0 Introduction

Do scarce natural resources provide additional difficultes for modern reconstructions of classical and Marxian theories of value? After all land can be sold or rented, and labor cannot produce more land. (I put aside Holland.)

This post presents an exposition of the theory of extensive rent, a start on examining possible difficulties. This type of rent provides the least dificulties, as I understand it, for such modern reconstructions. As usual, I present an example, close to the minimal complexity, needed to make my points. The model can obviously be generalized to include many more produced industrial commodities; many more types of agricultural commodities; and many more types of land, each specialized to support the production of one kind of agricultural commodity.

2.0 Technology

Table 1 specifies the technology for this example. Each column defines the coefficients of production for a process. For example, the only iron-producing process requires a_0,1 person-years of labor, a_1,1 tons of iron, and a_2,1 bushels of corn as inputs for every ton iron produced. I assume that each process requires a year to complete and exhibits constant returns to scale. The corn-producing processes each have an upper limit on how much corn they can produce.

Table 1: A Technology

	Iron Industry	Corn Industry
	Process a	Process b	Process c
Labor	a0,1	a0,2	a0,3
Land, Type 1	c1,1 = 0	c1,2 > 0	c1,3 = 0
Land, Type 2	c2,1 = 0	c2,2 = 0	c2,3 > 0
Iron	a1,1	a1,2	a1,3
Corn	a2,1	a2,2	a2,3
OUTPUTS	1 ton iron	1 bushel corn	1 bushel corn

I assume two types of land exist, distinguished by the processes that can be operated on them. A single corn-producing process can be operated on each type of land. Only a certain number of acres of each type of land exists. Each corn-producing process leaves the land unchanged at the end of operating the process. The given quantities of land limit how much corn can be produced. This model cannot accomodate a positive steady-state rate of growth without technical progress.

A full specification for this model should include requirements for use. I assume that the net output must be such that both types of land are farmed, but only one type is fully farmed. Two techniques for production exist, as shown in Table 2. All three processes are operated in each technique, but only one type of land is fully used.

Table 2: Specification of Techniques

Technique	Type 1 Land	Type 2 Land
Alpha	Partially farmed	Fully farmed
Beta	Fully farmed	Partially farmed

3.0 Parameters and Variables

I have already implicitly defined certain parameters above. Table 3 lists certain parameters I use in this model. Table 4 lists variables that I need. Some assumptions are imposed on the matrices A_α and A_β:

• All produced commodities are basic. Iron and corn enter directly or indirectly into the production of both commodities.
• The technology expressed by these matrices is productive. Each matrix satisfies the Hawkins-Simon condition.

Table 3: Selected Parameters

Symbol	Definition
a0, α	Two-element row vector consisting of first two labor coefficients.
a0, β	Two-element row vector consisting of first and third labor coefficients.
Aα	2x2 matrix, with columns consisting of iron and corn coefficients of production for first and second processes.
Aβ	2x2 matrix, with columns consisting of iron and corn coefficients of production for first and third processes.
d	Two-element column vector consisting of iron and corn quantities in the numeraire.

Table 4: Variables

Symbol	Definition
vα	2-element row vector of labor values when type 1 land is free.
vβ	2-element row vector of labor values when type 2 land is free.
p	2-element row vector of prices of unit quantities of iron and corn.
p1	The price of iron, in numeraire units per ton. The first element of p.
p2	The price of corn, in numeraire units per bushel. The second element of p.
rho1	The rent of type 1 land, in numeraire units per acre.
rho2	The rent of type 2 land, in numeraire units per acre.
w	The wage, in numeraire units per person-year.
r	The rate of profits.

4.0 Labor Values

Given the technique in use, how much additional labor would be employed throughout the economy if the net output was such that one additional unit of iron were produced? This is the labor value of iron, and it easily calculated in the theory. The answer to the same question for corn is its labor value.

Suppose type 1 land is free. Then labor values are:

v_α = a_{0, α} (I - A_α)^-1

Labor values, when type 2 land is free, are the corresponding Leontief employment multipliers for the Beta technique. Variations in net output require varying the amount of the land farmed on the type of land that is not fully farmed.

5.0 Prices of Production

With market prices, some operated processes will be obtaining a higher rate of profits than average, and some will be obtaining a lower rate. These variations in the profit rates are perhaps a signal to capitalists that they should disinvest in some industries or processes and increase investment in others. Models of cross-dual dynamics and other models explore these disequilibria.

Prices of production are such that these signals are absent. All operated processes obtain the same rate of profits. I assume profits, rents, and wages are paid out of the surplus product at the end of the year. The following three equations express the condition that all processes obtain the same rate of profits:

(p₁ a_1,1 + p₂ a_2,1)(1 + r) + w a_0,1 = p₁

(p₁ a_1,2 + p₂ a_2,2)(1 + r) + rho₁ c_1,2 + w a_0,2 = p₂

(p₁ a_1,3 + p₂ a_2,3)(1 + r) + rho₂ c_2,3 + w a_0,3 = p₂

The next equation expresses the condition that the price of the numeraire is unity:

p d = 1

Finally, one of the rents must be zero:

rho₁ rho₂ = 0

The last equation is a defining feature of the theory of extensive rent.

Suppose one of the types of land is rent-free. For deiniteness, let type 1 land be only partially farmed. Then the first four equations are in terms of five variables (p₁, p₂, rho₂, w, r). Just as in the case with only circulating capital, prices of production are specified up to one degree of freedom. In classical political economy, the wage is take as given.

6.0 Choice of Technique

Suppose the wage is non-negative and does not exceed a maximum defined by the technology. The system of equations for prices of production has two solutions. Each solution has the rent on one type of land set to zero. The cost-minimizing technique is the one in which the rent on the other land is positive. If, for a technique, the rent on a type of land is negative, that technique will not be adopted by capitalists. At a switch point, the rents on both types of land are zero.

But the analysis of the choice of technique can be expressed in terms of wage curves. Suppose rents were zero. Consider the first two equations in the system of equations for the prices of production and the equation setting the price of the numeraire to unity. These equations yield a function in which the wage decreases with an increase in the rate of profits. Similarly, the first and third equations yield another decreasing wage curve.

In the case of circulating capital alone, the cost-minimizing technique is found by the wage frontier formed out of the outer envelope of these wage curves. At a given wage, the cost-minimizing technique maximizes the wage.

In this example of extensive rent, the cost-minimizing technique is found by the wage frontier formed out of the inner envelope of the wage curves.

In either case, the appropriate wage frontier shows that a lower rate of profits is associated with a higher wage and vice versa. The maximum wage occurs when the rate of profits is zero. The maximum rate of profits arises when the wage is zero.

7.0 Special Cases

Which land is free and which land pays a rent depends on either the wage or the rate of profits, whichever is taken as exogenous in the system of prices of production. At any rate, a wage frontier exists in which the wage is higher the smaller the rate of profits. This frontier is not the outer frontier of the wage curves for the technique.

Without loss of generality, suppose the Alpha technique is cost-minimizing. Type 1 land is not fully farmed and pays no rent. Then labor values are defined, based on the iron-producing process and the process on type 1 land.

Consider the special case in which a_{0, α} is an eigenvector corresponding to the maximum eigenvector for A_α. Then relative prices of production are equal to relative labor values.

On the other hand, suppose that the numeraire is the standard commodity, as found from a_{0, α} and A_α. Suppose only the standard commodity is produced. In this case, only the process on the rent-free land would be used, in contradiction to the analysis of the choice of technique. And suppose the wage is paid out in the form of the standard commodity. Then the following hold:

• The labor value of gross output is equal to total gross output, evaluated at prices of production.
• The labor value of net output is equal to net output, evaluated at prices of production.
• The labor value of the proportion of the standard commodity paid out in wages is equal to wage goods, evaluated at prices of production.

This special case seems especially forced in the case of extensive rent. Is some reformulation available in which surplus value can be treated as the sum of profits and rent?

I do not address the use of labor values in Marx's account of exploitation, Marx-biased technical change, and so on. The special cases in which the labor theory of value hold make obvious that, for a given technology, a higher rate of profits require a lower wage. And this wage frontier continues to hold in models of extensive rent.

8.0 Conclusion

The inclusion of natural resources, insofar as they can be modeled by extensive rent, does not seem to pose any additional issues for modern formulations of classical and Marxian political economy. It does highlight some issues that arise in models with circulating capital.

Labor values can be calculated for all produced commodities, given the technique in use. They are calculated from the marginal land that receives no rent. But suppose that a choice of technique exists. Then, an analysis at the level of prices of production must be prior to the calculation of labor values. The theory of extensive rent highlights this issue.

As Ricardo and Marx noted, prices of production are generally not proportional to labor values. They are equal in the special case, in which all industries have equal organic compositions of capital, in both models of circulating capital and of extensive rent. In the latter case, the organic composition of capital is found for agriculture from no-rent lands partially farmed.

A commodity of average organic composition is picked out in both models. Total labor values and the labor value of wages are equal to the corresponding aggregates in the system of prices of production when this average commodity is used as numeraire and is produced. These invariants, though, have to restricted to the production of the numeraire with the iron-producing process and the process on no-rent land. It is not clear to me that Marx thought his invariants held in his chapters on rent, given their location towards the end of volume 3 of Capital.

Obviously, these observations on natural resources and rent are just a start. They do seem to match what Ricardo was about in the second chapter of his Principles. The analysis of the choice of technique can be thought of, somewhat, as a critique of Ricardo.

At any rate, prices of production are well-defined in models of extensive rent. And they can be used in an analysis of the choice of technique. As usual, I present the analysis with no mention of utility maximization, preferences, or tastes.

Machinery And The Honesty Of David Ricardo

Consider the introduction of new, advanced machinery into a capitalist economy. This will raise productivity and be good for the population as a whole. It will displace workers, at least temporarily, who were previously making the product of the machine with handicraft production or now obsolete machines with lower productivity. But the production of the machines requires workers too. So, ignoring short-run frictions, will the workers not remain as well off?

David Ricardo believed something like this at one point in his life. But he had come to the opposite conclusion when he revised his Principles for the third edition. And he was forthright in saying so. Some of the displaced workers will be more or less permanently unemployed. By the way, this was not a matter of coming to agree with Malthus on a point about effectual demand.

Ricardo's change of mind was not some abstract academic view. This was a time in England shortly after the Luddites were at their peak. The Luddites had been rioting and destroying new machinery being introduced by industrialists. Ricardo's friend, J. R. McCulloch writes to Ricardo, and he immediately saw the potential of these changes (Ricardo, Works, volume 8, pp. 381-386):

Edinburgh 5 June 1821

My dear Sir

I have to apologise for being so long in returning you my best thanks for the valuable present of the third Edition of your great work - I congratulate you on its success - It is the best proof that can be given of the growing attention now paid to this important science; and it must have a powerful influence in furthering the dissemination of sound principles -

At the same time I must say (and I say it with that regret which I ever must feel in differing widely from one to whom I shall always be proud to look up as to my master) that in my humble opinion the Chapter on Machinery in this Edition is a very material deduction from the value of the work... ...Excess of candour has in this instance occasioned your doing a very serious injury to your favourite science - It was certainly proper that you should have renounced your previous opinions the moment you were satisfied of their fallacy; but this may be done in various ways, and I do not think it was at all necessary for you to make a formal recantation - our object never has been and never can be any other than to endeavour to promote the real interests of the science...

However the manner in which you have published your change of opinion is of comparatively little consequence - It is what I consider the extreme erroneousness of the principles to which you have incautiously lent the sanction of your name that has excited my principal regret - It is impossible to fritter away your argument by fencing it about with conditions - If it is good for any thing at all it is conclusive against all employment of machinery - It is not with greater or less gross or net produce that we have the smallest concern in considering this question; but simply whether does machinery produce commodities cheaper or not? If it does not produce them cheaper it will not be erected, and if it does produce them cheaper its erection must be profitable to every class of persons - The example which you have given does not, as far as I can perceive, by any means warrant a single one of the extraordinary conclusions you have drawn from it - You have not said whether the machine worth £7,500 is to last one, ten, or one hundred years -

...Your argument is to be sure hypothetical; but the hypothesis will be thrown aside, and all those who raise a yell against the extension of machinery, and ascribe to it that misery which is a mere necessary consequence of the oppressiveness of taxation, and of the restraints on commerce will fortify themselves by your authority! If your reasoning and that of Mr. Malthus be well founded, the laws against the Luddites are a disgrace to the Statute book -

Let me beg of you to reconsider this subject - A heresy on a mere doctrinal point is of no moment; but really I could not recommend to any of my friends to bestow the least attention on the study of this science, if I was satisfied that it remained yet to be settled whether the reducing of the price of commodities was advantageous or not - Truly if we are not got this length, our disputes about profits and our other remote conclusions ought to afford infinite amusement to the scoffers - But, I, at least, am not in this quandary - I will take my stand with the Mr. Burke of the American war not with the Mr. Burke of the French revolution - with the Mr. Ricardo of the first not of the third edition - Were there nothing else to allege on the subject I should be perfectly satisfied with what I consider the inherent fallacy involved in all the arguments which have been advanced against machinery...

Were I not aware that in all your speculations you are actuated solely by a desire to contribute to the improvement of the science, I should not have presumed to address to you this hasty and ill-digested letter - But I am satisfied that opinions dictated equally by a regard to the interests of the science, and coming from one who is not the least sincere of your admirers, though they may seem erroneous, will claim and meet with your attentive perusal - I am with the greatest regard and esteem

ever faithfully yours

J. R. McCulloch

Those are extracts from a long letter. I have left out many details of the argument.

Ricardo's friendship with Malthus is another testament to his personality. They continually argued that the other was wrong on political economy. Ricardo would lend out his notes on one of Malthus' books (Works, volume 2) to his friends. He did not try to publish them, for they did not make much sense without the text of Malthus' Principles of Political Economy. Malthus explained to Ricardo that he was mistaken, both in person and through a long interchange of letters. It was Malthus' insistence that even in agriculture, no product and its capital advances consist of the same mixture of commodities that induced Ricardo, as I understand it, to take up the labor theory of value.

Anyways, despite these persistent disagreements, Ricardo continued as a life-long friend of Malthus. I do not think I have that temperament.

Edit: Reference as suggested in coments:

• Paul A. Samuelson. 1989. Ricardo was right! Scandinavian Journal of Economics 91(1): 47-62.

Did Marginalism Become Accepted As A Reaction to Marxism?

I take it for granted that marginalism became accepted partly because Marx had used the best in classical political economy in his account of why socialism would and should transcend capitalism. This post presents some who have argued for or asserted the same.

I start by summarizing an argument from Antonia Campus. Campus argues that the marginalists in the 1870s did not have an accepted theory of production, cost, and price. Only in the 1890s did the marginal productivity theory of distribution become accepted. Now that that theory has been demolished, in the 1960s, we are back into the confusion of the 1870s, with every person his own capital theorist.

"With the publication in 1867 of Volume 1 of Capital, Ricardo's theory of distribution and value had in fact reappeared, not in the conciliatory form of J. S. Mill's Principles, but in the dangerous one which had been typical of this theory in the decade following Ricardo's death. According to Böhm-Bawerk, this theory constituted for the Germany of 1884 'the focal point about which attack and defence rally in the war in which the issue is the system under which human society shall be organized'.

On account of the impasse in which the theory of distribution was, and the ensuing chaos in economic theory, there was the danger that Ricardo's theory of distribution - in the most advanced elaboration it had found in Volume I of Marx's Capital - might fill the gap, and become even in Britain the 'focal point' in the struggle for and against the established social order. This danger must have seemed not too abstract, in the climate of Socialist revival of the 1880s, and especially after the foundation of the Social Democratic Foundation in 1881 and the Fabian Society in 1883." -- Antonia Campus. 1987. Notes on cost and price: Malthus and the marginal theory. Political Economy: Studies in the Surplus Approach 3(1): 11.

Here is Luigi Pasinetti saying something along the same lines:

"What turned out to be so devastating was the social impact of [Marx's] writings. The immediate practical effect of Marx's call for a social revolution was to elicit a strong social reaction. The establishment of the Western nations, at the end of the nineteenth century, became scared by Marx's revolutionary call. This by itself explains a lot of the fortune that in academic circles blessed marginalism in the 1870s, whose success was essentially analytical...

...In academic circles, this no doubt represented a radical change, but not in the strict sense of a scientific 'revolution', though some historians of economic thought later hastened to call it so (the 'Marginal Revolution'). Conceptually, it was a 'counter-revolution', an anachronistic achievement, yet a beautiful one, reached with the most sophisticated tools of economic analysis (precisely what the Classical economists had lacked).

At the end of the nineteenth and the beginning of the twentieth century, marginal economic theory led to conclusions which were pleasing to the establishment, especially in terms of a splendid detachment from the hot social issues that were boiling up in the real world, and in terms of arguments that could easily be used for the advocacy of unrestricted laissez-faire policies, supposedly leading, in ideal conditions, to optimal positions..." -- Luigi L. Pasinetti (2007).

Pierangelo Garegnani summarizes some of Sraffa's unpublished notes:

"For the school of 'cost', Sraffa is here referring to Ricardo's 'cost value', influenced, Sraffa says, by the author's 'anti-landlord complex' whereby 'rent not entering cost is disgraced'. The second school, that of 'utility', and with it the conflict between the two, came instead into being, Sraffa continues, when Ricardo’s 'cost' theory was 'taken up by Marx and used as a weapon for the workers'. That provoked by reaction the 'immediate simultaneous success' of the utility-based theory of value of Jevons, Menger and Walras – a theory that, significantly enough was ignored when it made its first appearance in the work of authors such as Dupuit and Gossen, before Marx's work created the need to develop a substitute for labor values." – Pierangelo Garegnani. 2005. On a turning point in Sraffa’s theoretical and interpretative position in the late 1920s. European Journal of the History of Economic Thought 12(3).

Gunnar Myrdal says something similar:

"One point which emerges from our analysis of the classical exchange value and real value theory is that Marx's theory of surplus value is not the result of a 'gross misunderstanding.'...Marx was right in saying that his surplus value theory follows from the classical theory of real value...Moreover, Marx was not the first to draw radical conclusions from it. All pre-Marxist British socialists derived their arguments from Adam Smith and later from Ricardo. Economists did not welcome these inevitable conclusions...He thus touched upon a sore point of economic theory and, probably for this reason, caused so much irritation amongst economists. They often tried not so much to prove him wrong, which would not have been too difficult, as to show that he was an utter fool, a bungler, misguided by those despised German philosophers...The classical theory of value leads inevitably to a rationalist radicalism, if not necessarily in Marx's formulation, at any rate in that direction. For the historian of thought the real puzzle is why the classics did not draw these radical conclusions." -- Gunnar Myrdal, The Political Element in the Development of Economic Theory.

I know of W. J. Ashley from Sraffa's unpublished notes:

The marginal conception of value which this generation owes to Jevons and Menger was clearly enough expounded by Longfield in 1833, but it passed unregarded... It is evident that their inattention was due, not to dissatisfaction with what men like Longfield offered them, but to satisfaction with the apparently sufficient formulae they had already mastered...

...Meanwhile ... the dissemination of the teachings of the so-called 'scientific' socialists - of Lassalle's 'Iron Law of Wages,' and Marx's 'Surplus Value' - disposed conservatively minded thinkers to re-examine that Ricardian teaching to which the Socialists, with so much show of reason, were in the habit of appealing." -- W. J. Ashley (1907).

The idea that marginalism became accepted partly as a reaction to Marxism is an established take from those who have examined the question over more than a century. You do not even need to be a radical to believe it.

Other takes emphasize a reaction to Henry George, Mirowski's account of physics envy, and the extension of Ricardo's theory of rent to all so-called factors of production.

Ian Steedman edited Socialism and Marginalism in Economics: 1870-1930 in 1995. The essays in this book are intelligent, informed, and much more nuanced than this post. Some socialists adopted marginalism. George Bernard Shaw was convinced by Philip Wicksteed,\ and remained a Fabian. Apparently, in Denmark it was not even a controversy. Wicksell was a radical in Sweden, advocating birth control. But on economics he wasn't very socialist. Vladimir Dmitriev and Ladislaus Bortkiewicz interpreted Ricardo and Marx with linear production models, a tradition continued by Robert Remak, John Von Neumann, and Wassily Leontief.

Adam Smith, David Ricardo, And The Labor Theory Of Value

1.0 Introduction

I resolutely am not commenting on unhappy current events.

Smith and Ricardo thought a (simple) LTV was not applicable to capitalism. Prices do not tend to or orbit around labor values. At least that is their claim.

Ricardo had more to say about the LTV.

This argument is not new. Smith confined the LTV to a supposed "early and rude state of society which precedes both the accumulation of stock and the appropriation on land" (WoN, book 1, chapter 6; see also book 1, chapter 8). Ricardo thought this was sloppy reasoning. The LTV does not become nonapplicable merely because of the accumulation of capital and of the division of society into capitalists and workers (Principles, 3rd edition, chapter 1, section III).

2.0 Technology

A simple model of circulating capital can be used to make Ricardo's point. Let a₀ be a row vector of direct labor coefficients. Let A be the Leontief input-output matrix. An element of a₀ and the corresponding column of A specify the labor time and the capital goods needed to operate a process to produce one unit of the output of that industry. The technology satisfies the following common assumptions:

• Some labor is needed to operate every process in each industry.
• Constant returns to scale prevail.
• Each commodity enters, directly or indirectly, into the production of every commodity. Iron, for example enters indirectly into the production of automobiles if iron is needed to produce steel and steel is needed to produce cars.
• The technology is productive. For some level of operation of the processes for each industry, some commodities are left over after reproducing the capital goods used in producing them.

Now for the unusual special case. Let λ be the largest eigenvalue of the Leontief matrix. This eigenvalue is also known as the Perron-Frobenius root of the Leontief matrix. Assume that the vector of direct labor coefficients is a corresponding left-hand eigenvector:

a₀ A = λ a₀ (Display 1)

3.0 Labor Values

Let v be the row vector of labor values. By definition, labor values satisfy the system of equations in Display 2:

v A + a₀ = v (Disp. 2)

The total labor to produce a commodity is the sum of the labor values of the capital goods used in that industry and the direct labor coefficient.

Under the special case assumption, labor values are a multiple of direct labor coefficients:

v = (1/(1 - λ)) a₀ (Disp. 3)

One can check this solution by merely plugging it into the solution in Display 2:

(1/(1 - λ)) a₀ A + a₀ = (λ/(1 - λ)) a₀ + a₀ = (1/(1 - λ)) a₀ (Disp. 4)

Since the above is a one-line proof, I thought I would include it. Labor values are also an eigenvector of the Leontief matrix.

4.0 Prices

Under the usual assumptions, the row vector p of prices satisfies the system of equations in Display 5:

p A (1 + r) + w a₀ = p (Disp. 5)

The scalar w is the wage, and r is the rate of profits.

Let R be the maximum rate of profits, obtained when the wage is zero, and the workers live on air. For the special case, the solution to the price system is quite simple:

R = (1/λ) - 1 = (1 - λ)/λ (Disp. 6)

r = R (1 - w) (Disp. 7)

p = v (Disp. 8)

One can check this solution by plugging it into the system of equations in Display 5.

So Ricardo was correct. The LTV could apply to capitalism under a special case. The failure of the LTV to apply in general is because those special case conditions cannot be expected to arise.

5.0 Conclusion

Ricardo had a point. As any ent would tell you, Smith was too hasty. The simple conflict between the wage and the rate of profits in Display 7 applies more generally than the above special case. The LTV, even when it is not valid, points to theories of the returns to capital.

I suppose reconstructing arguments between Ricardo and Smith with modern economics may conflict with how some historians do history. Even saying that Smith was analyzing capitalism could be considered an anachronism.

Adam Smith On A Labor Theory Of Value

The following are the first three paragraphs of the introduction to the Wealth of Nations:

"The annual labor of every nation is the fund which originally supplies it with all the necessaries and conveniencies of life which it annually consumes, and which consist always either in the immediate produce of that labour, or in what is purchased with that produce from other nations.

According, therefore, as this produce, or what is purchased with it, bears a greater or smaller proportion to the number of those who are to consume it, the nation will be better or worse supplied with all the necessaries and conveniencies for which it has occasion.

But this proportion must in every nation be regulated by two different circumstances: first, by the skill, dexterity, and judgment with which its labour is generally applied; and, secondly, by the proportion between the number of those who are employed in useful labour, and that of those who are not so employed. Whatever be the soil, climate, or extent of territory of any particular nation, the abundance or scantiness of its annual supply must, in that particular situation, depend upon those two circumstances." -- Adam Smith

When people talk about Adam Smith having a labor theory of value, they are not normally referencing the above. They are usually thinking of his few pages on a supposed "early and rude state of society which precedes both the accumulation of stock and the appropriation on land (book 1, chapter 6; see also book 1, chapter 8). Or they are thinking of his use of labor commanded as a measure of welfare (book 1, chapter 5).

But consider the above quotation. One can break down the annual labor of a nation in several ways. One can look at the proportion of the labor of the country which is needed to produce the necessaries for the entire labour employed. The remaining labour produces commodities that make up profits, interest, rent, payments to unproductive laborers, and so on.

This surplus can be consumed as necessaries and conveniences of life. One might call the latter luxuries. Or it might be used for accumulation. If the size of the labor force is to grow and the consumption of the individual worker is not to decrease, some of it must be used for accumulation. Smith thought that as the market increased, so would the division of labor. In a virtuous cycle, a greater proportion would be available for accumulation.

So in the very beginning of his most well-known book, Adam Smith points to the question of the size, distribution, and use of the surplus.

A Derivation Of Prices Of Production With Linear Programming

1.0 Introduction

This post illustrates a derivation of prices of production, based on certain properties of duality theory as applied to linear programming. I strive to be more concise and elementary than previous expositions. This exposition is based on John Roemer's Reproducible Solution (Analytical Foundations of Marxian Economic Theory, Cambridge University Press, 1981).

You will find no utility maximization or supply and demand functions below. I have no need for such hypotheses. Nevertheless, one can read this derivation as consistent with marginalism.

2.0 Technology and Endowments

Two commodities, iron and corn, are produced in this example. Managers of firms know a technology consisting of the processes defined in Table 1. Each column shows the inputs and outputs for a process operated at a unit level. All processes take a year to complete and provide their output at the end of the year. Each process exhibits constant returns to scale (CRS). For convenience, assume all coefficients of production defined in the table are positive. The inputs to production are totally used up by operating these processes.

Table 1: The Technology

INPUTS	Processes
	Iron Industry		Corn Industry
	a	b	c	d
Labor	a0,1(a)	a0,1(b)	a0,2(c)	a0,2(d)
Iron	a1,1(a)	a1,1(b)	a1,2(c)	a1,2(d)
Corn	a2,1(a)	a2,1(b)	a2,2(c)	a2,2(d)
OUTPUT	1 ton iron	1 ton iron	1 bushel corn	1 bushel corn

The endowments of iron and corn in the firm's inventory at the start of the year are also given parameters. Table 2 lists the remaining variables in this post. Presumably, the endowments are from production during the previous year. They are unlikely to be in the proportions needed to continue production. For example, if the managers of a firm decide to specialize in producing corn, they will have no endowments of iron.

Table 2: Parameters and Variables

Additional Parameters
ω1	Endowment of iron (in tons) for the firm.
ω2	Endowment of corn (in bushels) for the firm.
Parameters taken as given by managers of the firm
p	Price of iron (in bushels per ton).
w	The wage (in bushels per person-year).
Decision Variables
q1(a)	Quantity of iron (in tons) produced by the first process.
q1(b)	Quantity of iron (in tons) produced by the second process.
q2(c)	Quantity of corn (in bushels) produced by the third process.
q2(d)	Quantity of corn (in bushels) produced by the fourth process.
r	The rate of profits.

3.0 The Primal Linear Program

Managers of firms choose the quantities to produce with each process to maximize the increment z in value, subject to the constraint that they can buy the needed inputs at the start of the year out of the revenue obtained by selling their endowment. The objective function for the primal linear program is:

z = {p - [p a_1,1(a) + a_2,1(a) + w a_0,1(a)]} q₁(a)

+ {p - [p a_1,1(b) + a_2,1(b) + w a_0,1(b)]} q₁(b)

+ {1 - [p a_1,2(c) + a_2,2(c) + w a_0,2(c)]} q₂(c)

+ {1 - [p a_1,2(d) + a_2,2(d) + w a_0,2(d)]} q₂(d)

The quantities in the square brackets above are the costs of operating each process at a unit level. A bushel corn is taken as numeraire. The quantities in the squiggly brackets are the net revenues (also known as accounting profits) of operating each process at a unit level. Scaling these net revenues by the level of operation for each process results in the total accounting profit for the firm.

The constraints are:

[p a_1,1(a) + a_2,1(a)] q₁(a)

+ [p a_1,1(b) + a_2,1(b)] q₁(b)

+ [p a_1,2(c) + a_2,2(c)] q₂(c)

+ [p a_1,2(d) + a_2,2(d)] q₂(d) ≤ p ω₁ + ω₂

q₁(a) ≥ 0, q₁(b) ≥ 0, q₂(c) ≥ 0, q₂(d) ≥ 0

The statement of the constraints is based on the assumption that wages are paid at the end of the year, not advanced at the start.

4.0 The Dual Linear Program

The above linear program has a dual. In the dual, the rate of profits r is chosen to minimize the charge y on endowments:

y = (p ω₁ + ω₂) r

Such that:

[p a_1,1(a) + a_2,1(a)](1 + r) + w a_0,1(a) ≥ p

[p a_1,1(b) + a_2,1(b)](1 + r) + w a_0,1(b) ≥ p

[p a_1,2(c) + a_2,2(c)](1 + r) + w a_0,2(c) ≥ 1

[p a_1,2(d) + a_2,2(d)](1 + r) + w a_0,2(d) ≥ 1

r ≥ 0

Each constraint in the dual specifies that the revenues obtained from operating a process at the unit level do not exceed the costs, where costs include a charge for the going rate of profits. In other words, no super-normal profits can be obtained.

5.0 Some Observations About Duality

The value of the objective functions are equal in the solutions to the primal and dual LPs. In other words, the increment in value obtained by the decisions of the manager of a firm is charged to the value of the endowment.

Suppose the solution of the primal LP results in some process being operated at a positive level. Then the corresponding constraint in the dual LP is met with equality in its solution. Likewise, if a constraint in the dual is met with inequality, then that process will not be operated in the dual.

If the rate of profits in the solution to the dual is positive, then the constraint in the primal LP will be met with equality. That is, the whole value of the endowment will be used for further production.

6.0 Prices of Production

I introduce a final assumption. The solution to these LPs must be such that the economy can continue. In the context of this exposition, some firms must produce iron, and some must produce corn. Thus, one of the first two constraints in the dual LP must be met with equality. One of next two constraints must also be met with equality.

Consider the case when only one of the processes for producing iron is operated, and the same is true of the processes for producing corn. The dual LP yields a system of two equations in three variables: the price of iron, the wage, and the rate of profits. This system specifies prices of production.

This formulation solves for the choice of the technique, as well as prices of production. It can be generalized to allow for the production of many more commodities and many more processes for producing each commodity. A generalization can allow for heterogeneous labor. Another generalization allows for the production and use of fixed capital, that is, machines that last for many years. For a given wage, prices and the rate of profits drop out of the equations for prices of production for the chosen technique. These prices do not support the parables often told in introductory economics classes with supply and demand. For example, unemployment cannot necessarily be eliminated by lowering the wage and encouraging firms to thereby hire more labor.

7.0 Conclusion

The above illustrates some elements of a theory of value. This is neither a labor theory of value, nor Marx's theory of value. The theory is focused on production and has implications about how labor is allocated among industries, a central concern of Karl Marx.

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.

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)

and

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)

References

• 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

'The' Labor Theory of Value

1.0 Introduction

This post argues that there is more than one labor theory of value.

2.0 The Labor Theory of Property

John Locke argued that what one mixes one labor with, one has a right to own. One could read Marx's Capital as a reductio ad absurdum of this labor theory of property. I disagree with this reading.

3.0 Labor Commanded as a Theory of Welfare

Given a unit of money - one dollar or one british pound - the labor commanded by that money is the amount of person-years of labor you can hire with that money. This quantity of the labor is the reciprocal of the wage. The following quotation from Adam Smith, I assert, is NOT a statement of a theory of value:

"The real price of everything, what everything really costs to the man who wants to acquire it, is the toil and trouble of acquiring it. What everything is really worth to the man who has acquired it, and who wants to dispose of it or exchange it for something else, is the toil and trouble which it can save to himself, and which it can impose upon other people. What is bought with money or with goods is purchased by labour as much as what we acquire by the toil of our own body. That money or those goods indeed save us this toil. They contain the value of a certain quantity of labour which we exchange for what is supposed at the time to contain the value of an equal quantity. Labour was the first price, the original purchase-money that was paid for all things. It was not by gold or by silver, but by labour, that all the wealth of the world was originally purchased; and its value, to those who possess it, and who want to exchange it for some new productions, is precisely equal to the quantity of labour which it can enable them to purchase or command." -- Wealth of Nations, Book 1, Chapter 5: Of the real and nominal price of commodities, or their price in labour, and their price in money.

Smith is interested in a measure of wealth. The money price varies too much for this purpose. I do not recall why Smith rejects the price of corn, that is, the price for the most common food of the people. I think he finds it also quite variable.

4.0 Labor Embodied as Natural Prices

Adam Smith, however, does has a labor theory of value. He states:

"In that early and rude state of society which precedes both the accumulation of stock and the appropriation of land, the proportion between the quantities of labour necessary for acquiring different objects seems to be the only circumstance which can afford any rule for exchanging them for one another. If among a nation of hunters, for example, it usually costs twice the labour to kill a beaver which it does to kill a deer, one beaver should naturally exchange for or be worth two deer. It is natural that what is usually the produce of two days or two hours labour, should be worth double of what is usually the produce of one day's or one hour's labour." -- Wealth of Nations, Book 1, Chapter 6: Of the component parts of the price of commodities.

This labor theory of value only holds for an imaginary pre-historic society with no private property. Under capitalism, the labor commanded by a commodity exceeds the labor embodied in it, the latter being what is most commonly meant by the labor value of a commodity. One can read Smith as asserting that the profits on stock and the rent of land result from the exploitation of workers. Profits and rent are the result of value added by workers not paid out in wages.

5.0 The Ricardian Socialists

John Francis Bray, John Gray, Charles Hall, Thomas Hodgskin, 'Piercy Ravenstone', William Thompson, and others are known as the Ricardian socialists. Thompson (2002) argues that they drew more on Smith than Ricardo. Generally, they read Smith as explaining the returns to capital and land as a matter of exploitation and took the labor theory of value as a normative theory about what prices should be.

Accordingly, they advocated reforms to get rid of parasitical returns to capital and land. Some suggested the founding of banks that would issue labor notes. I think this idea was advocated not only so that the worker would get the full value of their product, but had something to do with abolishing the instability seen in economic crashes and business cycles. Some actually founded banks and volutary communities to implement these ideas. Nearby here, Ithaca has HOURs as labor notes. I have seen stores that say they accept them, but have never seen one.

Karl Marx rejected the claim that workers had a right to the whole product of their labor. This was a point that Marx raised against Ferdinand Lasalle, as well as against the Ricardian socialists.

6.0 Ricardo and a Simple Labor Theory of Value

Ricardo presented a simple labor theory of value as a descriptive theory of prices in a capitalist economy. He takes the distinction between market prices and 'natural' prices from Smith, ultimately, I guess, from William Petty. Market prices tend to and bob around natural prices, also known as prices of production. Suppose the whole distribution over time of the labor inputs used to manufacture two commodities is the same. Then the ratio of their prices of production will, indeed, be the ratio of their labor values.

But Ricardo immediately considers, in later parts of the first chapter of his Principles what happens when, say, the ratio of fixed capital and circulating capital varies among the methods with which commodities are produced. And he realizes that a simple labor theory of value cannot be exactly true. This is why Ricardo is sometimes described as having a 93 percent labor theory of value. He does not think land presents a fatal complication. One can calculate embodied labor values on marginal land that pays no rent. He searches for an 'invariable standard' which he ultimately decides is best approximated by a commodity of average capital intensity.

James Mill, Jane Marcet, John Ramsay McCulloch, Harriet Martineau, Robert Torrens, and J. S. Mill followed, popularized, and built on Ricardo Some have claimed that such followers of Ricardo had a confused understanding of Ricardo's theory of value.

7.0 Marx, a Simple Labor Theory of Value in Volume 1, and the Volume 3 Invariants

Marx was appreciative of Ricardo. But Marx says that Ricardo does not examine the value-form. Ricardo, according to Marx, does not analyze the preconditions of capitalism, for example, how it is that workers are available to be hired for money, how their labor-power is available on the market as a commodity.

Not only did Marx criticize Ricardo for ignoring the distinction between labor-power and labor. The labor value of labor is a meaningless phrase. Marx also argued that Ricardo was not able to abstract interest on money, profits on capital, and rent on land into the generalization of surplus value. Ricardo has a distinction between fixed and circulating capital, but cannot see Marx's distinction between constant and variable capital. So Ricardo has no notion of the organic composition of capital. Ricardo's theory of value and distribution, like Marx's does not need the imposition of Say's law. According to King (1983) precursors for all these notions can be found in the works of the Ricardian socialists.

Marx, in volume 1 of Capital, considers how labor must be distributed among industries to sustain production in a commodity-producing economy. He focuses on how surplus value is generated when labor-power is a commodity bought and sold on a labor market. For these purposes, he adopts a simple labor theory of value. Market prices tend towards ratios in the proportion of embodied labor values.

In volume 3, Marx depicts value as generated as in volume 1, but redistributed among industries. Prices of production are such that the same rate of profits is obtained in all industries. He asserts the rate of profits is the same in the value system and in the system of prices of production. Furthermore, total profits is supposedly equal to total surplus value, and total values are equal to total prices. These invariants hold in the production of a commodity of average organic composition of capital, in some sense.

In later chapters in Volume 3, Marx proceeds to an even lower level of abstraction. He considers different types of rent and financial capital.

8.0 Conclusion

These theories present opportunities for confusion and muddle, for talking past one another. Does Smith have a labor theory of value? Ricardo? Marx? Is a labor theory of value supposed to be a measure of wealth, a descriptive theory for prices in a capitalist economy, or a theory of economic planning in a post-capitalist society? And then, of course, some are ignorant and of bad faith. And those who have their own, but different, interpretations of the transformation problem, can get into honest argument.

References

• J. E. King. 1983. Utopian or scientific? A reconsideration of the Ricardian Socialists. History of Political Economy 15(3): 345-373.
• Anton Menger. 1899. The Right to the Whole Produce of Labour: The Origin and Development of the Theory of Labour's Claim to the Whole Product of Industry.
• Noel W. Thompson. 2002. The People's Science: The Popular Political Economy of Exploitation and Crisis 1816-34. Cambridge University Press.

Translation Between The Language Of Classical Economists And Marginalists

Lately, when trying to write up my results I use terminology from classical political economy. The table below maps some terms from classical political economy to terminology for marginalists.

Terminology

Classical	Marginalist
Use value	Utility
Supply	Quantity supplied
Demand	Quantity demanded
(Normal) profits	Interest
Extra profits	(Pure) economic profits
Supernormal profits
Market prices	Short run prices
Natural prices	Long run prices
Prices of production

I probably am leaving some important mapping out. Nuances, at least, exist to distinguish between entries in rows in the tables. And maybe it depends on which classical or marginalist economist you read, and which of their works. I think the first row is the most questionable.

A Short History

William Petty began classical political economy in the 17th century. Classical economics was developed through the work of the physiocrats and such writers as Adam Smith, David Ricardo, and Karl Marx. Marx was also a critic.

About a century and a half ago, economists mistakenly accepted the marginal revolution. Jevons, Menger, and Walras had precursors, but they were regarded as cranks. Marx, however, posed a political problem. Some might mention Henry George here, or maybe even Silvio Gesell. Better have an imitation of physics than talk about the ideas of those opposed to capitalists.

Lionel Robbins made clear in the 1930s, when the theory plainly did not apply, that marginalist economics is about the allocation of scarce resources. Land and labor can be taken as given at a moment in time, but capital cannot.

About half a century ago, economists came to recognize that they were mistaken. By the way, this mistake was also noted in the Heckscher–Ohlin-Samuelson (HOS) model of international trade. The demonstration that marginalism is fundamentally wrong was pushed by Joan Robinson and Piero Sraffa.

So some economists returned to elaborating classical economics. Even in the marginal interregnum, some, such as Leontief and Von Neumann, elaborated classical themes.

But most economists have been spinning in a widening gyre, ignoring the incoherence of their teaching. If a sufficient political movement develops outside of academic economics, maybe more economists will return to serious work. If so, they may even find elements to repurpose in this half century of dissolution and confusion.

Three Quotations: Rousseau, Adam Smith, Engels

Here is Jean Jacques Rousseau:

"...whether those who command are necessarily better than those who obey, and if strength of body or of mind, wisdom or virtue are always found in particular individuals, in proportion to their power or wealth: a question fit perhaps to be discussed by slaves in the hearing of their masters, but highly unbecoming to reasonable and free men in search of the truth." -- Jean Jacques Rousseau, Discourse on Inequality (1755).

Early developers of political economy were not slavish. Here is Adam Smith explaining that returns to capital and land are the result of value added by labor not paid out in wages.

"In the early and rude state of society... the whole produce of labour belongs to the labourer; and the quantity of labour commonly employed in acquiring or producing any commodity, is the only circumstance which can regulate the quantity of labour which it ought commonly to purchase, command, or exchange for.

As soon as stock has accumulated in the hands of particular persons, some of them will naturally employ it in setting to work industrious people, whom they will supply with materials and subsistence, in order to make a profit by the sale of their work, or by what their labour adds to the value of the materials. In exchanging the complete manufacture either for money, for labour, or for other goods, over and above what may be sufficient to pay the price of the materials, and the wages of the workmen, something must be given for the profits of the undertaker of the work, who hazards his stock in this adventure. The value which the workmen add to the materials, therefore, resolves itself in this case into two parts, of which the one pays their wages, the other the profits of their employer upon the whole stock of materials and wages which he advanced. He could have no interest to employ them, unless he expected from the sale of their work something more than what was sufficient to replace his stock to him; and he could have no interest to employ a great stock rather than a small one, unless his profits were to bear some proportion to the extent of his stock...

...As soon as the land of any country has all become private property, the landlords, like all other men, love to reap where they never sowed, and demand a rent even for its natural produce. The wood of the forest, the grass of the field, and all the natural fruits of the earth, which, when land was in common, cost the labourer only the trouble of gathering them, come, even to him, to have an additional price fixed upon them. He must then pay for the licence to gather them, and must give up to the landlord a portion of what his labour either collects or produces. This portion, or, what comes to the same thing, the price of this portion, constitutes the rent of land, and in the price of the greater part of commodities, makes a third component part." -- Adam Smith, The Wealth of Nations, Book I, Chapter VI (1776).

Many read the above as an account of how labor is exploited under capitalism. I find something similar in an essay a young Engels wrote before his life-long partnership with Marx:

"We have seen that capital and labour are initially identical; we see further from the explanations of the economist himself that, in the process of production, capital, the result of labour, is immediately transformed again into the substratum, into the material of labour; and that therefore the momentarily postulated separation of capital from labour is immediately superseded hy the unity of both. And yet the economist separates capital from labour, and yet clings to the division without giving any other recognition to their unity than by his definition of capital as "stored-up labour". The split between capital and labour resulting from private property is nothing but the inner dichotomy of labour corresponding to this divided condition and arising out of it. And after this separation is accomplished, capital is divided once more into the original capital and profit-the increment of capital, which it receives in the process of production; although in practice profit is immediately lumped together with capital and set into motion with it. Indeed, even profit is in its turn split into interest and profit proper. In the case of interest, the absurdity of these splits is carried to the extreme. The immorality of lending at interest, of receiving without working, merely for making a loan, though already implied in private property, is only too obvious, and has long ago been recognised for what it is by unprejudiced popular consciousness, which in such matters is usually right. All these subtle splits and divisions stem from the original separation of capital from labour and from the culmination of this separation- the division of mankind into capitalists and workers-a division which daily becomes ever more acute, and which, as we shall see, is bound to deepen. This separation, however, like the separation already considered of land from capital and labour, is in the final analysis an impossible separation. What share land, capital and labour each have in any particular product cannot be determined. The three magnitudes are incommensurable. The land produces the raw material, but not without capital and labour. Capital presupposes land and labour. And labour presupposes at least land, and usually also capital. The functions of these three elements are completely different, and are not to be measured by a fourth common standard. Therefore, when it comes to dividing the proceeds among the three elements under existing conditions, there is no inherent standard; it is an entirely alien and with regard to them fortuitous standard that decides— competition, the cunning right of the stronger. Rent implies competition; profit on capital is solely determined by competition; and the position with regard to wages we shall see presently." -- Friedrich Engels, Outlines of a Critique of Political Economy (1844).

I think one can discard the conjectural history and moral overtones of the above and freely play in the mathematics of Leontief matrices. But many academic economists nowadays are imposing mind-forged manacles onto another generation.