Disproportionality (pt 2)

In a response to my critique of theories that explain crises by a long-term tendency of the rate of profit to fall due the rise in the organic composition of capital, reader Jeffery Curtis wrote: “I’m not sure this was a fair representation of the falling rate of profit crisis theory. For example, your bit about departments I and II I’ve never heard of in any interpretation of the falling rate of profit. The only crisis theory I’ve read about using that is a temporal disproportionality theory concerned with fixed capital (demand falls for department I goods as machines last for years, so they fall and take wages with them, department II slowly falls and crisis erupts).”

Jeffery makes other points in his response, most of which I agree with, that all readers of this blog should read carefully. In due course, all the questions that Jeffery raises will be dealt with. But it is the first question, the relationship between Department I and Department II, which is the main subject of this week’s post. What is really involved in the question of Department I and Department II is capitalist reproduction and its role in crisis theory.

Production and reproduction

The capitalist mode of production, and indeed all economic systems, involves not only production but reproduction. What is the difference between production and reproduction?

Let’s take any factory—for example, a garment shop that specializes in belt production. The output consists of belts. In order to produce the belts, the boss—industrial capitalist—needs workers, a building, raw materials in the form of leather, electricity to run the shop’s machines and provide lighting, and so on. The industrial capitalist then must combine these forces of production together to produce the belts. This is an example of production, in this case the production of belts.

What would happen, however, if the machines and tools used by our belt manufacturer were not replaced when they wore out, the building crumbled and was not repaired or replaced when it crumbled away, additional leather was not available when the existing supply was exhausted, the electricity failed, and the workers’ labor power was not renewed when their ability to work was exhausted?

Production of belts would cease. Of course, some of these inputs would last a lot longer than others. Generally, the human organism cannot work much longer than a 24-hour shift before it fails. (1) In the long run, the maximum workday allowed by human biology seems to be around 16 to 18 hours. (2)

At the other extreme, a building will continue to function even without repairs for many months, and can last virtually indefinitely if it is periodically repaired. In the case of building repairs, the building is replaced little by little rather than all at once. In the real reproduction process, both methods are used. The factory building must be continually repaired, and eventually it is torn down and replaced by a new factory building, perhaps much better suited to the new level of of technology that now prevails.

The same is true of machinery, though machines rarely last as long as buildings. In the course of their lifetimes, a machine must occasionally be repaired, but eventually it has to be scrapped and completely replaced.

For production to cease, however, we don’t have to wait for all the inputs to be exhausted. Production will cease as soon as the first necessary input fails—for example, human labor power.

Suppose the boss keeps the workers working around the clock. Within a day or so human physiology would cause the workers to collapse at their work stations, and production of belts would cease. (3) Any failure of electricity brings any factory that depends on electricity to a grinding halt. Suppose that for some reason the machines necessary to produce the belts could not be replaced. Production might continue for many years—especially if we allow for repairs—but eventually the machines will fail. At this point production would also cease.

Three cases of reproduction

So any system’s economic production must also of necessity be a process of reproduction. There are three possible cases of reproduction.

First, the forces of production might be in decline. As the workers’ labor power, the raw and auxiliary materials and the stock of fixed capital are used up, they are only partially replaced. (4)

Second, the economy might be just reproducing itself—it is neither expanding nor contracting. As labor power, raw and auxiliary materials and fixed capital are used up, they are exactly replaced but not expanded. This Marx described as simple reproduction.

Third, there is the case of expanded reproduction—the number of workers, the amount of raw and auxiliary materials, and the stock of fixed capital are expanding.

Capitalism is a system of expanded reproduction and can only exist as expanded reproduction, according to Marx. In volume II of “Capital,” where he dealt with the question of reproduction, Marx begins with simple reproduction. Why does he begin with simple reproduction, when according to Marx capitalism can only exist as a system of expanded reproduction?

Any system of expanded reproduction, Marx pointed out, of necessity contains within it simple reproduction. It is not possible to understand expanded reproduction without first grasping the laws of simple reproduction. Therefore, Marx begins with simple reproduction. In the rest of this post, I will examine simple reproduction.

Marx’s assumptions in dealing with reproduction

Marx treated the whole question of reproduction, both simple and expanded, in volume II of “Capital” before he developed the concept of prices of production, or the tendency of the rate of profit to fall due to a rising organic composition of capital. These he dealt with in volume III. Therefore, just as he had throughout volume I, Marx assumed that commodities sell at prices that are directly proportional to their labor values. Bringing in prices of production at this point would only complicate things without changing anything of essence, so Marx only dealt with them after he has dealt with the problem of reproduction under capitalism.

Marx also left out any changes in the forces of production. In Marx’s economic model of reproduction, there are no changes in the organic composition of capital, and therefore no tendency for the rate of profit to fall. This was the case in both his model of simple reproduction and his model of expanded reproduction.

The abstraction might seem strange, since didn’t Marx and Engels emphasize how competition among the industrial capitalists and the industrial capitalists and the working class forces the industrial capitalists to increase the power of their productive forces? Why did Marx leave out such an important feature of capitalism in his analysis of reproduction?

Again, this is an example of Marx’s method at work. Marx is abstracting—leaving out—some of the most important features of capitalist production in order to isolate and reveal the essence of the process of reproduction, both simple and expanded. Later on, other Marxists worked a rising organic composition of capital and thus a falling rate of profit into their reproduction models. These models became a subject of much controversy during the first part of the 20th century among Marxists, and played a crucial role in the “breakdown” debate.

In this post, however, I will start by examining simple reproduction with Marx’s assumptions. Under these assumptions, there is only simple reproduction, commodities sell at prices directly proportional to their labor values, and there is no change in the methods of production and the organic composition of capital or the rate of surplus value. The rate of profit, therefore, remains unchanged.

Marx also assumed that there are only two classes, the industrial capitalists on one side—the non-industrial capitalists are abstracted—and the productive workers on the other side—workers who don’t produce surplus value are also abstracted. The model assumes a pure capitalism—there are no noncapitalist modes of production in existence. (5)

Marx reduced this pure capitalist economy to the following two equations. The first equation represents the production of the means of production, consisting of all fixed capital and raw and auxiliary materials used up. The second equation represents items that are produced for personal consumption, both luxury goods consumed only by the capitalists and necessary goods consumed both by the workers and the capitalists. Since there is only simple reproduction, all the profits of the capitalists are spent on consumer goods, both necessities and luxuries. The workers spend all their incomes—wages—on necessities. (6)

Here are the equations:
I 4,000c + 1,000v + 1,000s = 6,000
II 2,000c + 500v + 500s = 3,000

The equations assume one period of reproduction, the exact length is arbitrary, lets assume it’s a year. We assume that the constant capital 4,000c + 2,000c = 6,000 is consumed in the course of a year and must be replaced—reproduced—within the same year. Therefore, if the economy is to be reproduced, the output of Department I must equal cI + cII, which yields the equation cI + cII = cI + vI + sI. That is, the total output of Department I in a year must exactly equal the constant capital used up in that year.

Also, the total value of consumer goods produced in a year, 3,000 according to Marx’s figures, must equal the total consumption of the workers employed in both departments of production plus the total consumption of the capitalists of both departments. Therefore 1,000vI + 1,000sI + 500vII + 500sII = 2,000cII + 500vII + 500sII = 3,000, the total production of consumer goods in a year.

According to Marx’s example, half of the consumer goods are consumed by the workers and the other half by the capitalists. The rate of surplus value is exactly 100 percent. The workers work half the time for themselves and half the time for the capitalists.

The production and the consumption of consumer commodities adds up to 3,000. The 3,000 represents some unit of abstract human labor measured in terms of time. Whether the unit of labor time is hours, days or months really doesn’t matter. The same is true of all the arithmetic values used in the formula. They represent a quantity of abstract labor measured in terms of some unit of time. Abstract labor—value—is always measured in terms of time. Indeed, if we wished we could dispense with the arithmetic examples and use algebraic values instead.

Here notice that 6,000, to use Marx’s arithmetic example, does not represent the total value of means of production in Department I but rather the total value of the means of production that are actually used up, or consumed productively, in the course of a year.

A source of crisis

We see a potential source of crisis that Jeffery mentioned in his reply to my post on the falling rate of profit theory. A machine—let’s represent its value as 100 of some time unit of abstract human labor—might last 10 years. Assuming it loses its value at a steady rate across its lifetime, that will mean it will lose a value of 10 every year. However, because of the nature of its material use value, it can only be replaced all at once. (7) Suppose of the 6,000 in the annual output of Department I, half of this output represents machines. Assume that these machines last 10 years and lose value at a steady rate. This will mean that machines used throughout the economy will lose a value of 3,000 every year.

What would happen if all the machines have to be replaced at the same time? For nine out 10 years, the machine-producing industry will lie idle, but in the 10th year, the machine-building industry will have 30,000 in orders. Now that’s a boom and bust cycle for you! (8)

To avoid cyclical swings in the machine-building industry, exactly 10 percent of all the machines in terms of value must be replaced on an annual basis, no more and no less. In the real world, this is, of course, extremely unlikely, and indeed the machine-building industries are extremely prone to sharp cyclical fluctuations in the course of the industrial cycle.

In fact, many economists, from Marx himself to John Maynard Keynes, saw in the periodic replacement of fixed capital a material basis for the length of the industrial cycle that runs about 10 years. So even on the basis of simple reproduction, we have discovered a source of potential crisis.

How is cII realized?

During the late 19th century, Russian populists argued that capitalist industry could never develop in Russia because the world market was already used up, and it would be impossible for Russian industrial capitalists to actually realize their surplus value. The early Russian Marxists strongly disagreed with this analysis, and used Marx’s reproduction formulas to prove that Russian industrial capitalists could fully realize the value and the surplus value embodied in their commodities as long as certain proportions between the two departments of capitalist production were maintained. They drew the conclusion that the question of markets pointed to by the populists would be no barrier to the development of capitalism in Russia.

The young Lenin, one of the participants in this debate on the Marxist side, observed that the real problem is not the realization of the surplus value but of the constant capital in department II, or cII. The capitalists of Department II, the producers of means of consumption, simply consume unproductively their surplus value in the form of means of consumption. In order to do this, of course, they must trade among themselves—the producers of fine wines, for example, with the producers of luxury automobiles. But all this represesents trade within Department II.

Similarly, the capitalists of Department I consume—productively—within their department cI, the means of production produced in Department I that is used within Department I. Again, they have to trade among themselves, exchanging a drill press for screwdrivers, for example. This is trade within Department I.

But this is of no concern as far as Marx’s diagram is concerned, since it is really concerned only with the exchange between the two departments of production, not the exchanges within each of them.

The production of cII, remember, like the entire output of Department II consists of consumer goods, both necessaries and luxuries as far as their use values are concerned. Using Marx’s example, having sold the commodities represented by 500vII and 500sII within Department II, Department II is stuck with an excess of 2,000cII, which cannot be sold within Department II.

Notice that this surplus is not surplus value but rather the portion of the commodity capital of Department II that contains the value of the constant capital used up in the annual production of Department II. Who will buy this surplus production that cannot be bought by either the workers or capitalists of Department II?

Department I had no problem consuming cI, but how does it consume vI and sI? Remember, the material use values represented by the symbols vI and sI, like all production of Department I, consists only of means of production. These commodities are completely unsuited for personal consumption. The industrial capitalists of Department I cannot pay their workers in drill presses and lathes, nor can they consume at the country club steel mills and oil refineries.

But fortunately for them, Department II is stuck with a surplus of consumer goods, both necessities as well luxuries fit only for the consumption of the “beautiful people.” If all is to go well within the limits of simple reproduction, the value of the surplus of consumer articles in the hands of the capitalists in Department II will exactly match the the surplus of commodities that cannot be consumed by the capitalists and workers of Department I.

So the two departments make a trade. The Department II capitalists send the consumer goods that neither they nor their workers can consume, within in the limits of simple reproduction, to the capitalists and workers of Department I. In return, Department I provides the capitalists of Department II with the means of production that replace the means of production used up by Department II during its annual production.

The most important equation

Translated into the concise language of algebra, we get the following equation:
cII = vI + sI.

This is the equation that unlocks the secret of simple reproduction. Of course, many things could go wrong and could become elements of crisis. First, the value cII—measured in terms of hours of labor—on the left side of the equation must precisely equal the value on the right side, vI + sI. If it does not, we actually have an inequality in terms of algebra and in the real world unequal exchange and disequilibrium.

Suppose for the sake of illustration cII in value terms was greater than vI + sI. Department II would then not fully realize the value of its commodities in terms of the use values of the commodities of Department I. There would be a crisis of overproduction in Department II backed up by an underproduction of commodities in Department I.

The industrial capitalists in Department I would tend to realize super-profits, but the industrial capitalists in Department II would realize less than the average rate of profit. (9)

The same would be true in the converse situation, cII < vI + sI. We would have underproduction of consumer goods and overproduction of producer goods. Then it would be the turn of the industrial capitalists in Department I to make less than the average rate of profit and for the capitalists of Department II to make super-profits.

Proportionality must be in terms of both value and use value

Above, I assumed disproportionalities in terms of values but not in terms of use values. If there were disproportionalities in use values, for example if Department I failed to produce the necessary raw materials or machinery to continue production of consumer goods at the prevailing level, we would see a physical decline in consumer goods production.

Similarly, if there was a shortfall in production of use values in Department II—for example, not enough food is produced because a harvest failure such as occurred in 1816, the year without a summer—there would be widespread hunger among the workers in Department I—as well as Department II—and a rise in money wages combined with falling real wages, leading to lower profits for the capitalists of both departments. Therefore, if the process of reproduction is to proceed smoothly, there must be perfect proportionality in terms of both values and use values between the two departments of production as well as within them. (10)

The problem of money

Most Marxists when analyzing simple as well expanded reproduction leave out the question of money just like I did above. (11) However, if we leave out the question of money, we are leaving out the possibility of a general overproduction of commodities affecting both departments of production at the same time.

We might have an overproduction of commodities in Department I relative to Department II, or an overproduction in Department II relative to Department I. We remain stuck in the world of Say’s Law, which allows overproduction of particular commodities relative to shortages of other commodities. Yet don’t we see today an overproduction of commodities in both departments of production? Isn’t this the essence of the current crisis? Commodities of all kinds—consumer goods and capital goods alike—are piling up unsold in warehouses around the world.

I also referred to the assumption that commodities sell at prices proportional to their values. But if I leave out the question of money, how can I even talk of price, which is, after all, a definite sum of money that realizes the value, including the surplus value, of the commodity. If I leave out money, I have to assume barter, not the sale of commodities for money, if I want to be consistent.

In order to avoid these difficulties, Marx did not leave out the question of money when he analyzed even simple reproduction. The way that Marx brought in money, however, seems very strange to us today. He assumed that money consisted only of circulating gold coins. Assuming simple reproduction, he assumed that a portion of the circulating gold coins would fall below their standard weight in the course of a year or whatever the reproduction period was. In the days when gold and silver coins were the main form of currency, coins had to be withdrawn from circulation when due to wear and tear or clipping they fell below a certain standard weight. (12)

If governments did not withdraw these coins from circulation, the currency would depreciate against gold or silver bullion—uncoined precious metals used as money—leading to currency devaluation and inflation. Indeed, from the invention of coined money in ancient times to early modern times before paper money was introduced, the circulation of underweight coins was a frequent source of currency crises and inflation.

Marx made a number of assumptions in bringing money into his model. First, he assumed that gold alone served as money. He also assumed that the government manages the currency in a “sound” way and withdraws all “light” coins promptly from circulation. In order to prevent a shortage of money, assuming simple reproduction, the gold mining and refining industries have to produce just enough gold to replace the coins that had fallen below the standard weight with full weight gold coins. Since gold when it does not serve as money is a raw material, Marx put the gold miners into Department I, the department that produces the means of production.

Rosa Luxemburg, who was one of the few Marxists after Marx who did not ignore money when dealing with reproduction, pointed out that monetary gold is not strictly speaking either a means of production or a means of consumption. She proposed instead that gold production be put in a special Department III. More on this in future posts.

Of course, Marx’s solution here seems divorced from reality even in his own day when the various forms of credit money, and what Marx called token money or paper money—today called fiat money by the bourgeois economists—circulated side by side with gold and silver coins. An example of credit money—which back in Marx’s day was sometimes called circulating credit—is a bank checking account, which is basically an IOU owed by the bank to the depositor. It can be transfered to another person either by check or today electronically by a debit card, either to purchase a commodity or make a payment.

We are now face to face with the problem of money. We saw that the formula of capitalist production, M-C—P—C’—M’, both begins and ends with money. In earlier posts, I have emphasized that the value and surplus value of commodities must be realized in terms of money. Indeed, since profit, the sole aim of capitalist production, is nothing but surplus value realized in money form, profits themselves must be measured in terms of money. But I carefully avoided explaining exactly what money is.

What is money, and what anyway is the unit of measurement that is used in measuring a quantity of money? It might at first seem obvious, but when you think about it, this is not so easy to answer. Exactly what are we measuring when we measure a given quantity of money? Is it simply the number printed on a note denominated in dollars, euros or some other currency? What exactly are these numbers measuring anyway?

Next week, however, I will deal with the question of expanded reproduction. After that, I am afraid that our accumulating contradictions will be getting out of hand, and I will have to deal with the puzzle of money head on.


1 In volume I of “Capital,” Marx gives an example of a young woman who died of overwork as a result of a brutal 24-hour-plus shift. If the industrial capitalists do not allow the workers to rest at periodic intervals, their ability to work and indeed live will soon cease. In the long run, the bosses must also pay enough wages to allow the workers not only to reproduce their ability to work—labor power—on a daily basis, but also to raise a new generation of workers. If the workers do not raise a new generation of workers, capitalist reproduction would fail, and capitalist production would come to an end within a generation. Therefore, the economic reproduction process is in part based on the biological reproduction process.

2 Ideally capital would like to extend the workday to 24 hours, seven days a week. However, the laws of biology make this impossible. Therefore, even in the absence of organized resistance on the part of the workers or intervention by the state in the form of setting a maximum workday, the basic biology of the human organism sets a certain limit.

3 This is all the more true in light of the fact that the workers are the sole source of surplus value. Even if the workers could be replaced by robots who could work 24 hours a day and even if the robots could last for decades without repairs, robots do not produce an atom of surplus value. If all the same production could somehow go on without workers, it would no longer be capitalist production.

4 The late Ernest Mandel called this contracted reproduction. Under capitalism, contracted reproduction has occurred during extreme crises of overproduction and during all-out war, such World War I in Europe and World War II. The United States experienced a period of contracted reproduction during and immediately following the worst period of the 1929-33 crisis. At that time, capital investment fell so low that it failed to replace the existing capital for a number of years. The same thing also happens in an all-out war economy, where the factories that are normally part of Department I that manufacture the means of production are converted to manufacturing means of destruction.

In current discussions of the various stimulus packages that are being implemented to combat the current global slump, many bourgeois politicians and economists are claiming that it was only the huge “stimulus package” of World War II that finally ended the Great Depression of the 1930s. The implication is that if a stimulus package—large-scale government deficit spending—is large enough, it will always generate enough effective demand to end any possible depression.

It is true that the onset of a full-scale war economy—not just a high level of military spending—is accompanied by a sharp rise in production, as previously idle or semi-idle plants are put to work. Production indeed soars and the unemployed are finally absorbed—some into the military forces and others into war production. If depression conditions prevail before the war, which was indeed the case to various degrees before both World War I and World War II, the depression quickly ends. But this is achieved at the price of repressing expanded reproduction—the very essence of capitalism—and ushering in a period of contracted reproduction. Once the economy is working at full capacity for war purposes, production will stop rising and will be doomed to gradually decline as society consumes its existing capital.

In the United States, a normal process of expanded reproduction after the economic collapse of the early 1930s didn’t resume with World War II, though the Depression ended, but rather at the war’s end. A permanent full-scale war economy such as those that prevailed in Europe during World War I and in Europe and elsewhere during World War II would not usher in a crisis-free capitalism. It would destroy capitalism altogether.

If a permanent full-scale war economy were really implemented, the periodic economic crises that have hit capitalism about every 10 years to one degree or another since 1825 would indeed cease, but only at the price of the destruction of capitalism and indeed modern society altogether. I will examine all this in more detail, especially when I get to the subject of “Keynesian economics” and so-called “stimulus packages” such as the ones that are currently being implemented by various governments as they struggle to prevent the current global depression from turning into a Depression on the scale of the 1930s or worse.

5 Such a pure capitalist economy has never existed and never will. Such abstractions are worthwhile only if they tell us something about the real concrete capitalism that does exist. Otherwise they are what Marx called “violent abstractions.”

6 Marx divided the capitalist unproductive consumption into necessities that all people must consume in order to live—basic food, for example, consumed by the workers and the capitalists alike—and luxuries—fine wines and Gulfstreams, for example—that are consumed by the capitalists alone. Therefore, Department II contains a considerable sub-department that produces luxuries that are consumed by the capitalists alone.

7 Abstracting the question of repairs.

8 We should remember that in the real world there is not only simple reproduction but expanded reproduction. Expanded if not simple reproduction will give the machine-building industry some orders in the “off years.” The machine, though it has lost one-tenth of its value, continues to be fully functional as a use value. Eventually, however, it will fail as a use value, and its value will then be fully used up, since a non-use value does not have a value. This disproportion between value and use value in the machine-building industry is indeed a major source of cyclical instability in the real-world capitalist economy.

9 Strictly speaking, this would be getting ahead of ourselves, since Marx hadn’t yet introduced the concept of the equalization of the rate of profit and the formation of prices of production in Volume II, where he dealt with reproduction.

10 Which is why it never does in reality. Even in the best of times, the process of reproduction is marked by constant minor crises, as I explained in the last post.

11 Marx, however, did not abstract money when he dealt with even simple reproduction. He could do this because he had already developed the concept of money in volume I of “Capital”—indeed in the first three chapters. These three chapters are, however, the most difficult and “Hegelian” part of “Capital” and therefore perhaps the least understood by Marxists of the entire post-Engels era.

Most Marxists who deal with the reproduction formulas of volume II simply leave out the question of money. Perhaps they assume that money is not much of a problem since the state or central bank can simply supply the necessary money with their printing presses. However, if the state can do this, shouldn’t it be easy to avoid a general overproduction of commodities once fiat money has replaced the old international gold standard?

That is what Ben Bernanke was counting on when he expressed his belief that the “Great Moderation” would continue. But how can we then explain the current crisis, which is taking precisely the form of a generalized overproduction of virtually all commodities with the exception of gold, the traditional money commodity?

The inability to explain money has led to a situation where the more particular Marxist writers know about economics, the more they avoid describing the periodic crises of capitalism as crises of overproduction. They prefer to use terms like the “overaccumlation” of capital but avoid the terms “overproduction of commodities” or “industrial overproduction,” which both Marx and Engels used to describe the cyclical economic crises in their time.

I have been purposely vague on the subject of money up to this point to show that not only is the concept of a general overproduction of commodities difficult to understand without a clear understanding of the nature of of money, but inevitably we sink into other contradictions as well. For example, profits are measured in terms of money—any businessperson can tell you as much—but what exactly are we measuring when we measure the quantity of money?

12 In the days of circulating gold and silver coins, swindlers sometimes clipped tiny amounts of precious metal off the coins hoping that nobody would notice that the coins were now lighter than standard weight. Once enough clippings were collected, they could be melted down into bullion—uncoined gold or silver—and sent off to the mint to be coined into additional coins. In the days of gold and silver coins, governments passed strict laws with severe punishments for those who violated the laws against clipping coins. For example, when he was in charge of the British currency, Sir Issac Newton himself sent more than one person to the gallows for violating the anti-clipping laws.

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