Sparks Commentary: Karl Marx contradicted himself about zero-sum games

A “zero-sum game” is one where you can only gain to the extent that others lose

Marx once argued that the economy was a “zero-sum game” – or, in other words, that one can only gain to the extent that others lose. But he seems to have undercut this idea within one of the same chapters where he proposes the idea. Thus, this is one of many areas where he contradicts himself, as I will show with some quotations from his work “Das Kapital.” Incidentally, all of the quotations from that work in this particular blog post are from Volume 1, Chapter 5 of the work – as published by Marxists.org.

Karl Marx

Marx argues that there is “There is no creation of surplus-value”

In that famous work, Karl Marx said that “If commodities, or commodities and money, of equal exchange-value, and consequently equivalents, are exchanged, it is plain that no one abstracts more value from, than he throws into, circulation. There is no creation of surplus-value. And, in its normal form, the circulation of commodities demands the exchange of equivalents.” (Source: “Das Kapital”) Thus, if the two items really are equivalent, then Marx believes that no one can really profit from the transaction. Or, in his terms, “There is no creation of surplus-value.” (When I hear “surplus-value,” I tend to think of “profit” – although Marx is not always clear about what he means by this. Nonetheless, for our purposes here, I’ll just mentally translate it here as “profit.”)

Karl Marx

This statement ignores the subjectivity of value, and the voluntary nature of transactions

This statement has a number of problems in and of itself. For starters, if Joe sells something to Bob for money, the money is worth more to Joe than his sold product. Otherwise, Joe wouldn’t have been likely to sell it. But if Bob buys that thing from Joe, then the purchased product would be worth more to Bob than is the money that he paid for it. Otherwise, Bob wouldn’t have been likely to buy it. Thus, in this kind of transaction, each of them may get more value to himself than he started out with, and both may thus realize some kind of gain. After all, if they hadn’t both gained by such a voluntary transaction, then neither one would have been likely to enter into it in the first place. It’s a simple argument, but it nonetheless seems to destroy Marx’s logic. Value is subjective (and therefore different) for both parties, whereas Marx’s argument seems to assume a totally objective (and fully shared) standard for both. Indeed, this would have to be true, if one is to believe his arguments that neither one realizes any “surplus-value.”

Marx argues that circulation is always based on the “exchange of equivalents”

Nonetheless, Marx concludes that “There is no creation of surplus-value. And, in its normal form,” he continues, “the circulation of commodities demands the exchange of equivalents. But in actual practice, the process does not retain its normal form. Let us, therefore, assume an exchange of non-equivalents.” (Source: “Das Kapital”) Marx then takes us through a tangled weave of arguments, and then concludes that “The creation of surplus-value, and therefore the conversion of money into capital, can consequently be explained neither on the assumption that commodities are sold above their value, nor that they are bought below their value.” (Source: “Das Kapital”) What, then, can explain all of this? This takes us to some of Marx’s later statements, which are among the most problematic of the chapter.

Karl Marx

Some explanations for this seem not to occur to Marx

Specifically, Marx later says that “The conversion of money into capital has to be explained on the basis of the laws that regulate the exchange of commodities, in such a way that the starting-point is the exchange of equivalents. [footnote] Our friend, Moneybags, who as yet is only an embryo capitalist, must buy his commodities at their value, must sell them at their value, and yet at the end of the process must withdraw more value from circulation than he threw into it at starting. His development into a full-grown capitalist must take place, both within the sphere of circulation and without it. These are the conditions of the problem.” (Source: “Das Kapital”) The idea that the value could have been created by transforming raw materials into finished goods, or by moving them from the location of the producer to that of the ultimate consumer, seems not to occur to Marx. But he then gives one of his clearest statements that the economy is a “zero-sum game,” even if he doesn’t use that modern phrase to describe it. Here is how Marx himself put it:

Karl Marx and Friedrich Engels

One of Marx’s clearest statements in favor of a zero-sum game

“A may be clever enough to get the advantage of B or C without their being able to retaliate. A sells wine worth £40 to B, and obtains from him in exchange corn to the value of £50. A has converted his £40 into £50, has made more money out of less, and has converted his commodities into capital. Let us examine this a little more closely. Before the exchange we had £40 worth of wine in the hands of A, and £50 worth of corn in those of B, a total value of £90. After the exchange we have still the same total value of £90. The value in circulation has not increased by one iota, it is only distributed differently between A and B. What is a loss of value to B is surplus-value to A; what is ‘minus’ to one is ‘plus’ to the other. The same change would have taken place, if A, without the formality of an exchange, had directly stolen the £10 from B. The sum of the values in circulation can clearly not be augmented by any change in their distribution, any more than the quantity of the precious metals in a country by a Jew selling a Queen Anne’s farthing for a guinea. The capitalist class, as a whole, in any country, cannot over-reach themselves. [footnote]” (Source: “Das Kapital”)

One wonders, then, how changing the “distribut[ion]” of wealth in a country will magically increase the total amount of wealth. But I digress. Back to the chapter.

The economic pie that his disciples want to redistribute is not fixed – it is constantly changing

After this passage, Marx then continues: “Turn and twist then as we may, the fact remains unaltered. If equivalents are exchanged, no surplus-value results, and if non-equivalents are exchanged, still no surplus-value. [footnote] Circulation, or the exchange of commodities, begets no value.” (Source: “Das Kapital”) Thus, Marx holds that “The value in circulation has not increased by one iota, it is only distributed differently between A and B.” He further holds that “What is a loss of value to B is surplus-value to A,” that “what is ‘minus’ to one is ‘plus’ to the other,” and that “The same change would have taken place, if A, without the formality of an exchange, had directly stolen the £10 from B.” (as cited above) This seems to be clear evidence that Marx believed this to be a “zero-sum game,” even if he didn’t use that modern phrase to describe it here. But as I’ve noted elsewhere, there are some serious problems with this argument. That is, it would seem that the economic pie that his disciples want to redistribute is not fixed – instead, it is constantly changing.

Statues of both Karl Marx and Friedrich Engels

Some things are consumed and destroyed, while others are produced and created

Some of the economic pie is consumed and destroyed, while other things are produced and created, and then added to the pie. Even without taking into account the harvesting of natural resources from the environment, labor is constantly turning raw materials into far more useful finished goods. Thus, useful goods and services are constantly being added to the pie, without anything being taken away from another person. There are serious problems with these zero-sum arguments, as Marx himself seems to admit later on in the chapter. Here is the passage where he undercuts his argument:

The passage where Marx undercuts his earlier zero-sum arguments a little

“The commodity owner can, by his labour, create value, but not self-expanding value. He can increase the value of his commodity, by adding fresh labour, and therefore more value to the value in hand, by making, for instance, leather into boots. The same material has now more value, because it contains a greater quantity of labour. The boots have therefore more value than the leather, but the value of the leather remains what it was; it has not expanded itself, has not, during the making of the boots, annexed surplus-value. It is therefore impossible that outside the sphere of circulation, a producer of commodities can, without coming into contact with other commodity-owners, expand value, and consequently convert money or commodities into capital.” (Source: “Das Kapital”)

Statue of Karl Marx

Other self-contradictions in the quoted paragraph

The last statement has some problems in and of itself. Marx seems to contradict himself when he says that “The boots have therefore more value than the leather,” but “the value of the leather remains what it was,” and has not annexed “surplus-value.” Nonetheless, if the commodity owner “can, by his labour, create value,” and “increase the value of his commodity, by adding fresh labour,” then who loses out from the creation of this additional value? Someone would have to lose out, if Marx’s arguments about a “zero-sum game” were really true – and, clearly, no one does actually lose out here. (Or, at least, Marx hasn’t specified who it is.) Therefore, Marx seems to have undercut the entire basis of his “zero-sum” arguments, and his conclusions about “surplus-value” that result from it. Labor can “create value,” but profits can only come at the expense of another. And “the value of the leather remains what it was,” but “The boots have therefore more value than the leather.”

Karl Marx

Conclusion: Marx contradicted himself about zero-sum games within a single chapter of his work

Thus, Marx seems to be saying that an economic exchange could not add “surplus-value” to either party, because such could only come at the expense of the other – thereby producing no total increase in “surplus-value.” But he says that labor can indeed add value without any specified loser to the transaction. Therefore, for Marx, the economy both is and is not a “zero-sum game” – one of many contradictions in the tangled weave of Marx’s writings. These contradictions cannot be reconciled with one another, showing Marx’s writings to be a confused (and tangled) mass of faulty assumptions.

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