# Capital Volume 1 Part 1 Chapter 1 Section 3A

This subsection is called, “Elementary or Accidental form of Value”

Page 48:  “x commodity A=y commodity B, or
x commodity A is worth y commodity B, or
20 yards of linen= 1 coat, or
20 yards of linen is worth 1 coat.”

Subsection 1: The two poles of the expression of value: Relative form and Equivalent form
“The whole mystery of the form of value lies hidden in this elementary form. It’s analysis, therefore, is our real difficulty.”

Intuitively, this makes sense. That is, if we say 20 yards of linen = 1 coat, we’re saying 20 yards of linen can be exchanged for one coat.  It makes sense that we can get from there to money.

“Here two kinds of commodities (in our example the linen and the coat), evidently play two different parts.  The linen expresses its value in the coat; the coat serves as the material in which that value is expressed.  The former plays an active, the latter a passive part.”

Right.  By saying 20 years of linen = 1 coat, then we are defining the linen in terms of the coat, or, we’re saying, “How much coat is needed to express the value of 20 yards of linen.”

“The value of the linen is represented as relative value, or appears in relative form.  The coat officiates as equivalent, or appears in equivalent form.”

The value of the linen is relative to the coat.

“The relative form and the equivalent form are two intimately connected, mutually dependent and inseparable elements of the expression of value; but, at the same time, are mutually exclusive, antagonistic extremes–i.e., poles of the same expression.  They are allotted respectively to the two different commodities brought into relation by that expression.”

Mutually dependent opposites, like positive and negative poles of a magnet.

“It is not possible to express the value of linen in linen.  20 yards of linen = 20 yards of linen is no expression of value.  On the contrary, such an equation merely says that 20 yards of linen or nothing else than 20 yards of linen, a definite quantity of the use-value linen.  The value of the linen can therefore be expressed only relatively–i.e., in some other commodity.  The relative form of the value of the linen pre-supposes, therefore, the presence of some other commodity–here the coat–under the form of equivalent.  On the other hand, the commodity that figures as the equivalent cannot at the same time assume the relative form.  That second commodity is not the one whose value is expressed.  Its function is merely to serve as the material in which the value of the first commodity is expressed.”

In order to express the value of a commodity, another commodity is required.

Page 49: “No doubt, the expression 20 yards of linen = 1 coat . . .implies the opposite relation: 1 coat = 20 yards of linen…But in that case I must reverse the equation, in order to express the value of the coat relatively; and, so soon as I do that, the linen becomes the equivalent instead of the coat…whether, then, a commodity assumes the relative form, or the opposite equivalent form, depends entirely upon its accidental position in the expression of value–that is, upon whether it is the commodity whose value is being expressed, or the commodity in which value is being expressed.”

Okay, yeah, I think I got that.  It caused me to do some serious thinking about the equal sign, which actually contains a lot more implied complexities than I’d ever realized.  But it does make sense.

### corwin

Site administrative account, so probably Corwin, Felix or DD-B.

## 0 thoughts on “Capital Volume 1 Part 1 Chapter 1 Section 3A”

1. In that last paragraph he is saying, in modern math terminology, that the relation is not commutative. If he were writing today, it would have been inappropriate to use the “=” symbol, which (to the best of my admittedly limited knowledge) is generally restricted to commutative relationships: that is, ones in which, for any a and b you choose,
a = b
if and only if
b = a

Hmmm… maybe those relations still hold in his thinking. Have to see where he goes with this. Nonetheless, I wish he had used some other notation, like
1 coat => 20 yards of linen
which clearly implies an asymmetrical relation.

2. I believe, Mark, that is exactly saying it IS commutative.

My impression is he is actually, in some measure, analyzing equality. The point is, if you will, philosophical. When you say a=b, you are defining a in terms of b; you are not defining b. The role of a in that equation is relative; ie, it stands to be defined relative to some other term. The role of b is as equivalent–it does the defining.

It is true that b=a; which changes the roles of the arguments; now b is the relative, and a does the work of defining.

3. georgmi says:

I agree that Marx seems to be claiming commutativity, but I think the concept of equality is misapplied here.

If I need a coat, and you offer me 2o yards of linen, I’m going to have to keep looking. Something is missing.

And while you may, given the appropriate tools and skill, be able to turn twenty yards of linen into a coat, you can’t then turn a coat back into twenty yards of linen. Something will have been lost.

There is surely a direct relationship, but especially in terms of value (either use- or exchange-), a coat is not equal to twenty yards of linen. If it were, tailors would never get paid. :)

4. Miramon says:

The meaning of = and other epistemological topics are not trivial matters for philosophers.

But I must say this particular chapter of Marx does seem to be pretty trivial, epistemology aside. So a TL;DR post in response to triviality….

As a practical matter, these two things, 20 yards of linen and a linen coat, are obviously not equivalent, even if they can be considered economically equivalent at a given time and place in a given market for some particular buyers.

Those qualifying particulars necessary to establish the equivalence are so contingent and ephemeral as to make the equivalence fall apart for most uses of the term.

At Tuesday at 9:15 March 17 1843 in the Hamburg Bourse (assuming there was such a thing as a Hamburg Bourse) 20 yards of linen vs 1 coat might conceivably have been a neutral choice for buyer Helmuth Gantz (of the famous firm Gantz et fils) perhaps because his firm not only resells coats but also makes clothing. Or perhaps he was a linen merchant who happened to need a new coat that day.

But on other days, in other markets, or for other buyers at the same market, the two goods will certainly have different values.

The linen allows people to make clothes; the coat allows people to stay warm, and the fact these two radically types of affordances happen to have the same worth at some point in spacetime is more or less a fluke.

Money, in contrast, while it changes value over time, does so in a somewhat less contingent manner. Assuming that 20 yards of linen cost 10 marks at that bourse, and so did that coat, the equivalence becomes much stronger and more consistent until eventually the prices change.

5. georgmi says:

…so the assertion must be that there is enough linen left over out of twenty yards to balance the labor put into creating the coat?

6. georgmi: He is very explicit, right there, in the first paragraph. “x commodity A is worth y commodity B” In other words, they are not the same, they are WORTH the same–ie, we are talking value, or exchange-value. To use the equal sign, we must abstract from the commodity its exchange-value. In other words, the same amount of labor is necessary to create 20 yards of linen (in this example) as to make 1 coat. Nothing whatever is said of it’s use-value. To put it in your terms, you are not out looking for a coat, you are out looking for something that can be exchanged for 20 yards of linen.

But an abstraction of that type is always made when using the equal sign, or, really, any other mathematical symbol. To say 20 < 19 we are abstracting all properties from an idea except count. To say "let c=the speed of light" we are engaged in a complex series of abstractions. We define "c" by making it relative to the speed of light; we cause the speed of light to act as the definer of "c" and we even go so far as to abstract from the natural phenomenon light everything except it's speed.

7. Exactly so. The thing to take away from this section is the concept of relative value in exchange: so much of this is worth so much of that.

If, down the road, you want to construct inequalities where so much of this is worth at least so much of that, you can do so, just like you can start adding complexities of changing exchange values at changing places over changing times, but all we’re doing here is the first step, constructing an equality of relative value.

8. Duffy Pratt says:

I think that the important point here, for Marx, is his insistence that the value of linen cannot be expressed in linen. This leads him to reject utterly the idea of the time value of money. And that in turn leads to the idea that the entire capitalist system is built on a contradiction.

9. Le Rouge says:

Thank you Duffy for taking a hacksaw to that particular Gordian knot.

It’s easy to miss the central point if you allow yourself to get bogged down in definitions of equivalency.

“Do not be distracted by the shadows, concentrate only on the target.”

10. Just to throw a few orcs in the cream cheese, if you follow Adam Smith, the relationship is a bit more complicated than implied by the “=” sign.

In a free, un-coerced trade, two parties to a trade will make that trade only if both parties feel they benefit from the trade. So for the person who has the coat, 20 yards of linen is worth more than one coat, so the trade is worth making. And for the person who has the coat, one coat is worth more than 20 yards of linen, so the trade is worth making.

On average, across an entire population, we might learn that 20 yards of linen = 1 coat, but each individual trader is made up of people who value one coat just a bit more than 20 yards of linen, coupled with people who value 20 yards of linen a bit more than one coat. Without this potential gradient, the reaction wouldn’t go.

11. Karl: If you can’t keep separate “value” in the sense of “it is of use to me” and “value” in the sense of a quantitative expression of comparable exchange, you will never make sense of economics. Adam Smith, by the way, was quite clear on the difference; it is only some of his followers who seem confused.

To make exchanges in the market, we must be able to assign numbers to the relationships between commodities. This has virtually nothing to do with the value I place on friendship, or the fact that I value the time I’ve spent reading. Same word, different meaning.

12. Thanks for taking the time to discuss this, I feel strongly about it and love learning more on this topic. If possible, as you gain expertise, would you mind updating your blog with more information? It is extremely helpful and beneficial to your readers.
עוזרת.

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