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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.

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.

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.”

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.

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.

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.

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. :)