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I don't understand the difference between the two. For example:

2 Shoes = 3 wood

Now Marx says that the first is the relative-form and the second is the equivalent-form. So the use-value expressed in the equivalent-form is represendet in the value of the relative-form. Why does the equivalent-form represent the use-value of the wood? Isn't it just a commodity with use-value and exchange-value? So why is the equivalent-form only the use-value of that thing?

Marx says in the simple-value form there is a contradiction because one is equating use-value and it's opposite, value. But aren't they both commodities with use- and exchange-value? Because they already exist as commodities in the system. Is it because the commodity is "new" in the market and exists only as use-value until I put it into the relationship with commodities in the market and therefore obtains value??

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It has nothing to do with new products in the market, nor with confusion of use-value and exchange-value. To make it a bit simpler:

1) Commodities in capitalism have a two-fold character. The use-value (they are useful products for the buyer to consume) and the exchange-value (they can be exchanged to another products in a given way).

2) The exchange-value of the product depends on the embodied labor of the product, which is named as Value by Marx. So in a sense, exchange-value = Value.

3) Products can only be compared in relation to one another. You cannot understand anything by saying ex. 2 apples = 2 apples.

Thus, we reach to the Elementary Form: 20 yards of linen = 1 coat
In this equation, linen plays the active role or Relative form and coat plays the passive role, or Equivalent form. In other terms, you define the Value of linen comparing it to the Value of coat.

Now, here is the core of the analysis. Marx claims that since there is a comparison (20 linen=1 coat), there must be a common element to compare. That common element is not the use-value (linen is not the same as coat). It is the exchange-value, or Value, or the human labor embodied in the two products. In other words, this equation states that labor needed to develop 20 yards of linen is equal to labor needed to develop 1 coat (given constant technological advancement, resources, etc.) Use-value, on the other hand, just acts as a carrier of Value.

The importance of this realization, is to understand the essence of exchange in capitalistic world and connect it to the money form (20 yards of linen = 1 coat = 100 Euros), and understand socio-economically how money was created and what does it really mean.

Karl Marx. Capital Volume One, Part I: Commodities and Money, Chapter One: Commodities

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