When you say that the capitalist steals from the worker by appropriating part of the value that the worker produced, aren't you neglecting the fact that the worker is producing using equipment that belongs to the capitalist? In effect the capitalist is renting out the equipment (the means of production I guess) to the worker. What is outrageous of course is the rent that he charges for it, but still I don't think it should be zero, the way you are suggesting. Thanks a lot.
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That being said I can paraphrase the core of the argument. It is built on several important premises. The first is that for a commodity to have an exchange-value, it must first have a use-value (subjective worth) and it must be the product of labor(manufacturing, gathering/mining etc). Thus all commodities are actually embodiment’s of human labor including labor itself. This is true for finished products as well as raw materials. Capitalists possess the commodity private property and the means of production. This is called constant capital and it has no worth beyond the labor already congealed within it. That is, it is not new labor and it does not generate additional value. The goal of a capitalist is to make money by transforming his constant capital into a new product. Workers, being dispossessed of the means to produce without a means of production, still possess a universal commodity to exchange at the market; labor-power. It is this labor-power that is hired as variable capital by the capitalist to impart value upon the raw materials provided by the capitalist using the constant capital he privately owns. If the capitalist sells the product of this labor at cost, then he doesn’t make any money. If he sells above the cost, then he will be undercut by his competition. So instead the capitalist pays labor less than the value they create in the finished product. The machines/tools they are provided are not creators of value. They are congealed labor that can only be released and transformed by living labor. They can only impart worth at the cost of their own degradation, but tools can degrade from use as well as time. Effectively every moment that a tool or machine lies fallow is corresponds to a diminishment in the congealed labor making it up due to entropy and social degradation( becoming technologically outdated). Thus without labor not only would the capitalist be unable to create a product to sell, his own constant capital would slowly decline in value with zero reciprocation. It is not the labor that rents the means of production, but the capital that rents the labor and always below the value of that labor. Additionally it is this expropriation of this surplus-value that allows the capitalist to purchase private property in the first place. There are other factors such as “primitive accumulation”, “reproduction” and the role of “money capital”(credit and banking) that both complicate and facilitate this system, but that is the general gist of the theory.