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Marx's real concern was to understand and analyze how the law of value determines or regulates exchange, i.e. how the balancing of the production of outputs and the demand for them could be accomplished, in a society based on a universal market such as capitalism, and how this was regulated by labour-time.
However, when they do so, they must provide something of equal value in accordance with the Law of Equivalent Exchange. The only things alchemists are forbidden from transmuting are humans and gold. There has never been a successful human transmutation; those who attempt it lose a part of their body, and the result is an inhuman mass.
Equivalent Exchange doesn't always have to relate to only alchemy. It's also the way life works. One cannot get anything such as money without sacrificing something in return, such as a job or assignment, meaning that one has to work for something to get something.
which, given the classical dichotomy and that real income must equal expenditures , is equivalent to M D = k ⋅ P ⋅ Q {\displaystyle M_{D}=k\cdot P\cdot Q} Assuming that the economy is at equilibrium ( M D = M {\displaystyle M_{D}=M} ), that real income is exogenous, and that k is fixed in the short run, the Cambridge equation is equivalent ...
The commodity form of exchange historically precedes the legal system which emerges from it. But it is not merely that the commodity form produces the legal form; it is that the commodity form exists prior to the legal form and that only with the full development of the commodity form is there the possibility of a fully developed abstract legal form at all.
Once the money-commodity (e.g., gold, silver, bronze) is securely established as a stable medium of exchange, symbolic money-tokens (e.g., bank notes and debt claims) issued by the state, trading houses or corporations can in principle substitute paper money or debt obligations for the "real thing" on a regular basis.
One Summer, 50 States
Third, value is not the same thing as exchange-value (or price). Rather, the value is the shared characteristic of the exchange-values of all the commodities. He calls this the "common factor", whereas someone else might call it the "essence". In contrast, the exchange-value represents the appearance or "form" of expression of value in trade.