Diego: I think that were Marx alive he would use matrix algebra. Fred: > I don't think so. Because matrix algebra does not fit with Marx's logical > method. Matrix algebra Marxism assumes that the rate of profit is > determined simultaneously with prices of production and that the initial > givens in Marx's theory of values and prices of production are the > physical quantities of inputs and outputs. Marx's own logic, to the > contrary, assumes that the rate of profit is determined prior to prices of > production, by the Volume 1 analysis of capital in general, and that the > initial givens are quantities of money-capital (constant capital and > variable capital), quantities of abstract labor, and the money-value > produced per hour of abstract labor. Diego: Since there are different vectors of prices (several theoretical and effective prices), the same result should be expected for the rate of profit. No problem for the LTV due to having an effective rate and one or two regulating rate(s) of profit. The crucial point is that labor time is a physical quantity!! And not only this: it is a continuos and continuosly derivable variable (quantity). As the human praxis consists first of all of human labor, the assumption that all other physical quantities can and should be reduced to physical quantities of labor time seems specially justified. I agree with you that Marx thinks that direct prices (and the corresponding rate of profit) are determined prior to prices of production (and the corresponding rate of profit), but this prior means *at the level of his process of explanation*. One does not need to reproduce the way of explanation used by Marx to get the same result he got. Fred: > How does matrix algebra improve the accuracy of Marx's theory? It seems > to me that the matrix algebra interpretation of Marx's theory only imputes > to Marx's theory a logical contradiction that otherwise would not be > there. Diego: Once one assumes Marx's true values are volume III values, matrix algebra helps us to calculate these values vector in a way very similar to Marx's own calculation, a way which is in the spirit of Marx and is empirically very close to the vectors which can be calculated using Marx's and Fred's assumptions. One additional and not minor advantage in doing so is that all quantitative arguments used by the critics of Marx in favor of production prices become in fact arguments in favor of the LTV, since this theory is the only one which can link the correct calculation with a true theoretical explanation. The explanation is: it is labor processes what is behind monetary prices. I am in favor of using matrix algebra and cannot see any contradiction in Marx's argument. The only thing I can see in him is the relative basckwardness one can see in every pioneer who goes in advance his time. Please, forgive the apparently bitter way of expressing myself. It is due to my poor English and my looking for clarity in expressing my present and may be mistaken) ideas. What do you all think? Comradely, Diego
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