ok, yeah, he's not doing derivatives, but that is what he means.
it's kind of hard to actually fully express the idea of the falling rate of profit mathematically. you'd essentially want to show that on average, p' < 1 (i would guess based on Marx's formula, given that it's positive-definite and therefore, the requirement certainly couldn't logically be that p' is on average negative-definite).
yeah, i mean i think forcing marx into a specific mathematical model misses the point entirely for the most part. it's just that there is a consistent mathematical way to phrase "tendency" which is in terms of time-averaged behaviors, which are a well-studied mathematical field. the tendency for the rate of profit to fall would be most accurately phrased mathematically as a statement about some abstract objects that have a specific time-averaged behavior, that marx therefore asserts is a dialectically correct interpretation of the aggregate behavior of capital. saying that it is "on average" falling is to actually say that it does have counter-tendencies that change the local behavior but not the behavior over sufficient time scales.
that's what i'm saying though is that you could do it, but to do so would be to miss the point. i don't think that makes a law of it though, just a model of a particular abstract thing. to proscribe mathematically is to insist that you can come up with a mathematically coherent and empirically observable set of quantities. no more, no less.
i have also not read capital, but my understanding is that the falling rate of profit is due to the competition of various businesses, and the profit-crushing nature of technological improvements in efficiency. the value of goods falls as they are produced more efficiently, and therefore, the profitability of commodities will trend downwards as competition compels businesses to become more efficient for the sake of the short-term.
ok, yeah, he's not doing derivatives, but that is what he means.
it's kind of hard to actually fully express the idea of the falling rate of profit mathematically. you'd essentially want to show that on average, p' < 1 (i would guess based on Marx's formula, given that it's positive-definite and therefore, the requirement certainly couldn't logically be that p' is on average negative-definite).
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yeah, i mean i think forcing marx into a specific mathematical model misses the point entirely for the most part. it's just that there is a consistent mathematical way to phrase "tendency" which is in terms of time-averaged behaviors, which are a well-studied mathematical field. the tendency for the rate of profit to fall would be most accurately phrased mathematically as a statement about some abstract objects that have a specific time-averaged behavior, that marx therefore asserts is a dialectically correct interpretation of the aggregate behavior of capital. saying that it is "on average" falling is to actually say that it does have counter-tendencies that change the local behavior but not the behavior over sufficient time scales.
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that's what i'm saying though is that you could do it, but to do so would be to miss the point. i don't think that makes a law of it though, just a model of a particular abstract thing. to proscribe mathematically is to insist that you can come up with a mathematically coherent and empirically observable set of quantities. no more, no less.
Yeah, iirc (I have not read Capital) the fall of the rate of profit is due to the competition of various businesses
i have also not read capital, but my understanding is that the falling rate of profit is due to the competition of various businesses, and the profit-crushing nature of technological improvements in efficiency. the value of goods falls as they are produced more efficiently, and therefore, the profitability of commodities will trend downwards as competition compels businesses to become more efficient for the sake of the short-term.
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