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.
So p' is not dp/dt it's dp/dv with c being the +C constant because capital costs are fixed directly into the end product (if materials cost 40 and you can make 40 units, that's exactly $1 per unit fixed cost, but if you can push workers to make 3/hr instead of 2/hr you've reduced your labor cost by 30%).
s' is defined as ds/dv where the rate of surplus is total surplus divided by wages.
So an increase in v will result in a decrease in both p' and s'.
And for clarity, the reason c is constant is because this process of surplus value extraction has already been applied to it. The fractional/raw materials are coming from another industry that has already extracted surplus and as a result turned the commodity into a store of use value and dead labor (profit). Something that can't have any more value extracted from it.
Yeah, most of Marx's formulas leave time out of the equation as all that you really need to understand the flow of capital generation of profit is the relations between capital, material, and wages.
If you read his examples though, time does come into play when dealing with time based pay (e.g. $20/week). But because time isn't in the base formulas, they still apply to wage relations that are per unit.
That being said, he did toy with the idea of time based labor vouchers and the concept of labor time. Something that is necessary as humans do live in a world where time progresses and time is a limited thing for all of us.
But when looking at profit, time only comes in as a secondary factor for reducing wages. E.g. getting people to make 3 widgets an hour instead of 2, which in the formula is represented as a change in s' because the share of C given out as v falls.
This is also what kick-starts the falling profit rate, as increasing worker productivity requires (in most cases) increases in the share of C given out as c (new machinery, training, better materials, etc.). Since profit is derived from v and not c, that means total profit can increase while rate of profit decreases. The total C goes up, but the share of v that makes it up decreases (while total v increases) which leads to decreasing rates of profit with increasing total profit.
my brain is poisoned from STEMland, is p' in this case
dp/dtwherepis profit?I believe it is technically, as it is the rate of profit, but I don't believe Marx does a derivative to find this formula. See here
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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https://www.marxists.org/archive/marx/works/1894-c3/ch03.htm
So the P' is Profit Prime I believe, and that is a mathematical doohicky to make a graph that illustrates the falling rate of profit
definitely a "sort of" derivative then. economists learn to apply calculus without concluding you need to eat the poor challenge (actually impossible)
Piketty did the impossible in Capitalism in the 21st Century
To disambiguate:
p' == profit rate
s == surplus value
C = capital
c == constant Ccapital (maintenance, materials)
v = variable capital (Wages)
So p' is not
dp/dtit'sdp/dvwithcbeing the +C constant because capital costs are fixed directly into the end product (if materials cost 40 and you can make 40 units, that's exactly $1 per unit fixed cost, but if you can push workers to make 3/hr instead of 2/hr you've reduced your labor cost by 30%).s'is defined asds/dvwhere the rate of surplus is total surplus divided by wages.So an increase in
vwill result in a decrease in bothp'ands'.And for clarity, the reason
cis constant is because this process of surplus value extraction has already been applied to it. The fractional/raw materials are coming from another industry that has already extracted surplus and as a result turned the commodity into a store of use value and dead labor (profit). Something that can't have any more value extracted from it.ok thanks, i actually wondered if i had guessed wrong because i'm so used to time being the quantity that rate is relevant to.
Yeah, most of Marx's formulas leave time out of the equation as all that you really need to understand the
flow of capitalgeneration of profit is the relations between capital, material, and wages.If you read his examples though, time does come into play when dealing with time based pay (e.g. $20/week). But because time isn't in the base formulas, they still apply to wage relations that are per unit.
which makes sense, it wouldn't make sense to model what he wanted with time.
That being said, he did toy with the idea of time based labor vouchers and the concept of labor time. Something that is necessary as humans do live in a world where time progresses and time is a limited thing for all of us.
But when looking at profit, time only comes in as a secondary factor for reducing wages. E.g. getting people to make 3 widgets an hour instead of 2, which in the formula is represented as a change in
s'because the share ofCgiven out asvfalls.This is also what kick-starts the falling profit rate, as increasing worker productivity requires (in most cases) increases in the share of
Cgiven out asc(new machinery, training, better materials, etc.). Since profit is derived fromvand notc, that means total profit can increase while rate of profit decreases. The totalCgoes up, but the share ofvthat makes it up decreases (while totalvincreases) which leads to decreasing rates of profit with increasing total profit.