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Source: Michael Roberts Blog

Norm’s note: for context, I’ll refer you to this post by Michael Roberts, titled ‘The two Michaels (Heinrich and Roberts) in Berlin – dogmatism versus doubt.’ Clearly, in claiming that Marx’s ‘ law of the tendency of the rate of profit to fall‘ is logically inconsistent, Michael Heinrich missed something, as the comment by ‘Borzooieh tabib‘ so elegantly demonstrates:

Borzooieh tabib Says:
June 4, 2015 at 4:06 am | Reply

Rate of profit
this line of thoughts
Let us calculate every thing based on socially necessary hours of Labor time, and calculate for every single worker, and for every single working day .
Rate of profit = S/C+V
If P would be the amount of value produced by a worker in one hour with a given technological condition:
S/C+V can change to sP/cP+vp
s would be the time(not value) spent for Production of S( expressed as value)and c the time of production of C and, v the time spent for production of V
But s+v is maximum 24 hr if we
assume that worker does not need any rest time and all the time working
Therefore s =24-v
So rate of profit = Ps/ Pc+Pv
Or. s/c+v
Or. 24-v / c+v
Or ( 24/v ) -1 / ( c/v)+1
With advancement of technology v decreases so (24/v), increases ,
and also c/v increases
Because we are talking about long run trend , the amount of v gets very small so 24/v and also c/v will be very large numbers so we can omit -1 and +1 in formula
So (24/v) -1 / (c/v) +1 can be changed to:
(24/v) / (c/v)
Or. 24 / c
But accumulation of capital means that c is increasing ,( the time spent in production of C expressed as value)
So 24/c as the formula of rate of profit in the long run , will fall, (inspire of technological advances which increases S/V (the rate of surplus value,)

Indeed.

And directly relevant to the issue at hand, see this: Unmaking of Marx’s Capital, final, 7-22-13.pdf

The abstract of the essay reads:

Michael Heinrich’s recent Monthly Review article claims that the law of the tendential fall in the rate of profit (LTFRP) was not proved by Marx and cannot be proved. Heinrich also argues that Marx had doubts about the law and that, for this and other other reasons, his theory of capitalist economic crisis was only provisional and more or less in continual flux. 

This response shows that Heinrich’s elementary misunderstanding of the law––his belief that it is meant to predict what must inevitably happen rather than to explain what does happen––is the source of his charge that it is unproved. It then shows that a simple misreading of Marx’s text lies at the basis of Heinrich’s claim that the simplest version of the LTFRP, “the law as such,” is a failure. Marx’s argument that increases in the rate of surplus-value cannot “cancel” the fall in the rate of profit is then defended against Heinrich’s attempt to refute it. Finally, the paper presents evidence that Marx was indeed convinced that the LTFRP is correct and that he regarded the crisis theory of volume 3 of Capital as finished in a theoretical sense. 

What is in bold is my emphasis, because what ‘Borzooieh tabib‘ demonstrates is precisely that “increases in the rate of surplus-value cannot “cancel” the fall in the rate of profit,that is to say, that in the pursuit of profits by means of technological innovation or industrial rationalization, you can simultaneously have an increasing rate of surplus-value AND a falling rate of profit. Therein lies the rub.


Related:

Marx’s law of profitability: answering old and new misconceptions

A Critique of Heinrich’s, ‘Crisis Theory, the Law of the Tendency of the Profit Rate to Fall, and Marx’s Studies in the 1870s’