[OPE-L:3013] Re: Defining accumulation

From: clyder (wpc@dcs.gla.ac.uk)
Date: Thu May 04 2000 - 11:34:11 EDT

Gerry:
> Re Paul C's [OPE-L:3007]:
>
> There are a number of problems that I see if one views the accumulation
> of capital only in stock terms. To begin with, the "primary" unit of
> measurement in the accumulation of capital is a *flow* -- i.e. the
> quantity of *money capital* that can be used for the purposes of
> unproductive consumption *or* accumulation.

A flow is just the derivative of stock with respect to time.

Accumulation is the rate of change of the capital stock with respect
to time. Thus it is equal to dK/dt where K stands for capital stock.
Since the dimension of K is person hours, its time derivative is
simple a number of persons. So the dimension of accumulation
is persons.

This is exactly the same as the dimension of a flow of value.
If surplus value is 1 million person years per year, and half
of that is accumulated, we have an accumulation of 500,000 person
years per year or, with the years per year cancelling, 500,000
workers whose material net product takes the form of the new
constant capital.

>If there is accumulation,
> then, the quantity of money capital advanced for the purchase of
> constant capital and variable capital increases. How this affects
> (relates to) the composition of capital is another matter. What is
> most relevant for the purpose of this discussion is that a) prior
> to the beginning of any "period of production" (yes, I know you
> don't like that term) there must be an expansion of the productive
> consumption of surplus value and capital; b) this requires that
> capitalists invest more *money capital* in c & v;

Money capital no longer constitutes part of the capital stock
value given that commodity money has been replaced.

>c) variable
> capital can not be thought of as a "stock".

I agree. Variable capital does not acccumulate, though
the number of workers may. The dimensions of variable capital
is person years per year - hence simply number of persons.

>
> that if you think of the accumulation of capital only in stock
> terms, how do you calculate the rate of profit?
>I.e. if you
> view c as a stock and v (and s?) as a flow, then how can we
> develop a meaningful measure with these diverse categories?

Again this is a question of dimensionality.
There are two possible measures of the rate of profit.
The flow rate of profit is given by s/(c+v) where s
c and v are all flows of value per unit time. It is
a dimensionless number- say 5%.

The stock rate of profit is given by s/K which divides
the flow of surplus value per annum by the value of
the capital stock. This has dimension

value per annum
--------------------- =
value

value / years
---------------- =
value

1/years = years^{-1}

so you now get figures like 50er annum for
the stock rate of profit.

Note that c is not the same thing as K. c is the
flow of constant capital per year - broadly speaking
it is the consumption of raw materials plus depreciation
on machinery.
K is the stock of raw materials and the stock of
machinery.

It is arguable that one should include in K some figure
for the stock of means of consumption that corresponds
to v in the flow model. However in arriving at an estimate
of this from national income accounts one has to beware
of the danger of double counting, and the need to
take into account the periodicity of wage payments.

Clearly if wages were paid weekly one would have to
divide the annual wage bill by 52.

But one cant simply count this money as the
stock of variable capital as it quickly returns
to the proprietors. One either has to measure
the mean cash balances in the hands of wage
earners during the week as v , or else to avoid
double counting, the weekly fluctuation in buffer
stocks held by the retail sector.

One would then have to take into account the fact
that the wages would have been spent in on average
less than 3.5 days of the week i.e concentrated on the weekend.
There will presumably be some weekly fluctuations in
stocks held by retailers and the correct figure to take
for the variable capital would probably be the peek
stock held during the week rather than the mean
stock held. The true figure for variable capital is
probably something like the difference between
the stocks held by the retail sector on monday
morning and the stocks they held on friday morning.

In any case these figures are so small relative to K,
the total stock of constant capital, that for practical
purposes they can be ignored.

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