Jerry wrote:
I had previously suggested the following formula for the aggregate
capital:
>
> surplus value
> ------------------------------------------------------------------------
> constant fixed capital + constant circulating capital + variable capital
Then John objected arguing that the above didn't take into account the
stratification of fixed capital.
Yes, I agree that a more concrete representation of the process would
include:
a) stratification of constant fixed capital by age (the usual measure);
b) stratification of constant fixed capital by quality (this would take
into account different "vintages");
(this would entail some specification of the notion of "choice
of technique")
c) specify, at least for accounting purposes, a projected rate of
depreciation;
(the projected rate of depreciation should take b) into account, even
though forced obsolescence and "moral depreciation" can't be
accurately accounted for in advance)
d) show differences in capital composition for each firm.
e) show transfers of surplus value among capitalists following the sale of
the commodity product.
(a useful, initial, simplifying assumption here might be to assume that
the commodity product is sold at one moment in time. The "end of the
period" would seem to me to be the most logical approximation).
In principle, the above could be done. It would involve some more
complicated math, to be sure.
I don't see a)-d) as that complicated (conceptually).
I realize that you have given a lot of thought to c) and have discussed
different forms of depreciation accounting on this list before.
My comments:
1. Your idea that we must deal with stratification and the
changes in it that occur as accumulation takes place at a more
concrete level of the analysis makes an assumption which I
do not think is true. Specifically, by abstracting from the
changing stratification of fixed capital as one deals with
how surplus value is allocated, one, at least, gives the
impression that he or she has abstracted from the manner
in which those changes effect the accumulation process.
That is, given a stratified fixed capital structure
how do we move via abstraction to one in which there is
no stratification? How did we get from the concrete to the
abstract?
What is the issue here? If we start with the assumption that
there is stratification and equal rates of return, why and
how are we considering a transformation process in which the
rates of profit are equal? Quite honestly, I think we have
ignored the problem and not abstracted from anything at all.
We simply hope that changes in stratification will not matter.
2. Your points (a-c) assume that somehow we are able to separate
depreciation from profit in each period. How? In c you suggest
we introduce a "projected rate of depreciation" while putting aside
the notions of forced obsolescence and moral depreciation. Let's
pursue this a bit. If a new machine cost 1000 and becomes useless
at the end of 10 years, what is the annual depreciation charge?
Clearly, the usual answer would be 100. However, when we look
at depreciation as the difference between the machine's value
to the capitalist at the beginning of the year and its value at
the end of the year, the usual answer becomes suspect. Changes
in the valuation of fixed capital--depreciation-- depends upon
profitability. What can we say?
First, if the machine costs 1000 and 1000 hours of living labor
are used over the 10 years of the machine's existence, then
the gross output in those 10 years is 2000.
Second, if we assume that the 1000 hours of living labor are
expended uniformly over those 10 years and that the output
for each of those 10 years is 200, we still must deal with
how capitalists themselves see matters. Generally, as capital
ages less would be allocated to depreciation and more to
profit. Depreciation seems to "accelerate" naturally as
capitalists use a RRI to reckon profitability.
Third, lest we fall into the trap of attempting to derive
the concrete from the abstract, I would suggest that we
consider a situation in which all capitals are earning the
same rate of return and then examine that same situation in
terms of value production. If we are able to do this, then
moving from abstract to the concrete would be simpler as
we have already moved from the concrete to the abstract.
Jerry concluded:
But, In my opinion, the hardest, and perhaps most vital, part of
the above procedure would be to show e). That pre-supposes, of course,
that the transfer of surplus value among capitalists is a key part of
the accumulation process. I must say that I've never seen a satisfactory
treatment of that issue.
However, I want to return to the question of where (at what level of
abstraction) this topic should be addressed.
Do you agree with the following statement by Fred (from [648])?
> The aggregate magnitudes are determined at the level of analysis of
> capital in general and remain invariant as we move to more concrete
> levels.
My response: Fred's remark is perhaps true. However, I do think
that as we work on this stuff, we first need to travel from the
concrete to the abstract. As I noted above, if we start from a
situation in which the RRI is the same for all capitals, then
the task would be to explain the allocation of surplus value
and profit in such a situation. We could then move from the
abstract to the concrete or, knowing we stand on firm ground,
continue to travel from the concrete to the abstract. At this
point, I'm not sure we can do this and, hence, I am reluctant
to agree with Fred's statement.
John