Andrew here, with a brief reply to Alan's ope-l 1325:
It took me some time to study Alan's post. I have tentatively concluded
that he didn't understand my point, which is perhaps not surprising,
since I was not laying out a theory, but simply explaining a calculation
to Paul C.
In my example, I had "a machine that lasts 4 periods and which has the
following values: Vo = 40, V1 = 28, V2 = 16, V3 = 12. Then the
value transferred to the products that emerge at times 1, 2, 3, and 4
is VT1 = 40/4 = 10, VT2 = 28/4 = 7, VT3 = 16/4 = 4, and VT4 = 12/4 = 3.
In sum a value of 24 has been transferred ...."
Alan writes:
"Agreed, I think, is the following: At the beginning of period 0 the
capital stock of the capitalist, who owns four machines each worth $40,
is $160. At the beginning of period 1, the capital stock of the
capitalist, who owns four machines now each worth $28, is $112. Hence
the decline in the value of the machines is $48."
No. The problems begin here, so what follows in Alan's post is also based
on a misunderstanding. First, I spoke of ONE machine. The division by
4 was the straight-line physical amortization of the one machine. I
have no problem, of course, with a four-machine, example, but I think
that Alan might have gotten confused right here.
More importantly, we're using the term "value of the machine" differently.
*I* meant that the social value of the machine, i.e., the labor-time
needed to reproduce it, i.e., the labor-time needed to produce new
*replicas* of it, falls from 40 to 28 to 16 to 12. *Alan* is using the
term differently. If I moved to a 4-machine example, their total value
at time 0 would be $160, as Alan says, and the social value of 4 NEW
machines of the same type would be, at time 1, $28*4 = $112, in my
interpretation of Marx. Thus, THIS $48 "decline in the value of the
machines" is pure capital loss, devaluation, devalorization, moral
depreciation, or whatever. I.e., not physical wear & tear.
The value of the physical capital in the hands of the firm at time 1
would be (3/4)*($112) = $84. But if the output produced between
times 0 and 1 was sold at value, then the firm also has a $40 sum of
money capital for replacment. Each machine transferred a value of
(1/4)*$40 = $10 to the products emerging at time 1, and with 4 machines,
this gives a $40 replacement fund.
Hence, ceteris paribus, the firm's capital (physical and money) is
$84 + $40 = $124. It started with $160, so its loss is $36. What does
this loss represent? $9 per machine, which is 3/4 of the loss
in the unit value of the machine ([3/4]*$12 = $9). Why only 3/4ths of
$12 per machine? Because 1/4th of each machine's use-value is used up.
Thus, although $112 is the social value of 4 machines of that type at
time 1, this figure is not directly relevant to the firm's accounts.
The other problems Alan found in my interpretation follow from this
basic confusion. I won't go into this at length, but note that
I have above clearly indicated how much loss is due to depreciation and
how much to moral depreciation.
Andrew Kliman