I post the following for comments, questions, etc.
Few treatments of Marx's CAPITAL consider the durability of fixed
capital as little more than a minor question. Indeed, treatments
of the accumulation process itself often abstract from fixed
capital entirely.
We make no attempt here to link its durability to the periodicty
of crises but confine ourselves to the question of the lifetime
of fixed capital. We begin with a simple example in three
stages. In the first, we introduce a process of production with
no fixed capital. We then consider the introduction of machinery.
The replacement of that machinery by better machinery concludes
our example.
STAGE I
We begin by looking at a process where fixed capital has not yet
been introduced. Let's say a capitalist invests $900 in raw and
auxiliary materials, $100 in variable capital or wages, and earns
a profit of $100. The rate of profit, p, for this capitalist is
given by
(1) p = s/(c+v)
where s is the profit or surplus value, c the price or value of
the constant capital, and v the wage. Using our assumed figures
and substituting in (1), we see that
(2) p = 100/(900+100) or 10%
Now any machinery introduced into this process will be "labor
saving" since the fixed capital per unit output now stands at 0.
If the capitalist is to introduce a machine into this process, he
must expect a greater rate of profit.
STAGE II
Let us assume that an investment of $200 in machinery would allow
the capitalist to double the output. If he were to make that
investment in machinery, he would, by assumption, double his
investment in raw and auxiliary materials so that it becomes
$1800. His cost in wages would remain the same -- $100.
Assuming no change in the price or social value of the commodity
produced the total output would be worth $2200. Clearly, if the
machine is completely useless at the end of one period, the
investment would not be made since the anticipated rate of profit
would be
(3) p = $100/($200+$1800+$100) or about 4.8%
But should the machine last longer than one period, then it may
be used. With fixed capital to calculate the rate of profit, we
use the following relation between the amount of fixed capital
invested, C, the periodic payment for depreciation and profit, A,
and n the number of periods.
(4) C = A * (1 -(1/(1+r)^n))/r
Should the machine worth $200 be used for 10 periods, then the
rate of profit would be
(5) r ~= 12.8%
But what determines the length of time the machine will be used?
Obviously, if it is worn out physically at the end of the 10th
period, then the answer is simple. Marx himself observed:
"The physical deterioration of the machine is of
two kinds. The one arises form us, as coins
wear away by circulating, the other from lack of
use, as a sword rusts when left in its scabbard.
There is second kind is its consumption by the
elements. Deterioration of the first kind is
more or less directly proportional, and that
of the second kind to a certain extent inversely
proportional, to the use of the machine."
(CI,p528)
If capitalism were an economy without technical change and the
consequent changes in prices and values, then consideration of
physical deterioration of the machine would be sufficient to
determine the period by period depreciation charges and profit
calculation. However, for Marx, the technical changes that occur
within the accumulation process are central to his analysis.
Hence, he states that
"But in addition to the material wear and tear,
a machine also undergoes what we might call a
moral depreciation. It loses exchange-value,
either because machines of the same sort are
being produced more cheaply than it was, or
because better machines are entering into
competition with it." (CI,p528)
In a footnote, Marx then adds
"The 'Manchester Spinner' ... enumerates, as
part of the cost of machinery, 'an allowance for
the deterioration of machinery.' 'It is also
intended,' he says, 'to cover the loss which is
constantly arising from the superseding of
machines before they are worn out, by others of
a new and better construction.'" (CI,p528)
Thus, for Marx, deterioration of machinery is not simply physical
but social as well. In our example, we have assumed that the
social values and prices of commodities are constant. Hence, for
us, it is not a question of "cheaper" machines but rather of
"better" machines. In capitalism, the introduction of new
technology is spurred by the search for greater profitability.
Recall that in our example, the capitalist predicted that the new
machine would last 10 periods. That is, he estimates that at the
end of the 10th period newer machines would be available to
enable him to achieve an even higher profit rate. Indeed, this
rate of profit would be so high that he would abandon the machine
even though he his depreciation charges are 0. Let's look at this
a bit more closely.
Should the capitalist use the machine first introduced for an
11th period, his profit rate would be given by (1) as at the end
of 10 periods since he has recovered his entire investment in
fixed capital.
(6) p = ($2200-$1900)/($1800+$100) or, about, 15.8%
Note that the machine itself has no value in this period and
hence from the standpoint of price or value, the process of
deciding whether or not to replace the machine is identical to
that of deciding whether or not to introduce a machine into an
unmechanized process.
Stage III
Let us assume that a technique becomes available such that by
doubling the fixed capital input, the output increases by a
factor of 3. Raw and auxiliary materials would grow at the same
rate as output and the labor costs are assumed constant. Using
the same relation given in (4), after using an iterative process,
we see that
(7) r is about 18.8%
Since this profit rate is greater than that of the older
mechanized technique, even with an investment in fixed capital of
0, the old technique is abandoned. Thus, the process of moving
from techniques where the investment in fixed capital is
negligible or zero to techniques requiring ever-growing
investments in fixed capital as well as in raw and auxiliary
repeats itself.
The Basic Principle
By way of the above, we have shown the manner in which fixed
capital is introduced and ultimately replaced. This places gives
Marx's treatment of the transition from the period of manufacture
to that of large scale industry still more meaning. Indeed, the
initial decision to introduce machinery or to move from Stage I
to Stage II is similar to that of moving from Stage II to Stage
III since both involve the replacement of a process in which the
value of fixed capital is negligible. Further, we see that it is
capital itself in the form of fixed capital that it is both
created and destroyed as capitalists seek greater profits by
changing techniques. Yet, our example is laden with assumptions
and gives rise to more than a few questions.