[OPE-L:4043] RE: Depreciation Answers

andrew kliman (Andrew_Kliman@msn.com)
Thu, 23 Jan 1997 10:01:58 -0800 (PST)

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A reply to *one* aspect of John's ope-l 4041. I hope to get to other aspects
in the near future.

John assumes a machine that can last physically for 6 years, but firms expect,
correctly (?) that it will become obsolescent after 3 years, when a BETTER
machine comes along. They thus depreciate it over 3 years. He writes:

"My question to Andrew is - 'How do we incorporate such losses into the rate
of profit calculations?' Note that capitalists who use the 3 year schedule
would have recovered their investment but would have gotten a lower rate of
profit than those who use a 6 year schedule.

"(Andrew, note that I am asking you for something different than we found in
your earlier examples concerning moral deprecitation. Here, the machine is
not cheapened but replaced by a better machine at the end of the 3rd year.)

"I do agree with Andrew when he maintains that capitalists' bookkeeping cannot
alter the rate of profit. Indeed, in the above example we could assume that
one capital is depreciated over 6 years even though it lasts only 3 years
while the other is "correctly" depreciated over 3 years. Clearly, in either
case the gross returns would be the same no matter how the fixed capital is
depreciated. Here, it is a question of how to separate depreciation from
profits, on the one hand, and, on the other, how to calculate the rate of

OK. Good questions. Clearly there are different ways to calculate the profit
rate. It is not all that important, actually, since it is largely a matter of
bookkeeeping, given that, as John notes, the gross returns are the same in
either case. Let me illustrate how the profit rate would be calculated,
according to my view, if we measure the rate as surplus-value per year divided
by capital advanced in that year.

I'll use different figures from John's, but retain the 3 yr/6 yr dichotomy.
The machine is bought at time 0 for 18. The firm depreciates it over 3 years,
thus figuring that its value is reduced by 6 each year. Actually, it
transfers a value of 3 during each of the first three years, so it is worth 9
after 3 years, right before it gets knocked out by a BETTER machine, whereupon
it is worth zilch.

I'll also assume that value added is 12, and wages are 7, so that
surplus-value is 5, during each of the first 3 years. And I'll assume that
the firm sells its stuff at its value, which equals 3 (value transferred) + 12
(value added) = 15, during each of the first 3 years.

I'll also assume that the firm commits a value of 6 at the end of each year,
out of gross revenues of 15, in a replacement (sinking) fund. This 6 is
additional *money capital*. The profit rate is formed on wages plus total
constant capital, including both physical and money capital. The value of the
physical capital, as noted above, is 18, 15, 12, and 0, at times 0, 1, 2, and
3, respectively, and the firm's money capital is 0, 6, 12, and 18, so total
constant capital is 18, 21, 24, and 18.

Note that the net revenue of the firm each year equals 2, which is the 15 in
gross revenue, minus the 6 in depreciation charges, minus the 7 in wages.
This is 3 less than the surplus-value of 5, since the depreciation charge of 6
exceeds the value transferred, 3, by the same 3 units.

Constant + variable capital is thus 18 + 7 = 25; 21 + 7 = 28; and 24 + 7 = 31
during the first 3 years. Surplus-value is, again, 5 during each of these
years. Hence, the annual profit rates are 5/25, 5/28, and 5/31. No further
adjustments need to be made, since at the end of the third year, the firm
holds a money capital of 18, which is the sum with which it began when it
invested in the machine.

For comparison, note what would have happened had the firm committed only the
actual value transferred to its replacement fund. The physical capital would
go down each year by 3, but the money capital would go up by 3, so total
constant capital would remain 18, and constant + variable capital would equal
18+7 = 25. With a surplus-value of 5, the profit rate would be a constant
5/25 = 20%. However, the firm would incur a capital loss of 9 at the start of
the fourth year, since its machine, which a moment ago was worth 9, is
suddenly worth zippo. So the year 4 profit rate would plummet, ceteris
paribus, if a one-time capital loss were charged against profits of year 4.

In either case, we see that the moral depreciation lowers the profit rate -
either gradually, if firms anticipate the moral depreciation, or suddenly, if
they don't.

Also for comparison, it might help to think of how the firm might measure its
annual profit rate. It may think that its machine is being reduced in value
by 6 each year, but that its total constant capital remains at 18 each year,
because of the money capital of 6 being added each year. It counts its
variable capital as 7, making its capital advanced a constant 18 + 7 = 25.
If it counts the apparent loss of value of the machine as a depreciation cost,
that equals 6, and with wages of 7 per year, it would figure its annual costs
as 6 + 7 = 13, which leaves a profit of 15 - 13 = 2 as profit. Dividing this
2 by the capital advanced, 25, it figures its profit rate as 2/25 = 80er
annum. So it looks as though the profit rate is constant. But that is
simply because the capital loss, which actually occurs suddenly, at the start
of the fourth year, is being anticipated and the prior years' profits are
artificially being reduced -- on the books --- thus lowering the profit rate
artificially in the earlier years and masking the FRP.

Andrew Kliman