[OPE-L:3999] Re: More Depreciation Questions

andrew kliman (Andrew_Kliman@msn.com)
Thu, 16 Jan 1997 11:38:45 -0800 (PST)

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A reply to Michael Perelman's ope-l 3998.

Jerry had written:
> For all of the above reasons, any decision that a firm makes about future
> depreciation of constant fixed capital is very uncertain and, ultimately,
> is no more than a "guesstimate" regardless of the mathematical
> sophistication of the depreciation method chosen or the state of market
> research within the firm. Quite simply, they don't know. They can't know.

and Michael replied:

"Yes, yes, yes. I think that John was intending just this point. It is
the one issue that I have been raising all along. Unless you have
rational expectations marxism, you cannot calculate the c in c+v+s."

Does this conclusion depend on the notion that the "depreciation" part of the
used-up c is determined by firms' "depreciation" methods? Is what they
estimate to be, or consider, "depreciation" necessarily the same as the actual
"depreciation"? Is it necessarily the same as what Marx meant by
"depreciation" when referring to the value transferred from fixed capital?

And does this conclusion imply that individual firms can determine the value
of the commodities they produce by determining their accounting methods?

Or don't I understand what Michael meant by "you cannot calculate the c"?

Let me expand a bit to see if we're talking about the same thing. I suspect
we aren't. As I understand Marx, the c is calculable *in principle*, given
that the *technological* life of a machine is known. Here's how. As I
interpret Marx, the total depreciation of the machine is composed of two
distinct parts, the depreciation due to wear & tear --- which is the value
transferred to the product --- plus the moral depreciation. The latter is a
loss to the capitalist.

Now assume (note that "assume" doesn't constitute a claim that something is
true in reality) that the machine has the technological capability of lasting
3 periods, that it cost $15,000 at time 1, and that the prices of new machines
of that type are $9,000 at time 2 and $4500 at time 3.

Since the machine can last 3 periods, it is as if 1/3 of it vanishes during
each period it is used, assuming straight-line depreciation. (One it is no
longer used, of course, it transfers no value.) So between times 1 and 2, it
transfers a value of (1/3)*$15,000 = $5,000. But at time 2, it would only be
worth $9,000, if new, so it transfers a value between times 2 and 3 of
(1/3)*$9000 = $3000. At time 3, it would be worth only $4500, if new, so it
transfers a value of (1/3)*$4500 = $1500 between times 3 and 4. Then it

Total value transferred is thus $5000 + $3000 + $1500 = $9500, so moral
depreciation equals $15,000 - $9500 = $5500.

It is also possible to compute the moral depreciation period-by-period. At
time 2, a new machine would have lost a value of $15,000 - $9,000 = $6,000,
but the firm now only has the equivalent of 2/3 of a machine, so it suffers a
loss of value of (2/3)*$6000 = $4000. At time 3, a new machine would have
lost another $9000 - $4500 = $4500, but the firm now only has the equivalent
of 1/3 of a machine, so it suffers a loss of value of (1/3)*$4500 = $1500. At
time 4, the firm has no more machine, so there's no more loss of value.

Note that the sum of moral depreciation by this accounting squares with that
above: $4000 + $1500 = $5500.

Now, assume instead that the machine is replaced by a different model at time
3, and is sold for, say, $2000. Again, between times 1 and 2, it transfers a
value of $5000, and between times 2 and 3, it transfers a value of $3000. But
now, that's the end of it. So $8000 of value is transferred, and the loss due
to moral deprecation is $15,000 - $8000 = $7000, which is the amount the firm
would have lost had it not sold the machine. So its actual loss is $7000 -
$2000 = $5000.

At time 2, the moral depreciation (loss of value) is again $4000, and it is
again $1500 at time 3, up to the moment of sale. That's a total of $5500.
The firm now has the equivalent of 1/3 of a machine, which, if new, would be
worth $4500, so the remaining value of the machine is (1/3)*$4500 = $1500.
But it now sells the machine for $2000, not $1500, and so it gains $500.

Counting this against the losses from moral depreciation, the firm's losses
total $5500 - $500 = $5000, which checks.

It thus seems to me that c could be calculated if one (a) used the above
concepts, (b) assumed straight-line depreciation, and (c) knew the
technological life of the machine, i.e., how long it is physically capable of
operating, at normal intensity.

Andrew Kliman