# RE: Addendum, re Marx and historical costs

andrew kliman (Andrew_Kliman@CLASSIC.MSN.COM)
Sun, 8 Feb 98 09:56:22 UT

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From: owner-ope-l@galaxy.csuchico.edu on behalf of aramos@aramos.bo
Sent: Saturday, February 07, 1998 8:44 PM
To: ope-l@galaxy.csuchico.edu
Cc: Multiple recipients of list
Subject: RE: Addendum, re Marx and historical costs

"Advanced capital could be defined alternatively as:

k[t] = v[o]*f[o] + v[1]*f[1] + v[2]*f[2] + ... + v[t]*f[t]"

Only by negating the concept of capital *advanced*, since, as Ale notes, this
"... implies a *retroactive* valuation of the money advanced at the begining
of the circuit."

Ale also calls k[t] "the so-called "replacement cost" valuation of the
advanced capital." In a certain sense, that's true, but that's not what is
usually meant by "replacement cost" valuation. Instead, what is meant is

k(RC)[t] = v[t]*F[t] = v[t]*f[o] + v[t]*f[1] + v[t]*f[2] + ... + v[t]*f[t]

"After some manipulation, I think that this boils down to:

k[t] = (Lo/Xo)Fo + h*{b + b^2 + ... + b^t}

Lo*Fo*(a-1)
h = ------------- = H*(b/a) "
b*Xo*a

I think the denominator of h is Xo*a (no b). If that's true, then so is h =
H*(b/a).

"So, the only difference between both formulas is the term H, not equal to h."
Right. This is the difference between the value of capital advanced when (a)
an increment to the capital stock is "valued" according to the actual amount
of capital advanced for it (based on the input price of the period in which it
is acquired) and (b) it is valued at the output price of the period in which
it is acquired. Again, I know of no one who suggests (b). (However, David
Laibman did use this measure, without endorsing it, in a critique of the TSS
interpretation of Marx's value theory at the last EEA.)

"3. Now then, my question is: Is the "moral depreciation" S[t] the difference:

S[t] = K[t] - k[t]?"

Well, K[t] = (Lo/Xo)Fo + H*{b + b^2 + ... + b^t}, so

K[t] - k[t] = (H - h)*{b + b^2 + ... + b^t} = H*(1-(b/a))*{b + b^2 + ... +
b^t}.

You had originally used S[t] to denote the MD of a single period:

S[t] = F[t]*(v[t] - v[t-1]).

This can be written as S[t] = Lo*Fo*(1 - [a/b])*b^t/Xo, which isn't at all the
same as K[t] - k[t]. But is the *sum* of the S-series the same? The sum of
the S's, from period 0 to period t, is (since we know there's no MD in period
0)

sum S = {Lo*Fo*(1 - [a/b])/Xo}*{b + b^2 + ... + b^t},

so that the ratio

(sum S)/[K[t] - k[t]] = - a/(a-1)

(note the minus sign)

So they're not the same. They're closely related, but the sum of moral
depreciation is much greater. E.g., if a = 1.05, then the ratio is -21. I
don't have an intuitive interpretation of this offhand. It's late. Also,
because it is late, and because I don't have an intuitive interpretation, I
suspect that I may have made an error.

"Is this term what we need to substract from the numerator of the profit rate
in order to obtain a "non-overvaluated" profit rate?"

I'll come to the "overvalued" issue in a moment. *IF* all capital losses are
written down each period, then one subtracts S[t] = F[t]*(v[t] - v[t-1]), as
you did originally.

"This definition of advanced capital implies that "moral depreciation" is NOT
taken into account. In other words, capitalists never
"revaluate" their assets, "writing down" their losses. As their assets are
"over-valuated" the profit rate seems lower than the profit
rate they would calculated after acknowdledging the destruction of
value-capital provoked by the technical change."

I have difficulty with this interpretation. What you are calling the
overvalued profit rate is, I think, the actual historical tendency of the
self-expansion of capital. As I said, I'm willing to be persuaded instead
that the profit rate with revalued capital AND losses deducted from profit is
the tendency. But I don't see it. The problem is that the latter has a
continually changing starting point from which to measure self-expansion. In
each period, you get the rate of self-expansion of that one period, but you
wipe out the past.

Look at it in terms of a particular investment undertaken at time 0 (for
instance). The internal rate of return formula, which is widely used in the
real world, equates the additional capital advanced at time 0 with the entire
stream of discounted returns it generates throughout its "lifetime." It has a
fixed starting point, and measures each return in relation to that.

Before you came onto the list, I think, I was able to prove that, at least
under the conditions of the present examples (whether b = 1 or not, whether a
= 2 or not), the profit rate of my paper in M&NE is the weighted average of
the IRR's of the investments of different periods.

"Are you agree with my formulation of "moral depreciation" in the
preceding post?"

If you mean "Moral depreciation in period t is given by the amount of existing
fixed capital AND the difference between *output* prices and *input* prices of
this period:

S[t] = F[t]*(v[t] - v[t-1])

[...]

"Net profit is obtained as the sum of gross profit (Lo) and moral depreciation
S[t]:

NP[t] = Lo + S[t]"