Addendum, re Marx and historical costs

andrew kliman (Andrew_Kliman@CLASSIC.MSN.COM)
Tue, 3 Feb 98 16:55:44 UT

Rereading my reply to Fred of Sunday, February 01, 1998 7:55 PM, I noticed a
potential source of confusion. In the post, I wrote:

" (Had either the money price or the relation between money and labor-time
changed during Dec. 1997, then the Jan. 1 figures, not the figures at time of
acquisition (Dec. 1997), should really be used to assess the capital advanced.
But in practice, firms don't always do this.)"

The possible source of confusion is that, in my "A Value-Theoretic Critique of
the Okishio Theorem" in _Marx and Non-equilibrium economics," I introduce the
assumption that firms *don't* do this. "The discussion below is confined to
an investigation of the *tendency* of the rate of profit -- that is, to the
historical movement of the rate of profit considered in abstraction from the
forms in which it appears. It will thus be assumed that ... existing capital
is 'kept on the books' at its historical value" (p. 213).

How do things change if we assume that, in *every* period, firms *do* revalue
the capital advanced? Two things happen. First, the denominator of the
profit rate is the value of capital advanced according to start-of-period
prices (e.g., Jan. 1, 1998 instead of Dec. 1997). But, second, if the value
of assets has (for instance) fallen during 1997, they must charge the "write
down" of their assets against profit. This is Marx's "moral depreciation."

Thus, the capital advanced in 1998 is lower than I had assumed, but the profit
of 1997 is likewise lower.

Let me illustrate this with a simple unrealistic example. I assume no
circulating constant capital, zero wages, and I assume that the (homogeneous)
fixed capital doesn't depreciate *physically*. I assume also that $1 = 1
labor-hour, so all value figures are the same in money and labor-time terms.
The stock of fixed capital doubles from period to period, that the ratio of
fixed capital to (homogeneous) output is constant, and that the amount of
living labor (= surplus-value, by virtue of the zero wage assumption) is
constant from period to period.

Thus, we may have, in physical terms:

Period Living Labor Fixed Cap. Output
====== ============ ========== ======
0 8 1 1
1 8 2 2
2 8 4 4
3 8 8 8

Now, as I interpret Marx, the unit *output* value of each period is the ratio
of living labor to output of this period. Hence:

Period Unit Output Value
====== =================
0 8
1 4
2 2
3 1

I will, in addition, assume an initial static equilibrium, so that the unit
*input* value of period 0 is 8.

Assuming that losses are written down each and every period, the capital
advanced in a period is the physical capital stock times its unit value at the
start of the period (which is, of course, the same as the unit output value at
the end of the prior period):

Period Cap. Advanced
====== =============
0 8
1 8
2 8
3 8

We also know that surplus-value, equal to (the monetary expression of living
labor) is a constant amount, also 8. However, the rate of profit is NOT a
constant 8/8 = 100%, because, if capital is being devalued, losses must be
charged against profits. The capital loss (moral depreciation) in each period
is the change in the value of the physical capital stock between the beginning
and end of the period. Thus:

Period Cap. Loss
====== =========
0 0
1 -8
2 -8
3 -8

So, charging these losses against profit from production (i.e.,
surplus-value), we have, in the denominator of the profit rate:

Period Profit
====== ======
0 8
1 0
2 0
3 0

Hence, the profit rate is 100% in period 0, but it falls to 0% (and remains
there) thereafter.

Given the assumption in my chapter in M&NE, surplus-value and profit would be
computed as a constant 8. The value of capital advanced would grow as
follows: 8, 16, 24, 32, .... (all output becomes new fixed capital, fixed
capital doesn't depreciate physically, and the total value of output is 8 in
every period. So the value of capital, abstracting from write downs,
increases by 8 in every period. So again, the initial profit rate would be
100%, and again, it would fall to zero. But it would do so gradually instead
of suddenly.

I think of the latter measure as expressive of the tendency of the profit
rate, but I'm willing to be persuaded that the former is.

The end-of-period "replacement cost" profit rate is, of course, a constant
100%. There's nothing "wrong" with this measure, but note that it doesn't
measure the self-expansion of value. Another way of putting the same point is
that it devalues capital but ignores the moral depreciation. So you get the
bizarre result that all output is being re-invested, and the "profit rate" is
100%, but capital isn't accumulating at all in value terms -- the capital
advanced is a constant 8.

Andrew Kliman