[OPE-L:4398] Depreciation and the Rate of Profit

Duncan K. Fole (dkf2@columbia.edu)
Sun, 16 Mar 1997 20:36:47 -0800 (PST)

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I've been meaning to try to address some of John Ernst's posts for a while now.

The way I think about the problem of the rate of profit is basically the
same as Allin's. Ex post, after all the costs connected with an investment
have been paid and all the revenues collected (perhaps by selling the
"scrap" to Costa Rican capitalists or whatever), you can calculate an
internal rate of return that equates the present discounted value of the
net revenues to the present discounted value of the costs of the
investment, which is an unambiguous measure of the profitability of the
investment. Notice that because this measure is ex post, it does not
require any separate accounting for "depreciation". Furthermore, you can
retrospectively give an unambiguous value to the investment at any
intermediate point in time by using this ex post rate of return to discount
the remaining costs and revenues. This ex post IRR will automatically
account for all types of gains and losses during the period of the
investment due to whatever causes: natural catastrophes like fire and
flood, or economic catastrophes like price changes due to technical change
or shifts in monopoly power.

The concept of "depreciation" is an _accounting_ concept that arises in an
attempt to estimate the profitability of investments that haven't yet run
their course. Since "depreciation" is a concept involving time, it arises
whatever price system one is using to value inputs and outputs in
production, embodied labor coefficients, or prices of production, or market
prices. As such, it seems to me that the same problems arise whether we are
approaching the accounting problem from the point of view of Marxist theory
or neoclassical theory or plain old accounting. The difficulty, from the
capitalist's point of view, is that he or she doesn't know the true
profitability of the investment (in any price system, or using any
particular numeraire), because it depends in part on flows of revenues and
costs in the unknown future. The accountant's practical and necessarily
imperfect method for addressing this problem is to estimate the residual
value of the investment by some kind of rule-of-thumb or formula, such as
the straight-line average over an estimated lifetime. Given this inevitably
arbitrary estimate, an equally arbitrary estimate of the rate of profit can
be made. This whole issue becomes even more tangled in countries like the
U.S. where "profits" are taxed, so that the method of "depreciation"
becomes a matter of considerable significance to after-tax profits.

Three observations on some of the discussion on the list:

1: In some cases people are trying to put forward a theory of the prices at
which capitalists will sell particular commodities based on the notion that
competition will equalize the rate of profit across sectors. It seems to me
that the most competition can do is to establish prices that equalize the
_anticipated_ rate of profit across sectors, not the ex post _realized_
internal rate of return across sectors. The anticipated changes in the
values of the stocks that arise in the course of the investment
(depreciation) are an important factor in these anticipations, but there
are others as well, such as the anticipated price of output, or changes in
the value of whatever asset one is using as the numeraire. It would help if
this discussion were framed in terms of a complete model specifying all
these factors, rather than as fragmentary arithmetical examples that leave
a lot of the bounday conditions unspecified.

2: It's doubtful to me that the long-run reproductive health of the
capitalist system has much to do with the inherent ambiguity of any
particular accounting system of depreciation. Thus I tend to question
whether issues like the tendency of the rate of profit to fall turn
fundamentally on depreciation issues. I agree with John that it is
desirable to define what we mean by the rate of profit before we discuss
its tendency to rise or fall. But on the whole the Marxist literature does
define this pretty clearly as the ratio of the current flow of gross
profits to the reproduction cost of the capital stock. This is not the same
thing as the anticipated rate of profit, which is important to remember,
but most of the literature on the rate of profit is trying merely to get
the ex post historical record straight, on the assumption that this measure
of the rate of profit is not very far off the ex post internal rate of
return. Dumenil and Levy, for example, take the trouble to calculate the
IRR by keeping track of the "vintages" (which John calls "stratification")
of the capital stock, and find that its deviation from the simple ratio of
gross profit to reproduction cost of the capital stock is relatively small.

3: The circuit of capital model is a framework in which these issues can be
addressed explicitly and rigorously. The general idea (though by no means
all of the possible models) are worked out in my JET 1982 paper and Money,
Accumulation, and Crisis, 1986 (the latter still in print from Gordon and
Breach, though I'm afraid at an excessively high price!)


Duncan K. Foley
Department of Economics
Barnard College
New York, NY 10027
fax: (212)-854-8947
e-mail: dkf2@columbia.edu