[OPE-L:5193] Re: RRI and The Rate of Profit

Duncan K. Foley (dkf2@columbia.edu)
Fri, 6 Jun 1997 05:28:57 -0700 (PDT)

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In reply to John's OPE-L:5168:

>What follows is my attempt to show
>how the rate of profit can fall with a stable RRI,
>with no technical change.
>Rate of Profit and the Rate of Return on Investments
>with Fixed Capital

>Here, as an example, we assume that an investment of
>of $1000 is expected to return 5 annual payments of $250.
>For the sake of simplicity the entire investment in fixed
>Generally, the annual rate of profit, p, is defined as the
>amount of profit divided by the amount invested in a
>particular year. But to evaluate a particular investment
>over its lifetime, one would need to figure the overall
>amount invested by summing the amounts invested in each
>period and summing the profit earned in each year and then
>dividing the latter sum by the former. Note that the
>amount invested in each year is obtained by subtracting
>the depreciation charge in the previous year from the
>amount invested in that year. Using the figures we have
>assumed with straight-line depreciation, we can construct
>Table I.
> Table I
> Rate of
>Year Amount Depreciation Profit Profit(p)
> Invested Charge
> 1 $1000 $200 $50 5%
> 2 $800 $200 $50 6.25%
> 3 $600 $200 $50 8.33%
> 4 $400 $200 $50 12.5%
> 5 $200 $200 $50 25%
>Total $3000 $1000 $250 8.33%

This is why accountants are not too happy with the rate of profit, of
course. Now, in most capitalist firms and in larger aggregates like sectors
or whole economies, we would expect that a lot of these investments would
overlap, so that the rate of profit would tend to approximate better the

>While this manner of looking at returns on individual investments
>may or may not useful, the rate of profit computation becomes
>problematic in evaluating the direction of an overall economy.
>That is, suppose the investments in Table I represented those
>of 5 different capitalists and that "Year" column represented the
>age of each of their machines. To be sure, the average rate of
>profit for the five would be 8.33% but the rate of profit for each
>would increase with the age of the machine.

But this is why the rate of profit on the whole investment of a sizable
company, or on the whole sector or economy is in fact a better estimate of
the profitability of production than the rate of profit on a particular


>Thus, as we move from Table 1 to Table II, we note that the
>rate of profit falls without any technical change whatsoever.
>In other words, using the simple notion of the rate of profit
>the manner in which investments are stratified can generate
>a falling rate of profit.

This is why more sophisticated studies of the rate of profit, like Dumenil
and Levy's or Robert Gordon's, actually keep track of the vintages of
capital, to try to control for these stratification effects. In fact,
however, the stratification effects are not very big, because the
fluctuations in the scale of investment year to year are bounded, and
growth rates are not very high absolutely. So while in principle this could
be a big conceptual problem, it doesn't seem to be so in practice.

>This type of change in the stratification of investments would
>appear as "Marx biased" technical change with a FRP. Yet, here
>all we see is an increasing rate of investment as we move from
>the situation depicted in Table I to that of Table II.
>>From this example, where there is no technical change, it seems
>clear that empirical studies of the FRP should take into account
>the changing in stratification as technical change takes place.

This is surely a possibility, and since capitalist economies typically
grow, it's worth trying to correct for it. As I've said, Dumenil and Levy
do take the trouble to correct for it, and find no basic change in the
pattern of underlying vintage-corrected profitability that results. (To
recapitulate, a falling rate of profit from 1869 to around 1920, with a
falling productivity of capital, a sharp rise in the productivity of
capital from 1920 to 1950, with a fluctuating rate of profit that recovers
in around 1945 to its mid-19th century levels, and a return to a falling
productivity of capital and fluctuating but falling rate of profit from
1950-1990 in the U.S.)

At this point I'm not too sure whether we have any theoretical argument at
all. If the issue is simply how much of the observed fluctuations in the
macroeconomic rate of profit are due to vintage effects and how much to
changes in vintage rates of profit, it's possible to get an answer by
looking at the data, I guess.


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