Duncan (OPE5162) and Andrew(OPE5160),
I know I'm unclear when both of you seek further
clarification. 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
Let's assume that each labor hour is represented by $1.
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
capital.
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%
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. Further, if in
our example we introduced 2 more capitalists each making a $1000
investment, Table II presents a strange situation in which the
average rate of profit falls.
Table II
Rate of
Age of Amount Depreciation Profit Profit(p)
Machine Invested Charge
1 $3000 $600 $150 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 $5000 $1400 $350 7.00%
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 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.
John