# [OPE-L:5750] rri and profit rate

David Laibman (DLaibman@brooklyn.cuny.edu)
Mon, 24 Nov 97 15:48:00 EST

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I have not been able to follow all aspects of the discussion between John and
Duncan on this topic, and have not kept copies of all of their posts. Are
the following observations relevant?

The rate of return on investment is essentially the internal rate of
return to a specific purchase of capital goods, computed by discounting the
(finite or infinite) stream of future returns and equating the sum of such
discounted returns to the cost of the capital goods. As we all learned in
school, this is formulated as
K = P1/(1+r) + P2/(1+r)^2 + . . . + Pn/(1+r)^n (for the finite case)
Now I think a close association with the accounting rate of profit can
be shown. First, since this is based on an estimate of the stream of returns
to a given investment (up to an anticipated moment of scrapping), the various
Pi fluctuate around an expected center, P, which is then the best (unbiased)
estimate of Pi in each period. In other words, random movements provide no
reason not to use the expected P as the best estimate of profit in each
future period; this is the best capitalists can do. With P1 = P2 = . . .
Pn = P, the present value formula becomes
K = P[1/(1+r) + 1/(1+r)^2 + . . . + 1/(1+r)^n],
which (ignoring a small residual term) collapses to
K = P/r,
setting the cost of capital equal to the capitalized stream of (constant
expected) returns, and implying
r = P/K
(which, of course, is our old accounting-Marxian friend).
I'm sure that situations can arise in which the rri and r move in
opposite directions, and I entirely share Duncan's (and John's) interest in
such cases. But for most purposes, I wonder if too much isn't being made of
this. Capitalists estimate expected profits by using rK (two current, or
immediate past, numbers which they do indeed know). Since these expected
profits Pi determine the rri, r and rri are bound to move closely together in
most cases.
I can't offer any suggestions concerning depreciation. I have been
working with "pure fixed capital" models too long!

Best,

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David Laibman dlaibman@brooklyn.cuny.edu

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