# [OPE-L:4795] RE: max and actual profit rate

andrew kliman (Andrew_Kliman@msn.com)
Tue, 15 Apr 1997 15:10:25 -0700 (PDT)

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A reply to another aspect of David's ope-l 4768.

David: "as I explained in detail in my paper ... in the conditions assumed,
it is simply not true that L/C falls, let along falls to 0.
For a circulating capital case with L constant and material-input-to-labor
ratio and output-to-labor ratio rising at the same rate,
L/C = (Y - A)/A, or the ratio of net output to material input, and is
constant."

Yes, you "explained" this, i.e., asserted it. And it will be true given
certain theoretical premises, such as

(a) value is not determined by labor-time, but, instead, an hour of labor
creates value in proportion to its use-value productivity (Roberts, Foley), or

(b) a commodity has two different values (prices) at the same place and time,
one as the output of one period, and another as the input of the next period
(traditional simultaneist "labor theory of value").

But it is not true according to Marx's value theory, as understood by the TSS
interpretation.

Let us examine the following case: call the corn input of period t,t+1 A[t],
and the corn output of the *same* period Y[t+1]. Assume that A[t] =
4*(1.25)^t and Y[t+1] = 4*(1.25)^(t+1), so that Y[t] = 4*(1.25)^t = A[t]. In
other words, all corn output emerging at time t is immediately reinvested as
corn input.

Let living labor, L[t] = 5, a constant.

Thus we have "a circulating capital case with L constant and
material-input-to-labor ratio and output-to-labor ratio rising at the same
rate."

Now, letting V[t] be the unit value at time t, C[t] = V[t]*A[t], and L/C =
L[t]/(V[t]*A[t]).

My equation for value determination in my paper in _Marx and Non-equilibrium
Economics_ -- as rewritten by David in his EEA paper -- is

V[t+1]Y[t+1] = V[t]*A[t] + L[t] (1)

(except that I there used Q instead of Y and N instead of L, which doesn't
affect anything, of course.)

In this case, (1) can be rewritten as

V[t+1] = (V[t]*4(1.25)^t + 5)/(4(1.25)^(t+1)) = 0.8*V[t] + (0.8)^t

So that

V[t] = V[0]*(0.8)^t + 1.25*t*(0.8)^t

and thus

C[t] = V[t]*A[t] = 4*V[0] + 5*t

so that

L/C = L[t]/(V[t]*A[t]) = 5/(4*V[0] + 5*t)

and, since everything on the RHS is constant except t, L/C always declines,
and it approaches 0 as t approaches infinity.

Assuming that V[0] = V[1] = 5, the aggregate value figures are

t C L C+L L/C (%)
0 20 5 25 25.0
1 25 5 30 20.0
2 30 5 35 16.7
3 35 5 40 14.3
4 40 5 45 12.5
5 45 5 50 11.1
6 50 5 55 10.0

etc.

Now, even though the above figures seem to be "derived" from the use-value
figures, that really is not the case. Since, in this example, all of the corn
output of one period becomes the corn input of the next, the total value of
one period becomes the constant capital of the next. So, using W[t+1] to
indicate the total value produced during period t,t+1, C[t] = W[t] and the
equation of value determination is

W[t+1] = C[t] + L[t]

or

W[t+1] = W[t] + 5

so that

W[t] = C[t] = W[0] + 5*t.

Setting C[0] = 20, we get the same exact results as before, WITHOUT even
appearing to derive the value magnitudes from the use-value magnitudes.

Of course, in this example, the material rate of profit, (Y - A)/A, is

(Y[t+1] - A[t])/A[t] = (5*(1.25)^t - 4*(1.25)^t)/(4*(1.25)^t) = 25.0%, a
constant.

Andrew Kliman (AX)