# [OPE-L:3532] productive and unproductive labor

Fred Moseley (fmoseley@laneta.apc.org)
Fri, 25 Oct 1996 22:01:41 -0700 (PDT)

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This is a reply to Simon's (3506). I want to respond to the question of how
prices production are determined with unproductive labor. This is an
interesting and important question that I think no one has really adequately
dealt with yet.

1. First, a brief review of my interpretation of the determination of
prices of production WITHOUT unproductive labor (as in Part 2 of Volume 3 of
Capital).
I assume that the rate of profit (R) is determined prior to the
determination of prices of production by the aggregate analysis of capital
in general; i.e. the rate of profit is equal to the total surplus-value (S)
divided by the total (productive) stock of capital invested (M); i.e. R =
S/M. (I assume for the purpose of simplification that the STOCK of variable
capital = 0. This is very different from the recent discussion about
assuming that the FLOW of variable capital = 0. Since all workers are paid
only after they have worked and most are paid after their product is sold,
the actual stock of variable capital is in fact very small.). The rate of
profit thus determined is then taken as given in the determination of prices
of production, along with the quantities of constant capital and variable
capital. Therefore, prices of production are determined according to the
following equation:

(1) ppd(i) = c(i) + v(i) + R m(i)

where c(i) and v(i) are the flows of constant capital and variable capital
consumed in the given industry and m(i) is the stock of capital invested in
the given industry.

2. Next assume unproductive labor (sales and supervision) employed by
industrial capital (i.e. no specialized merchant capital), who are paid
wages u(i). Assume for simplicity that there are no unproductive costs of
materials, etc. (I would be happy to relax this assumption; it would only
make the math messier). In this case, the rate of profit is still
determined prior to prices of production, but is a somewhat different way:

a. Total profit (P), the numerator in the rate of profit, is now equal to
the difference between the total surplus-value and the total wages of
unproductive labor (U); i.e.

(2) P = S - U

b. Since we have assumed that there is no unproductive capital invested in
materials, etc., the total capital invested, the denominator in the rate of
profit, is still = M.

c. Therefore, the rate of profit (r) with unproductive labor is:

(3) r = P / M = (S - U) / M

I think this is essentially what Paul C. said in (3523), following Gillman.

d. Prices of production are then determined according to the following
equation:

(4) ppd(i) = c(i) + v(i) + u(i) + r m(i)

e. The sum of prices of production determined in this way is still equal to
the predetermined total price of the total commodity product ( = C + V + S).
This can easily be seen as follows (where E stands for summation):

E[ppd(i)] = E[c(i)] + E[v(i)] + E[u(i)] + r E[m(i)]

= C + V + U + r M

= C + V + ( U + P )

= C + V + S

f. It can also be seen from this equation that the costs of unprouctive
labor are paid of a portion of the surplus-value produced by productive labor.

I think I will stop for now and leave for a later post the case of
specialized mechant capital. I look forward to your comments.

Comradely,
Fred