A reply to Simon's ope-l 3506, which I found very interesting.
Simon: "Consider the l vector in the standard value equations. This refers to
'value-creating labour-power hired'."
I don't think this is the case. In Marx's theory, labor-power does not
produce value. Labor does. IMO, the l vector indicates the amounts of
productive (value-creating) *labor* extracted per unit of output. We have, in
money terms, elx = V + S, where e (dimensions: money unit/labor-time)
indicates the monetary expression of value. V is the money wage bill paid to
workers who perform productive labor: V = w(lpp)x, where w is the money wage
per-unit of labor-power (assume it is scalar for simplicity), and lpp is a
vector (for simplicity) of productive labor-power hired per unit of output.
Note that lpp can only be known ex post. It is not purely a labor market
relation *or* a technological relation. It depends on the amounts of
labor-power hired and the amounts of outputs produced. There is no necessary
relation between these amounts. The relation depends on the degree of
exploitation in production.
Simon: "Now the l vector in the price of production equations refers to hours
of
labour worked, which when multiplied by the wage gives the wage cost of
production. On the face of it, this is not the same l vector."
I agree that there is a confusion often involved here. It stems from the
non-Marxist origin of these equations --- labor and labor-power are conflated.
But there's a way around this. I agree with Simon's understanding of the l
vector in the POP equations, which I however think is actually the same l
vector as in the value equations, labor-hours per unit of output. What is
different is that the the WAGE RATE here is not the same wage rate as w,
above. The wage rate in the POP equations is not a wage per unit of
labor-power hired, but a wage per unit of *labor* extracted.
This follows from the interpretation that Simon and I agree on concerning "l"
in the POP equations. The wage bill is pblx; pb does not equal w. The
dimensions are different. Since lx is an amount of labor-time, and pblx is a
money sum, pb is the money wage per unit of labor-time extracted, not
labor-power hired (b is the product wage per unit of labor-time extracted).
So pb and b are very misleading, because they fail to accord with the
institutional fact that firms pay wages to hire labor-power, not labor. There
is no mathematical inconsistency created, however, because one can convert
between w and pb if one knows the degree of exploitation in production,
l/(lpp), which is basically the same as Lipietz's "tensor." Assume it is
scalar for simplicity. So we have w = pb[l/(lpp)], and V = w(lpp)x =
pb[l/(lpp)](lpp)x = pblx.
The math is a bit more complex if wage rates, tensors, etc., aren't uniform,
but it does work out.
I think the other issue Simon raises is essentially distinct from that above:
"Now suppose some labour is unproductive.
"... in the price of production equations the labour cost to the firm must
presumably be both the cost of productive and the cost of unproductive labour,
such labours being undifferentiated in cost terms to the firm. How then do we
understand prices of production in firms which employ both productive and
unproductive labour? As transformed value? But if unproductive labour costs
are omitted, such a definition bears no relation to long run supply price, or
to a centre of gravity around which market prices fluctuate, or to a lower
level of abstraction as theory attempts to comprehend the world.
"And what of firms which are wholly unproductive of value, such as commercial
and financial capitals, which do not expand value themselves but whose
operations are essential to valorize value in an M-C-M' circuit? What of their
prices?"
I agree that "labor" costs --- strictly, labor-*power* costs --- are
undifferentiated to the firms and that the wages both of workers who do
productive labor and those who do unproductive labor are indeed costs. In Ch.
13 of Vol. I, Marx clearly refers to the wages of supervisors, managers,
foremen, etc. as part of the _faux frais de production_, hence an element of
cost. (Of course, some managers also do productive labor when they aren't
bossing the workers, just as someone working at McDonald's may work the cash
register but also apply pickle slices to the burgers, but that just means that
in both cases they do two different kinds of work, one unproductive, the other
productive.) He indeed criticizes the economists for considering the cost of
supervisory labor as _faux frais_ under slavery only, and not also under
capitalism. And in Vol. II, when dealing with circulation labor, he likewise
indicates that the cost is part of the _faux frais_.
Now often Marx implicitly distinguishes constant capital from _faux frais_,
but if one is dealing with three categories only, C, V, and S, then _faux
frais_ are part of C. In other words, they are indeed costs of production,
but not part of V. Not even _faux frais_ paid in the form of wages are part
of V, because they are not used to purchase labor-power that performs
*productive* labor. Indeed, the _faux frais_ function in value terms just
like the rest of C. Capital is advanced for them, they are in the denominator
of the profit rate, their value is transferred to the value of the product.
All this is because they are indeed *costs* of production, as the term the
_faux frais de production_ indicates.
The problems to which Simon refers seem to arise if the cost of hiring workers
who do unproductive labor is not considered as a cost of production. As I've
noted, I think Marx clearly did consider it a cost of production, so the
problem doesn't arise.
Some people seem to think that the above contradicts the concept that the
profits of firms engaged in unproductive activity are purely a redistribution
of surplus-value. It does not. To see this clearly, assume a two-sector
economy without fixed capital. One sector produces cars, the other sells
them. Assume the car sector lays out 15 for materials, 5 for bosses, and 10
for workers who do productive labor. Assume the add a value of 20. Assume
the sales sector lays out 10 for materials (cars of last period), 3 for
bosses, and 7 for sales workers. Call M, B, and SW the expenditures on
materials, bosses, and sales workers, respectively. Assume for simplicity an
equalized rate of profit:
C
========== V S value price profit
M B SW
cars 15 5 0 10 10 40 36 6
sales 10 3 7 0 0 20 24 4
25 8 7 10 10 60 60 10
The uniform rate of profit is 20%. The sales sector produces no
surplus-value, but gets a 200rofit rate because a value of 4 is transferred
to it from the car sector. This lowers the profit rate of the car sector from
10/30 = 33% to 6/30 = 20%. Note that total price equals total value, that
total profit equals total surplus-value, and that the aggregate "value" rate
of profit, S/(C+V) equals the aggregate "price" rate of profit, profit/(C+V).
Note also that no value is created in the sales sector. The existing values
of 10+3+7 are *preserved* by means of the sales (production) process.
I'm not sure whether or not this would work out were determination of input
and output prices simultaneous.
Andrew Kliman