[OPE-L:5213] RE: Luxury goods and profit rate

andrew kliman (Andrew_Kliman@msn.com)
Sun, 8 Jun 1997 09:38:32 -0700 (PDT)

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A reply to Duncan's ope-l 5208.

Duncan has argued that, even though the New Interpretation (NI) is
simultaneist, i.e., it revalues inputs at their replacement costs (output
prices), it nevertheless replicates Marx's result that the conditions
prevailing in luxury production do have an influence on the general rate of
profit, against the contrary claims of Ricardo and of Bortkiewicz and the
simultaneist tradition. Duncan at first argued that the NI definition of the
monetary expression of labor-time (MELT) is what produces the (allegedly)
variant results:

"Actually, this is one point where the New Interpretation differs from
Bortkiewicz. Since we define the monetary expression of labor
time in terms of the value added in the whole mass of commodities, that
includes luxury goods."

In my ope-l 5179, I showed that this was not the case. Using a 3-dept.
equation system, I showed that "the definition of the MELT has no effect on
the profit rate ... production conditions in luxury sectors continue to be
irrelevant to the determination of the profit rate, as long as input and
output prices are constrained to be equal, as the replacement cost
interpretation requires."

Duncan has now replied that "you've departed from the New Interpretation
definitions, because you've incorporated the wage goods into the input-output
matrix, thus implicitly accepting the definition of the value of labor-power
as the labor embodied in the commodities the workers consume. But the New
Interpretation defines the value of labor power as the wage divided by the
value added (including luxury goods) at market prices. The independence of the
profit rate from the luxury sector is a consequence of holding the workers'
consumption constant, not of the replacement cost interpretation."

Some comments in response:

(1) This has nothing to do with the MELT. The NI "value of labor power" is
dimensionless, and its magnitude is invariant with respect to the MELT. Thus,
it seems that Duncan has here implicitly acknowledged that the definition of
the MELT has no effect on whether luxury production influences the general
profit rate. Since others read these posts, and since it seems that the
simultaneist ranks treat what I have to say with skepticism, it might be good
if this were acknowledged explicitly. Then we might have actually established
something, learned something, by means of discussion.

(2) The reason that Marx disagreed with Ricardo's claim that luxuries have no
effect on the general profit rate had nothing to do with whether workers'
consumption bundles are fixed. Marx's argument is rather that the total
surplus-value produced throughout the economy is redistributed (ideally and,
tendentially, in reality) in proportion to capital-value advanced. Even if
Duncan's new claim were correct, therefore, the NI still wouldn't be able to
employ Marx's assumptions to obtain his results. Although I agree of course
that workers' consumption bundles are not fixed, such an assumption is -- in
*this* context -- a piece of ad hocery.

(3) How one defines the value of labor-power is totally irrelevant to the
issue at hand. First, because it is irrelevant whether workers are paid the
full value of their labor-power or more or less. To replicate Marx's result,
one must do so in the general case, not just in a special case. Second,
because the denominator of the NI value of labor-power (money "value added")
is irrelevant to the issue at hand. The numerator -- the wage -- is what is
part of capital advanced, and thus it is the wage that enters into the price
and profit-rate equations.

And, most important:

(4) Although my prior example did indeed assume fixed workers' consumption
bundles, it is not the case that my result *depends* on that assumption. I
will show this by demonstrating the independence of the profit rate from
luxury production in the general case.

The equal-profit-rate, simultaneist, price equation for the jth sector is:

[1] Pj = (PAj + wj)(1+r)

where wj, a scalar, is money wages paid by sector j per unit of output j.

Now, partition the economy into basic sectors 1, ... m, and luxury sectors n1,
n2, .... Workers consume none of the products of the latter sectors, only
some or all of the products of sectors 1 through m. The aggregate budget
constraint of the workers in sector j can thus be written as

[2] wj = P1*b1j + P2*b2j + ... + Pm*bmj

where bij is the total amount of good i consumed by workers of sector j, per
unit of output j.

Therefore, combining [1] and [2], we get

[3] Pj = (PAj + PBj)(1+r),

Now, examine the subsystem of [3] comprised of the equations for the basic
sectors, 1 through m. The sources of all the elements in the Aj and Bj are
sectors 1 through m and, because of this, only the prices P1 through Pm are
relevant. Without specification of the Bj, of course, the subsystem is
underdetermined (I count m equations, and m + m^2 unknowns -- m-1 relative
prices, 1 profit rate, and m x m workers' consumption coefficients). But the
subsystem is self-contained in the sense that it is wholly independent of
conditions in sectors L1, L2 ....

Now, what determines the Bj? Obviously, given the prices P1, ..., Pm (the
luxury prices are irrelevant), the the budget, wj, they are determined by the
workers' demand functions, based on their utility functions or whatever. So
with this additional information -- which has nothing to do with production
conditions in luxuries -- the Bj are determined, m^2 unknowns in the basic
subsystem are eliminated, and we are left with a fully determinate system of m
equations in m unknowns. The profit rate is determined in the usual
simultaneist manner, purely within the basic subsystem. Prices of luxury
goods must adjust upwards or downwards so that they yield the firms that
produce them this profit rate determined independently of luxury production.

Hence, the "independence of the profit rate from the luxury sector is" NOT "a
consequence of holding the workers' consumption constant." It IS a
consequence of the replacement cost interpretation. Neither of the two
respects in which the NI differs from the standard simultaneist interpretation
(invariance postulate, definition of wage) has any bearing on whether luxury
sectors influence the general profit rate. What matters is only whether input
prices are forced to equal output prices (via the "replacement cost"
interpretation, etc.).

An adequate interpretation must be able to replicate Marx's results -- if they
are indeed replicable. The TSS interpretation has shown, in this case and in
many others, that his results are replicable. The replication of Marx's
result, in this case and in many others, requires that input and output prices
be allowed to differ. Therefore an adequate interpretation, in this case and
in many others, requires that input and output prices be allowed to differ.

Andrew Kliman