# [OPE-L:5218] RE: Luxury goods and profit rate

Duncan K. Foley (dkf2@columbia.edu)
Sun, 8 Jun 1997 16:17:47 -0700 (PDT)

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In response to Andrew's OPE-L:5213:

First of all, let me clarify my treatment of the equalization of the profit
rate (this material appears in _Understanding Capital_ and also in my 1982
RRPE paper).

Taking A as the matrix of input-output coefficients, and l as the vector of
labor inputs, P as the vector of prices, r as the profit rate, and w as the
scalar wage rate, the equalization of the rate of profit conditions are:

P = (1+r)(PA + wl)

I took the value of labor power, w*, as given, and defined it as wm where m
is the reciprocal of the MELT, in my definition, then we have, writing X
for the vector of gross output, so that (I-A)X is the vector of net
product, lX the total living labor, and P(I-A)X the value added:

w = w* (P(I-A)X)/lX

This equation determines w, and it is clear that changing w will change the
profit rate. Since the vector X includes both wage and luxury goods, in
general the surplus value exploited in the luxury sector will influence the
rate of profit, as Marx says.

>
>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."

>(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.
>

In the method outlined above, the luxury sector enters into the
determination of the rate of profit through the definition of the MELT,
which in turn is part of the definition of the value of labor-power in this
approach.

..
Andrew continues:
..

>
>(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.

The derivation above accounts for the surplus value produced in the luxury
sector to be redistributed by the equalization of the rate of profit.

>
>
>(3) How one defines the value of labor-power is totally irrelevant to the
>issue at hand.

I don't agree with this. If you define the value of labor-power (a la
Bortkiewicz, Seton, Morishima, Roemer) as the labor embodied in a fixed
bundle of workers' consumption, then, as Andrew's example shows, the profit
rate is determined only by "basic sectors", and not by the luxury sector.

Andrew continues:

>
>(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.
>
But this amounts to assuming the workers' consumption bundle as fixed,
which is precisely what I argued against in putting forward the definitions
of the value of labor power and the value of money (or the monetary
expression of labor time) in _Understanding Capital_.

Duncan

Duncan K. Foley
Department of Economics
Barnard College
New York, NY 10027
(212)-854-3790
fax: (212)-854-8947
e-mail: dkf2@columbia.edu