SIMULTANEOUS VALUATION INCOMPATIBLE WITH LTV ??
This is a continuation of my response to Andrew on the issue of the
determination of constant capital.
Andrew has argued in a number of recent posts that the simultaneous
valuation of the values (or prices) of inputs is incompatible with the labor
theory of value. The main argument seems to be the following:
1. The simultaneous determination of the values of inputs and outputs
implies that values are determined by the following equation:
(1) v = vA + L
2. A PORPORTIONAL increase in the labor required to produce all commodities
will leave their relative values, as determined by equation (1), unchanged,
and also the value rate of profit unchanged. Therefore, labor-times are
irrelevant to the determination of relative values and the rate of profit.
For example, Andrew argued in (1092):
The "value rate of profit" of the simultaneists is uniquely determined by
physical quantities and relative values (this is likewise true of each
sector's profit rate). Now imagine the vector of unit living labor
coefficients changes from L to kL, where k is a scalar. Then the vector
of unit values will change from
V = L{(I-A)**-1)
to kL{(I-A)**-1) = kV
and all reltive values will remain the same. Hence, no matter how much
L changes, if the physical outlays and outputs remain the same, and
each L changes proportionately, each and every profit rate will remain
the same!
My brief response to this argument is as follows: Even if one accepts
equation (1) - which I do not, but that is a separate issue to which I will
return below - the "irrelevance" of labor-times in this framework is true
only for the special case of a PROPORTIONAL increase in all labor-time
requirements, and is true only for relative values and not necessarily for
the rate of profit.
The rate of profit does not appear in this equation, so it is not clear from
Andrew's argument what will be the effect on the rate of profit. The effect
would seem to depend on the extent to which there is an increase in the
total labor time proportional to the increase in labor-time requirements,
which Andrew does not specify. If there is a proportional increase in the
total labor-time, then there would be a proportional increase in
surplus-labor-time and thus in surplus-value, and the rate of profit would
remain unchanged. However, if there is a less than proportional increase in
the total labor, then the rate of profit will decline. In the extreme, if
there is no increase in the total labor-time, then both the amount of
surplus-value and the rate of profit will fall. In both these latter two
cases, this change in labor-time requirements would have an effect on the
rate of profit, contrary to Andrew's argument.
Furthermore, if the changes in the labor-time requirements are not
proportional (which is the more general case), then changes in labor-time
requirements will change both the relative values and the rate of profit.
Therefore, Andrew's argument, as summarized above, is extremely limited. It
applies at most only to the special case of an effect of a proportional
increase on the relative values of commodities. It is not valid to infer
from this special case argument the general conclusion that labor-times can
have no effect on the relative values of commodities or the rate of profit
in this framwork. The limitations of Andrew's argument seem so obvious,
that I fear I have missed something. If so,
I am sure Andrew will let me know.
I wonder: according to Andrew's interpretation of the determination of
values, would a proportional increase in labor-time requirements change the
relative values of commodities? Please explain how.
Let me add a few words about my own interpretation and the extent to which
Andrew's argument applies to it. I have argued in recent works that Volume
1 of Capital is not about the determination of individual values, as in
equation (1) above, but is rather about the determination of the aggregate
price of commodities and the aggregate amount of surplus-value. According
to this interpretation, the aggregate price of commodities (P) and the
aggregate amount of surplus-value (S) are determined according to the
following equations:
(2) P = C + mL
(3) S = m(L - Ln)
where C is the aggregate flow of constant capital, m is the
money-value-added per labor-hour, L is the aggregate current labor, and Ln
is the aggregate necessary labor. I argue that C is taken as given as the
current reproduction costs of the means of production; i.e. that C is
determined at the same time as the aggregate price of commodities, but is
logically prior to the latter. Now, according to this interpretation, an
increase in the labor-time requirements will increase Ln and may or may not
increase L (again, it is not clear to me what Andrew is assuming about L).
If L does not increase, then the amount of surplus-value, and hence the rate
of profit, will decline. If L increase less than proportionally to Ln, then
the rate of surplus-value and the rate of profit will still decline. In
these cases, a change in labor-time requirements has an effect on the rate
of profit, even though it is assumed that C is determined at the same time
as P.
Finally, according to my interpretation, prices of production are determined
according to the following formula:
(4) Pi = Ci + Vi + r Mi
where Ci and Vi are the individual industry flows of constant capital and
variable capital, Mi is the individual industry stock of constant capital,
and r is the general rate of profit as determined by the aggregate analysis
of Volume 1. According to this interpretation, a non-proportional increase
in labor-time requirements will change relative prices because it will
change one or more (and maybe all) of the variables on the right-hand side
of equation (4) in non-proportional ways. Even in the case of a
proportional increase in labor-time requirements, the rate of profit will
change in all cases except a proportional increase in the total current
labor-time, and thus relative prices will change to the extent that [ rMi /
(Ci + Vi) ] differs from commodity to commodity.
Therefore, as these counter-examples show, the simultaneous determination of
constant capital and the price of output is not incompatible with the labor
theory of value, contrary to Andrew's argument.
Looking forward to further discussion.
Fred