Andrew here, replying to Allin (ope-l 1089)
He says I should be bothered by his matrix example, because the
"definition" of the value vector v = L{(I-A)**-1} is the correct,
unambigous vector of embodied labor-times.
Come on now! This is precisely what I deny. So I couldn't care less that
the standard interpetation gives different answers from the TSS
interpretation.
In fact, I'm glad that it does. As my posts on the "transformation problem"
and "Torrens vs. Marx" showed, simultaneously determined values (and
prices) are simply incompatible with the determination of value by labor-
time. WHEN ONE STIPULATES THAT A COMMODITY'S VALUE (PRICE) CANNOT CHANGE
BETWEEN TWO DIFFERENT TIMES, NO MATTER HOW MUCH THE LABOR-TIME NEEDED
FOR ITS PRODUCTION HAS CHANGED, THEN ONE HAS STIPULATED THAT LABOR-TIME
IS IRRELEVANT TO THE DETERMINATION OF ITS VALUE (PRICE).
It surprises me that the simultaneists don't seem much bothered by this.
But no one has refuted it, because it is true. In the simultaneist
models, the profit rate (both the "value" rate and the "price" rate)
depend only on physical quantities of inputs, outputs, and relative
values (prices). No matter how many sectors there are, if the
physical quantities remain the same, and the relative prices remain the
same, then all changes in labor-time requirements are irrelevant. In
static "production price" models, the relative prices are uniquely
given on the basis of the physical quantities. Hence, my theorem is
proved. Labor time requirements will rise or fall, but will not affect
the relative prices or the profit rate.
Now Allin is not a big fan of production prices, but my theorem is true
for values as well--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!
Rather than me being bothered by the fact that the TSS values aren't
L{(I-A)**-1), I'd suggest that proponents of the latter get a little
bit bothered by the fact that their "values" are wholly incompatible
with the determination of value by labor-time, and thus with Marx's
_Capital_. And this is the case even apart from price/value deviations,
as the above has made clear.
Andrew Kliman