Part I made it on the 2d try. A bunch of junk at the beginning, telling
me it got bounxed back the 1st time, should be ignored. Sorry.
Part I argued that Fred's interpretation of Marx's value theory comes
to the same quantitative conclusions regarding the profit rate, relative
prices (of production), and the *functional* determinants of profitability
as does the "Sraffian" interpretation, even wrt (with respect to) the
irrelevance of tech. change in luxury production on the level of the
profit rate.
Here, in Part II, I will argue that the TSS interpretation comes to
different quantitative conclusions.
Hence, again, in Fred's interpretation, value theory is quantitatively
redundant; but in the TSS interpretation, it is not.
In ope-l 2193, Fred asserts: "ACROSS PERIODS OF PRODUCTION, or over the
entire transformation process, they [Kliman-McGlone], in my opinion,
essentially revert to the Sraffian interpretation of the determination
of constant and variable capital - the init[i]al givens that remain
unchanged across periods of production are the physical quantities of
the means of production and means of subsistence ..."
Well, this first part is easy to take care of. I'll work with a
(very unrealistic) 2-sector example, in which sector 1 produces X1
and sector 2, X2. Sector 1 uses good 2 as physically nondepreciating
fixed capital, and sector 2 uses good 1 as physically nondepreciating
fixed capital. I'll assume workers live on air and that there are
no materials used in production. I'll also assume that each sector's
physical capital stock increases by 100er period, and that each
sector's output increases by 100er period. *Hence, physical
quantities of means of production do NOT remain unchanged.*
In addition to fixed capital, I'll assume that sector 1 uses 7 units
of living labor each period, and that sector 2 uses 1 unit. No
increase in either over time. Hence, labor productivity and the
technical composition of capital increase each period in both sectors.
Fred continues, still wrt Kliman/McGlone: "...constant capital and
variable capital are derived from these given physical quantities and
change from period to period as a result of the transformation from
values into prices of production."
Here, clearly, constant capital will change from period to period, but
will it be because of the transformation or because of the increased
employment of means of production, or both?
Finally, Fred writes: "These results, contrary to Marx's own results,
are essentially the same results as in the Sraffian interpretation ....
I argue that the reason KM's interpretation leads to the same results
as the Sraffian interpretation is that, across periods of production,
they have adopted essentially the Sraffian interpretation of the
method of determination of constant capital, variable capital, the
rate of profit, and price of production - all derived from given
unchanging physical quantities."
Let us see.
Note, BTW, that Fred is making a claim regarding our interpretation,
not a specific example used to illustrate it. So the present example
should serve fine.
Additional assumptions: one unit of labor is always expressed
monetarily as $1. Initial unit prices equal unity in both sectors.
Profit rates are equalized each period. In the initial period,
period 0, each sector's output is 4 units, each sector uses 40 units
of the other's good as fixed capital. (And maybe something else I've
forgotten.)
Now, according to the "Sraffian interpretation," as in Roemer's
extension of the Okishio theorem, the rate of profit is computed on
the basis of a *stationary* price vector. This is also true of Fred's
interpretation--by definition, not due to an argument concerning
equilibrium, expectations, the lack of importance of the profit rate
computed on historical costs, etc. Calling the unit prices p1 and
p2, and the profit rate r, the price of production equations in *every*
period are:
p2*40(1.1)^t * r = p1*4(1.1)^t
p1*40(1.1)^t * r = p2*4(1.1)^t
which can be solved for the (constant) relative price p1/p2 = 1 and
the *constant* profit rate r = 10%. This is the Sraffian profit rate
AND it is what Fred considers to be Marx's profit rate. Notice that
even though extraction of living labor and thus surplus-value stagnates,
while investment in fixed capital goes on and productivity rises, there
is no fall in the profit rate. And notice that value is quantitatively
irrelevant, both for the Sraffians and for Marx as interpreted by Fred.
The same profit rate is computed whether one works with value magnitudes
or not. (Fred's equations *look* nothing like the above, but he
postulates stationary unit prices which, as I showed in Part I, means
that his profit rate MUST be identical in size to the Sraffians.)
Now, how do I write the price of production equations in this case?
Let Kit be the value of the capital employed by sector i in period
t. Also give the prices, etc. time-subcripts. Then the equations are:
Kit*rt = p1t+1*4(1.1)^t
K2t*rt = p2t+1*4(1.1)^t
and the K's are determined by
Kit+1 = Kit + It
where It is the value invested between periods t and t+1. Since
the fixed capital grows by 10 0n each sector each period, we have
I1t = p2t+1*4(1.1)^t, I2t = p1t+1*4(1.1)^t
(remember the *other* sector's output is used as means of production in
"this" sector. If fixed capital is to grow 10 0.000000e+00ach period, and the
initial stock is 40, as assumed, physical investment must be 4(1.1)^t .)
This is not enough information to determine the prices, and because
prices are not assumed to be stationary, the problem *cannot* be
sidestepped by computing relative prices--it won't work. So in comes
Marx's equation for the determination of total price--it equals the
total value of output. Since workers live on air and no material inputs
are used, and the fixed capital doesn't depreciate, total value of output
is the sum of the living labor extracted, 7+1 = 8 units each period.
Hence
p1t+1*4(1.1)^t + p2t+1*4(1.1)^t = 8
(total price = total value. Remember that each labor unit = $1 by
assumption. Note that I'm using pit for input prices of period t, so
pit+1 is the input price of period t+1 = output price of period t.)
Also note that there is need for transformation each and every period.
This is true in period 0, where, given the input prices (1,1), the
value compositions are 40/7 and 40/1 respectively. But the capital
investments are equal (40, 40), so value is redistributed. Sector 1
extracts 7 units of labor but sells its output for 4 units. Sector 2
extracts only 1 unit but sells for 4 units. And the interesting thing
about this example (or maybe not interesting) is that the relative
price remains constant each period, the relative compositions remain
constant, each sector's capital investment is equal to the other's
each period, and the value each sector receives from the sale of its
output remains 4 units each and every period.
What about the profit rate?
Actually, in this example, there's a quick shortcut to computing the
profit rate. The general rate is
rt = (p1t+1*4(1.1)^t + p2t+1*4(1.1)^t)/(K1t + K2t) = 8/(K1t + K2t)
and by adding the two "K" equations together, we get
(K1t+1 + K2t+1) = (K1t + K2t) + (I1t + I2t).
But (I1t + I2t), as we've seen, = p1t+1*4(1.1)^t + p2t+1*4*1.1)^t = 8,
so (K1t+1 + K2t+1) = (K1t + K2t) + 8.
Hence, the value of the capital stock, initially 40 + 40 = 80, grows
as follows: 80, 88, 96, 104, 112 ..., which we can express as
K1t + K2t = 80 + 8*t
so that
rt = 8/(80 + 8*t) = 1/(10 + t).
Hence, this rate of profit is the same as the Sraffian one only in
period 0 (when t = 0), when it equals 10%. By period 10, it has
fallen to 5%, by period 90, down to 1%, and it asymptotically
approaches zero from above. A classic Marx-ian falling rate of profit,
due to rising productivity, a rising composition of capital, stagnation
of surplus-value, the whole 9 yards. The example, again, is surely
not realistic, but it was put together to illustrate the difference
between TSS and Sraffian relations of determination. And this is has
certainly done, I would submit.
This has been, inter alia, an answer to Fred's argument that the TSS
transformation is "incomplete," and needs to continue into subsequent
periods (an argument David Laibman also makes). Whether it is
"complete" in each period is something I'll have to address in a later
post, but certainly in this illustration the transformation needs
to take place again each period, because in each new period, one
sector extracts more surplus-value than the other, though the capitals
advanced are identical. I'd like to know if Fred thinks that there
doesn't need to be a transformation each period--one takes place
even in the stationary price model (the Sraffian one, above), no?
But this is what takes place in our illustrations without technical
change as well. The transformation takes place as long as surplus-values
per unit of capital advanced are unequal--even if input and output prices
happen to be equal.
Yet, even though the transformation in this illustration seems never
to be "complete," there is absolutely NO convergence to a Sraffian
profit rate. There is a systematic and growing divergence. (And that
is because input and output prices are never equal, due to continuous
mechanization.)
Are the value sums derived from physical quantities? Not really. The
specification of physical quantities and unit prices (values) enables
the determination of the value sums (as is true in every interpretation
but Fred's, to my knowledge). But note that the fixed capital requirements
per unit of output remain constant over time in both sectors, but the
value of the capital stock rises faster than the value of output,
which is impossible in the Sraffian--or any other stationary price
model--precisely because of the stationary price assumption.
Stationary prices = redundancy of value
Nonstationary prices = nonredundancy of value
Andrew Kliman