This is a reply to Duncan's very helpful (3287), which clarified his
critique of Andrew's concept of value added. I think I understand Duncan's
critique better now. But I still think that he misinterprets Andrew. The
following is offered in "further search of clarity".
1. I understand that the main point of Duncan's critique is that the time
paths of prices and the rate of profit derived by Andrew depends on his
definition of value added which includes an inventory valuation adjustment.
2. It seems to me that the key issues here are:
exactly how is the price path derived by Andrew?
and exactly how is value added determined by Andrew?
There are two possible sets of answers to these questions:
A. What I think are Andrew's answers:
prices are determined by the equation: p(t)X(t) = p(t-1)aX(t) + VA(t)
where ap(t-1) is taken as given as the historical costs of inputs
and VA is taken as given as determined by current labor
as already stated, value added is determined by current labor.
B. A second possible set of answers, which at times seems to be the way
Duncan interprets Andrew:
prices are taken as given, as the actual path in a real capitalist economy
value added is determined as a residual by the following equation:
VA(t) = p(t)X(t) - p(t-1)aX(t)
where both p(t) and ap(t-1) are taken as given.
What I wish to emphasize is that (A) and (B) are mutually exclusive logical
alternatives - one cannot have both logics at the same time. If VA is
determined prior to the prices of output, then VA cannot be derived from the
prices of output.
It seems to me that Duncan attributes (B) to Andrew, but Andrew's logic of
determination is really (A).
3. Duncan begins (3287) in the following way:
Suppose we start with some data from a real economy that includes a series
of prices of output p(t), and a measurement of the quantity of output X(t),
and of the inputs to production, including a measure of the social labor
expended per unit of output l(t) ...
What does this mean to "start from data from a real economy that includes
prices of output"? Are then prices taken as given in the equations
presented (or some of them), or are they determined by these equations?
4. Later Duncan says:
The measure of the money value added depends on the price and output data.
This sounds very much like the logic of (B). The value added "depends on"
the prices of inputs and outputs" (the prices of output taken as given?).
And a little further:
Andrew's examples are based on the definition of the money value added as
the difference between the sales price of the output and the cost of the
inputs ...
Then Duncan presents the following equation for Andrew's value added:
VA = p(t)X(t) - p(t-1)aX(t)
Again, this looks like the logic of (B). Value added is "defined" as a
residual, as the difference between the prices of inputs and outputs.
"Defined" here seems to imply determinaton. But in order for VA to be
determined by this equation, p(t) would have to be determined independently
of VA (presumably taken as given), and this is contrary to Andrew's logic.
According to Andrew's logic, value added is not determined by this equation,
but is instead determined by current labor and taken as given in the
determination of the prices of output. The prices of output are not taken
as given, but are instead determined by the sum of historical costs and VA.
One can write this equation for VA in this way in an accounting sense, and
then decompose the right hand side into the conventional value added and an
IVA, but this still does not mean that VA is determined by this equation,
and in particular does not mean that VA depends in part on an IVA. It seems
to me to be that Duncan is confusing an accounting definition with a method
of determination.
In an earlier post (3207), I argued:
Duncan's interpretation of this equation makes it appear as if this is the
way that value added is determined, as a residual, with both p(t) and
p(t-1) determined prior to value added.
Duncan responded in (3226):
This is a subtle point, since there are two concepts of value added being
equated to determine prices in Andrew's examples, the price value added
(which Andrew calculates as above) and the labor time expended.
I disagree. I do not think that there are two different ways to determine
value added in Andrew's interpretation. There is only one way to determine
value added - by current labor. Value added is not determined according to
the above accounting equation.
5. It seems to me that Duncan's misinterpretation is further indicated by
the conclusions he draws about Andrew's derivation of the time paths of
prices of output and the rate of profit. Duncan argues:
When Andrew correctly solves his equation for the price path
assuming a constantly increasing labor productivity, he finds that prices
decline more rapidly than the social labor input per unit of output, and
that as a result the money profit rate defined above declines to zero.
But this is not true. Andrew's prices decline LESS rapidly than the labor
input per unit of output. Andrew's prices for the first four periods are:
100, 96, 87.6, and 81.9, while the labor input per unit of output is
declining by 20 0.000000e+00ach period. Prices decline less rapidly than productivity
increases because the "cost of inputs" component of the price of commodities
declines only after a lag of one period (i.e historical costs in a
circulating capital model). It seems to me that Duncan thinks that prices
decline more rapidly than productivity because the above accounting equation
for VA makes it look like, as we move from period to period, VA is reduced
by an IVA. But this is not true. Total VA remains constant from period to
period, as determind by a constant current labor (= 100 for all 196 periods
of Andrew's example). The time path of VA in Andrew's example is presumably
the same as in Duncan's own derivation (= 100 in all periods).
Similarly, the fact that the rate of profit declines to zero over time has
nothing to do with the effect of an IVA on value added. The rate of profit
does not decline because an IVA reduces the amount of profit. As already
mentioned, value added remains constant over all the periods and is not
affected by an IVA. Rather, the rate of profit declines because this
constant amount of value added is related to a larger and larger "cost of
inputs", which is itself the result of the assumption that the cost of
inputs are determined at historical costs.
Therefore, I conclude that the time paths of prices and the rate of profit
in Andrew's example does not depend on the effect of an IVA on value added.
Andrew's time paths are different because of the assumption of historical
costs, which itself does not necessarily imply an effect of an IVA on value
added.
Comradely,
Fred