# [OPE-L:3322] Re: TSS and value added

Duncan K. Fole (dkf2@columbia.edu)
Tue, 8 Oct 1996 14:09:41 -0700 (PDT)

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>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

Strictly speaking MVA(t) is equal to m(t)l(t)X(t), where m(t) is the
current monetary expression of value, and l(t)X(t) the living labor input.
I use "money value added" to mean the standard NIA concept of net domestic
product.
>
>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:
> MVA(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.

But shouldn't the method be consistent with either setting? I would put
this in somewhat different language: one problem is to measure the monetary
expression of value given data on inputs, outputs, prices, and labor
expended. Andrew's examples arise from an inverse situation, where he takes
the monetary expression of value as given, and then looks for price paths
that are consistent with the LTV.

I agree that one wouldn't be doing both problems at the same time, but it
seems that the method ought to be able to handle both consistently.

> 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).

Here we have a semantic problem. I use "money value added" to refer to the
accounting that we see at actual prices in the economy, whereas you and
Andrew want to use it to mean "living labor expended". Since in my
interpretation of the LTV these two concepts are proportional, this doesn't
create a problem for me, but it does create some potential confusion in
language.

>
>
>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?

Given by observation, as in the NIA.

>
>
>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?).

Well, given price, input and output data you could define money value added
either as p(t)X(t) - p(t)aX(t) (the NIA definition) or as p(t)X(t) -
p(t-1)aX(t) (what I take to be Andrew's definition).

>
>And a little further:
>
> Andrew's examples are based on the definition of the money value
> 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)

I put "MVA(Andrew)" on the lefthand side here to try to keep things straight.

>
>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.

Well, I don't think I'm making this confusion. Go back to the problem of
measuring the monetary expression of value from real data to see that you
have to have some definition of monetary value added to work from. Andrew
turns the LTV into a determination in his examples when he uses the
language "assuming that one hour of labor is always equivalent to \$1", or
the like.

>
>
>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).

I was wrong to say that Andrew's example prices decline more rapidly than
the labor input per unit of output. I don't think this has anything to do
with misinterpreting him, however. The important implication of the
examples is that the money profit rate would fall to zero with a constantly
rising labor productivity and a constant ratio of output to capital
invested. I'm trying to establish that this result depends crucially on
equating p(t)X(t)-p(t-1)aX(t), which is standard money value added plus the
IVA to m(t)l(t)X(t).
>
>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
>
Do you think a capitalist economy with a constant positive rate of labor
productivity increase and constant ratio of output to capital would
experience a fall in the money rate of profit to zero?

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