[OPE-L:3163] Value added, IVA and TSS

Bruce Robert (broberts@usm.maine.edu)
Fri, 27 Sep 1996 07:52:23 -0700 (PDT)

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The comments on this and related threads are coming fast and furious, and
I'm having a hard time keeping up, but I do want to put in some thoughts.

Several times in past posts, in commenting on TSS arguments, I've suggested
without elaboration that I thought that a big part of our differences
stemmed from using different labels for the same numbers, and that the
concept of "release of capital" is involved in thinking the differences
when productivity changes cause falling prices and values. In light of
Duncan's comments on value added and IVA, which I think have raised a
similar set of issues, I'll try to elaborate.

Andrew's example (in 3063) is a good one to focus on. His comments (in
3097) present his conception of how one accounts in labor-time terms, and
his effort to "measure l and v directly in labor-time" is exactly what's
needed. But I don't think that job is as easy, in the sense of being
doable in an unambiguous way, as Andrew seems to believe. There are
different ways to proceed, particularly with respect to C. Andrew believes
he is consistently applying the premise that 1 dollar = 1 hour. And by
saying that he "believes" he's doing it consistently, I don't mean to seem
demeaning--he *is* being consistent, according to his own protocols of
accounting for commodities in terms of labor-time. And therefore when he
looks at the numbers that emerge from simultaneous valuation they make no
sense to him--hence the challenge, posed by Alan, to explain how output
sold at one price can be valued as capital at a different price than that
which was paid for it. I'll try to answer that.

Typing tables is difficult on email, so I'll transmit info. as a series of
lists instead. To recap a few periods worth of Andrew's example:

Year 0:

total physical capital advanced: 4 units
Andrew's input price per unit: \$100
Andrew's C: \$400
total physical output: 5 units
Andrew's output price per unit: \$100
Andrew's total revenue: \$500 (equal also to C plus the value added by
living labor, which is \$100 in every period)
Andrew's profit: \$100 (equal to value added in money terms in each period)
Andrew's replacement cost of physical capital: \$400 (output price times
physical capital advanced at the beginning of this period)
Andrew's (implicit) "release of capital": \$0 (C minus replacement cost)
Andrew's "deployable surplus revenue": \$100 (the term is mine, not
Andrew's, but by it I mean Andrew's profit plus his release of capital: the
money capitalists have left at their disposal after paying to replace
physical capital; it is the fund available for net accumulation)
Andrew's profit rate: 25% (profit divided by C)
ratio of deployable surplus to the replacement cost of capital: 25% (in
this example, always equal to the rate of growth)

Year 1

total physical capital advanced: 5 units
Andrew's input price per unit: \$100
Andrew's C: \$500
total physical output: 6.25 units
Andrew's output price per unit: \$96
Andrew's total revenue: \$600
Andrew's profit: \$100
Andrew's replacement cost of physical capital: \$480
Andrew's "release of capital": \$20
Andrew's "deployable surplus revenue": \$120
Andrew's profit rate: 20%
ratio of deployable surplus to the replacement cost of capital: 25%

Year 2

total physical capital advanced: 6.25 units
Andrew's input price per unit: \$96
Andrew's C: \$600
total physical output: 7.8125 units
Andrew's output price per unit: \$89.6
Andrew's total revenue: \$700
Andrew's profit: \$100
Andrew's replacement cost of physical capital: \$560
Andrew's "release of capital": \$40
Andrew's "deployable surplus revenue": \$140
Andrew's profit rate: 16.67%
ratio of deployable surplus to the replacement cost of capital: 25%

Year 3

total physical capital advanced: 7.8125 units
Andrew's input price per unit: \$89.6
Andrew's C: \$700
total physical output: 9.765625 units
Andrew's output price per unit: \$81.92
Andrew's total revenue: \$800
Andrew's profit: \$100
Andrew's replacement cost of physical capital: \$640
Andrew's "release of capital": \$60
Andrew's "deployable surplus revenue": \$160
Andrew's profit rate: 14.29%
ratio of deployable surplus to the replacement cost of capital: 25%

And so on. I accept *everything* in these lists. I accept the prices
listed as a perfectly legitimate possible sequence of money prices in an
contest that the price paid in money terms at the beginning of each period
differs from the (lower) price at which output is sold (and new inputs
purchased) at the end of the period. I accept that the profit rate, as TSS
conceives it, will fall (while reserving judgment as to why that matters
very much). What I don't accept, though, is that the dollar magnitudes here
directly represent equal magnitudes of labor-time. Andrew believes they
do, and that's the way he accounts in labor-time terms. I do it
differently.

The basic difference is this: labor-saving technical change here means
that each unit of the social net product represents less living labor-time
than in the previous period, and less (*current*) labor-time than was paid
to acquire it as an input at the time it was purchased. That does not, of
course, repeal the fact that a certain amount of money *was* paid for it at
the time of purchase, but it does mean that, when new output emerges, the
*current* labor-time represented by that sum of money is less than the
labor-time the money represnted *at* the timeof the advance. And equally,
when output emerges, the *current* labor-time represented by the money
actually advanced at the time of purchase of inputs is greater than the
current labor-time that those physical input commodities now represent.

Since those distinctions are probably not immediately obvious to anybody,
let me present the sequence of numbers that I would use in accounting for
the same set of events that Andrew poses, and the same money prices, in
terms of labor-time.

Year 0

social net product: 1 unit (output minus physical capital advanced)
living labor performed: 100 hours
Bruce's value or price per unit output in terms of current labor-time
[p(t)]: 100 hours (total living labor divided by social net product)
Bruce's "labor-time expression of money (LEM)": 1 hour per \$ (ratio of
Bruce's (labor-time) value per unit output to Andrew's (money) output price
in this period--here, 100 hours/\$100; this is the amount of current
labor-time represented by a dollar)
Bruce's "historical capital": 400 hours (Andrew's C times LEM) (this
expresses, as a magnitude of *current* labor-time, the *money* paid at the
beginning of the period for physical inputs)
Bruce's value of capital: 400 hours (physical capital advanced times its
current value, given by p(t); this is also, by definition, the replacement
cost of capital in terms of current labor-time)
Bruce's revenue realized, in labor-time terms: 500 hours (physical output
times p(t); also by definition equal to Andrew's total revenue in money
terms times LEM)
Bruce's profit, in labor-time terms: 100 hours (revenue realized minus
value of capital, always equal to value added by living labor, which is 100
hours)
profit in excess of historical capital: 100 hours (realized revenue
expressed in terms of current labor-time minus the (current) labor-time
expression for the money advanced for physical capital)
Bruce's "release of capital": 0 hours (historical capital minus the
(current) value of capital; in other words, the current labor-time
represented by the *money* advanced for physical capital minus the current
labor-time represented by the *commodities* advanced as physical capital;
or again, the current labor-time expression for the capital freed up by the
fall in the value of the commodity)
Bruce's rate of profit: 25% (profit in labor-time terms divided by the
(current) value of capital)
The ratio of profit in excess of historical capital to historical capital:
25% (this is, in fact, identical to Andrew's TSS rate of profit)

Year 1

social net product: 1.25 units
living labor performed: 100 hours
Bruce's value or price per unit output in terms of current labor-time
[p(t)]: 80 hours
Bruce's "labor-time expression of money (LEM)": .833 hour per \$
Bruce's "historical capital": 416.67 hours
Bruce's value of capital: 400 hours
Bruce's revenue realized, in labor-time terms: 500 hours
Bruce's profit, in labor-time terms: 100 hours
profit in excess of historical capital: 83.33 hours
Bruce's "release of capital": 16.67 hours
Bruce's rate of profit: 25%
the ratio of profit in excess of historical capital to historical capital: 20%

Year 2

social net product: 1.5625 units
living labor performed: 100 hours
Bruce's value or price per unit output in terms of current labor-time
[p(t)]: 64 hours
Bruce's "labor-time expression of money (LEM)": .71429 hour per \$
Bruce's "historical capital": 428.571 hours
Bruce's value of capital: 400 hours
Bruce's revenue realized, in labor-time terms: 500 hours
Bruce's profit, in labor-time terms: 100 hours
profit in excess of historical capital: 71.429 hours
Bruce's "release of capital": 28.571 hours
Bruce's rate of profit: 25%
the ratio of profit in excess of historical capital to historical capital:
16.67%

Year 3

social net product: 1.953125 units
living labor performed: 100 hours
Bruce's value or price per unit output in terms of current labor-time
[p(t)]: 51.2 hours
Bruce's "labor-time expression of money (LEM)": .625 hour per \$
Bruce's "historical capital": 437.5 hours
Bruce's value of capital: 400 hours
Bruce's revenue realized, in labor-time terms: 500 hours
Bruce's profit, in labor-time terms: 100 hours
profit in excess of historical capital: 62.5 hours
Bruce's "release of capital": 37.5 hours
Bruce's rate of profit: 25%
the ratio of profit in excess of historical capital to historical capital:
14.29%

Etc.

I suspect that Duncan may agree with at least some of this (the net product
valuation is consistent with his longstanding views), but I won't put words
in his mouth. Still, what I take to be his point is likely to be
misunderstood, because of the different ways that accounting can proceed in
terms of labor-time. For example, profit, looked at *in* the accounting
terms presented by TSS, is here equal in every period to \$100, which is
precisely the money expression of the value added by living labor--*all* of
it. Release of capital, as TSS would calculate it, is something else
entirely. Thus I suspect that TSSers will not recognize themselves in
Duncan's characterization of them as having "attributed to living labor"
devalued here. And, indeed, Andrew's reply (3097) says exactly that when
he concludes that "it is temporal valuation, not simultaneous valuation,
that equates value added and the monetary expression of living labor
expended."

But in the accounting terms I favor, Duncan's point is exactly right.
Profit or surplus value is in every period equal to total living labor
performed (100 hours), since all of that is unpaid labor here; that total
can be *decomposed*, if we choose to, into two parts, one representing TSS
profit and the other representing release of capital. So what TSSers call
profit is, looked at in the accounting terms I favor, only a *part* of
value added, and a declining part at that, since here a rising share of
value added is accounted for by what I'm calling release of capital.
Hardly surprising, then, that the rate of profit falls, if this is what we
mean by profit, rather than the *whole* of the unpaid labor performed by
the workers.

In this example, as near as I can tell, nothing much happens to the
situation of capitalists. Capital grows at a steady rate (25%), and since
everything available is being accumulated in every period, it makes sense
to me to say (as simultaneous calculation does) that capital earns its
profit at that same steady rate of 25%. I understand, I think, how TSS
accounting determines its rate of profit, but if this scenario is supposed
to represent the FRP, it's not obvious to me why capitalists would *care*
whether their rate of profit falls.

One other point: among the numbers as I calculate them, the value of
commodity capital ("C" in my sense) is 400 hours in every period, and the
value of output is similarly 500 hours in every period (they stay the same
because the rising physical quantities are exactly counterbalanced by the
falling unit values in terms of *current* labor-time). Andrew questions
these numbers (in 3097), arguing that they "violate Alan's principle that
the money paid for the inputs ought to equal the money received for the
inputs." But there is no inconsistency here. These numbers, 400 and 500
(neither of which is directly an amount of money), make perfect sense here,
even though, in terms of money paid, Andrew's money prices reign. These
numbers are *not* inconsistent with the events that Andrew has created here
in this numerical example--they simply *mean* something different from the
(seemingly quite silly) meaning they have when used by TSSers to poke fun
at the absurdity they see in the results of simultaneous equations.

So I think I have answered the critique Alan makes at the end of his
"Okishio 5 of 4 1/2," echoed by Andrew: the claim that simultaneous
valuation must defend the absurd idea that goods are purchased at a price
different from that at which they are sold. That claim depends on
confusing the labor-time units appropriate within TSS with those
(different) labor-time units appropriate in the simultaneous approach to
calculation. There is no logical inconsistency, if we keep the units
straight. And Duncan's stress on the different ways of approaching value
added has, at the very least, the implication that we need to understand
and acknowledge the different ways we each set up our own units, as a
prerequisite for the ongoing discussion about which we each prefer.

Bruce

Bruce B. Roberts
broberts@usm.maine.edu
Department of Economics
University of Southern Maine
Portland ME 04104-9300
(O) 207-780-5503
(H) 207-772-7047
fax 207-780-5507-------------------------------------------------