[OPE-L:3100] Re: Clarity on IVA

Duncan K. Fole (dkf2@columbia.edu)
Mon, 23 Sep 1996 13:02:48 -0700 (PDT)

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>I appreciate your comments on my OPE-L 3088
>and apologize for the unclarity. Let
>me see if I can get a handle on what you
>refer to as the IVA.
>Here, again, is my example in its unclear
>Let's say that I buy $90 worth of the commodity in a
>one-commodity world and spending next to nothing on wages
>manage to produce $120 worth of that commodity. The living
>labor created a value of $30. Clearly, with this informa-
>tion we would agree that my rate of profit is 33.3%. Of
>that $120, I invest $100 in constant capital in the next
>period and introduce a new technique, which I hope will
>increase my profits as well as my profit rate. Despite
>my hopes, it doesn't since the price of the commodity
>falls after production such that the total price of
>the output is $130. If we in the world of TSS look at
>this situation, we see that there is $100 invested in
>constant capital and, as before, $30 added to the product
>by the living labor. For us, the given amount of living
>labor is adding the same exchange value to the product in
>both periods -- $30. To be sure, the rate of profit has
>now fallen to 30% as the living labor created the $30 in
>exchange value.
>Now I add:
>As I begin producing with my $90 investment, let's further
>assume that 120 units of the commodity are produced. Each
>then has a price of $1. In the next period, having invested
>$100 to buy 100 units of the commodity produced in the
>previous period. Let's say that I can now produce 200 units
>of the commodity. Thus, I would expect that the gross output
>would sell for $200. It doesn't. As stated above, it sells
>for $130. Why $130? Here, I think, we see the assumption
>of the LTV. That is, I invested $100 and the living labor adds
>$30. The price of the total is thus, again, $130. The price
>of the individual commodity fell from $1 in the first period.
>to $130/200 or $.65 after production in the 2nd.

Here is the nub of the issue. No problem with the fall in price due to the
labor theory of value, but the question is how much. In period 0 we have 90
units of output + 30 units of labor producing 120 units. In my notation
this corresponds to a(0) = .75 (=90/120) and l(0) = .25 (=30/120). The
price of a unit of output is $1, so that value added is $.25 per unit, or
$30 altogether for the 120 units. The inventory valuation adjustment is
zero. The profit rate , calculated either in commodity numeraire or in
money terms at historical cost is r(0) = (1-a(0))/a(0) = (.25/.75) =
($30/$90) = .333.... (Pace Gerry, we assume that the wage, though finite,
is vanishingly small.)

In period 1 100 units of output plus 30 units of labor produce 200 units of
output. In my notation this corresponds to a(1) = .5, l(1) = .15. I would
calculate the value added here as p(1)(1-a(1)) = l(1) = .15, giving a price
p(1) = $.30. The commodity numeraire profit rate is (1-a(1))/a(1) = (.5/.5)
= 1.000, much higher, since there has been both labor-augmenting and
capital-augmenting technical change. The profit rate on historical cost is
($.30-$.50)/$.50 = -.40. The reason for this negative return is the money
loss on the inventory of inputs held during the production period while
prices are falling. The inventory valuation adjustment = a(1)(p(1)-p(0)) =
..5($.30-$1.00) = -$.35 per unit of output, or -$70 altogether.

Notice that this method makes the price fall farther than your calculation.
You propose a price of $.65 in the second period. But this corresponds to a
conventional value added (without the inventory valuation adjustment) of
p(1)(1-a(1)) = $.65(.5) = $.375 per unit, or $65 altogether from the 30
units of labor expended. In my way of reckoning, this implies that the
value produced by a unit of labor has risen from $1 in period 1 to $2.16...
in period 2, thus not satisfying the assumption we agree on that a unit of
living labor will add $1 to the value of the product. With a price of $.65,
the inventory valuation adjustment would be a(1)(p(1)-p(0)) =
..5($.65-$1.00) = -$.175 per unit of output, or -$35 in all. When you count
this $-35 inventory valuation adjustment as part of the value added you
reduce the value added from the conventionally measured $65 to $30. At a
price of $.65, the money profit rate on historical cost would be
($.65-$.50)/$.50 = .300.
>Here, I think TSS, as I use it in the above, is indeed following
>the LTV. If not, I am really unclear on how my example differs
>from what you see Andrew doing. You may be seeing something
>in Andrew's efforts that I am simply missing.

As far as I can see, your method of calculating value added in this example
includes the inventory valuation adjustment and in this respect is
consistent with Andrew's examples. I am not yet persuaded, however, that
this is the appropriate definition of value added to represent Marx's Labor
Theory of Value.

>Striving for clarity,

Duncan K. Foley
Department of Economics
Barnard College
New York, NY 10027
fax: (212)-854-8947
e-mail: dkf2@columbia.edu