[OPE-L:57] [OPE-L:290] Re: Negative Value Added and the MELT

Ajit Sinha (ecas@cc.newcastle.edu.au)
Thu, 05 Nov 1998 15:04:55 +1100

At 12:09 3/11/98 -0500, you wrote:
>In February, Andrew posted an example questioning how the New
>Interpretation definition of the Monetary Expression of Labor Time would
>handle situations with negative value added. I've been thinking about this
>issue on and off over the past months. I haven't arrived at what I regard
>as a very satisfactory answer, but I have some observations which may serve
>to push the discussion forward.
>First, to remind you, here's Andrew's example:
>Assume a two-sector capitalist economy, with the following input-output
>100 lbs. of wheat + 1 hr. of living labor --> 101 lb. of wheat
> 4 lbs. of wheat + 1 hr. of living labor --> 1 box of bread
>Note that the economy is "productive" -- the Hawkins-Simon conditions are
>satisfied (less than 1 unit of each good is used, directly and indirectly, to
>produce 1 unit of it).
>Assume also that the unit price of each good is $1 (we'd get the same results
>with numeraire prices).
>Finally, wages are zero.
>Hence, measured in either numeraire, "profit" is negative:
>"profit" = $1*101 + $1*1 - $1*100 - $1*4 = -$2.
>However, surplus-labor is positive, 2 hrs.

This makes no sense to me. In the above system, wheat is the basic and
bread is the non-basic good. Given the assumption that wages are equal to
zero, the first equation determines the rate of profit to be 1%. If we take
wheat as the numeraire, the the price of bread comes out to be 4.04 in
terms of wheat. So where is the problem? The problem is with Andrew's
meaningless imposition that prices of the two goods happen to be $1 each
(where the sign $ always remains a mystery). One cannot do 'theory of
prices' by imposing arbitrary and miningless prices on the system. This is
the fundamental mistake TSS makes all the time. Cheers, ajit sinha
>The problem, of course, is that when the aggregate price of the net
product is
>negative, the simultaneist MELT is also negative. In this case it equals
>-$2/2 hrs. = -$1/hr. Each hour of labor is expressed monetarily as -$1.
>Equivalently, the monetary value added (?) by each hour of labor is -$1. We
>can also conclude that the $101 received by the wheat producers represents
>-101 labor-hours, and the $1 received by the bread producers represents -1
>labor-hour. I have difficulty understanding how these are meaningful
>These problems do not arise under the temporalist interpretation of the MELT.
>No actual temporal computations can be done without knowing the MELT at the
>start of the period as well as prices at the start of the production period.
>So, for purposes of illustration, I'll assume that input prices equal output
>prices and that the MELT at the start of the period is $1/hr.
>Hence, constant capital outlays were $1*100 + $1*4 = $104. They represented
>$104/[$1/hr.] = 104 labor-hours. 2 labor-hours were added. The total value
>of output in labor-time terms is thus 104 + 2 = 106 hrs. The total price of
>output is $1*101 + $1*1 = $102. Hence, the end-of-period MELT is $102/106
>hrs. This is not a negative number.
>The rate of inflation of the MELT, using the procedure outlined in the above
>example, is i = -4/106. Hence, 1+i = 102/106. By the former discounting
>method, we have
>real profit = $102/(102/106) - $100 - $4 = $2
>which is the monetary expression of the 2 hrs. of surplus-labor according to
>the original MELT of $1/hr.
>By the latter discounting method, we have
>real profit = $102 - (102/106)*($100 + $4) = (102/106)*$2
>which is the monetary expression of the 2 hrs. of surplus-labor according to
>the new MELT of $102/106 hrs.
>Duncan's observations:
>1) The economic source of the negative value added is the extremely low
>price of bread here. The net product is (-3 wheat, 1 bread). At the prices
>assumed in the example, ($1/wheat, $1/bread) the value added is -$2. The
>bread sector is failing to cover even the costs of its raw materials,
>wheat, and its huge losses lead to a negative value added.
>This would not occur at prices that were proportional to embodied labor
>coefficients or to prices of production. The embodied labor coefficients
>(the "simultaneist" "labor values") are (1 labor/wheat, 5 labor/bread).
>The value of the net product at these coefficients is 2 labor. The prices
>of production (calculated in the "simultaneist" manner) are proportional to
>($1/wheat, $4.04/bread), giving a value added of $1.04 (or, more generally,
>1.04 times whatever the price of wheat is).
>These observations give us some insight into what the underlying economic
>situation in the example is, but the NI definition of the MELT is supposed
>to work for any market prices, so they do not answer the challenge of
>Andrew's example in and of themselves.
>2) It's unlikely that any real economy would record a negative value added
>in a year, so one might argue that the example is interesting but not
>realistic. There are two objections to this type of answer. First, some
>country might turn up with negative value added sometime (perhaps in a
>period of very wildly fluctuating foreign exchange rates). Second,
>countries with positive value added could have sectors with negative value
>added, so the theory should deal adequately with this problem.
>The best line of analysis I have come up with so far is to question whether
>the bread sector here is in fact a productive sector of the economy, since
>the labor time expended in it has not been validated by the market. In this
>case one would regard the labor employed in the bread sector as
>unproductive, and its using up -3 wheat as consumption. The net product of
>the economy would be (1 wheat), with a value added of $1, produced by (1
>labor), and the NI MELT would be $1/unit labor. This raises the problem of
>correcting real world national accounts for negative value added sectors
>(or perhaps, just sectors with negative profits) in calculating the NI
>MELT. Of course, this problem already exists, since dividing NDP, or GDP by
>labor time is only a first approximation to the MELT, which could be
>further refined by taking account of unproductive labor, differences in
>skills, and so forth.
>3) The discussion allows us to clarify the relation between the NI and TSS
>definitions of the MELT, which may help to move the issue toward
>resolution. Let's assume a circulating capital economy, in which inputs at
>the beginning of the period together with labor expended during the period
>produce output at the end of the period. Let A be the matrix of input
>coefficients, each column representing the inputs required to produce 1
>unit of the output, l be the row vector of labor inputs, p0 and p1 the row
>vectors of prices at the beginning of the period (end of the last period)
>when inputs are purchased, and at the end of the period, when outputs are
>sold, and x the column vector of gross outputs.
>To simplify the notation, I'll write vector and matrix products as ordinary
>products, keeping track of the row and column vectors. Thus lx is the total
>labor expended, (I-A)x is the net product, and so on.
>The NI MELT, m1 = p1(I-A)x/lx, the ratio of the value of the net product at
>end of period market prices to the labor expended during the period.
>To calculate the TSS MELT, which I will call u, as I understand Andrew's
>procedure, we note that the value of stocks at the beginning of the period
>prices is p0Ax, and we assume we know u0, the MELT last period. So the
>labor time equivalent of these stocks is p0Ax/u0. During the period labor
>lx is added to these, so that the labor time equivalent of the end of
>period stocks is lx + (p0Ax/u0). The value of the stocks of commodities in
>existence at the end of the period, before consumption, is p1x, so we
>define the current period MELT as u1 = p1x/( lx + (p0Ax/u0)). If we then
>had price and output data for succeeding periods, we could calculate a
>series of TSS MELTs in the same way.
>We can see the relation between the NI MELT and the TSS MELT:
>m1 = u1 + (((u1/u0)p0-p1)Ax/lx)
>This shows that the difference involves the change in the valuation of the
>stocks already existing at the beginning of the period due to price changes
>during the period. The TSS MELT attributes this value to the labor time
>expended during the period, while the NI MELT does not.
>4) From a purely formal point of view, the TSS MELT has a property,
>nonnegativity, that the NI MELT lacks. From my perspective, the TSS MELT
>has an offsetting formal disadvantage, which is that it can be measured
>only by stipulating an initial period MELT, u0. We know from Andrew's
>examples in other contexts that the choice of this initial value can lead
>to quite different time series for the TSS MELT, and it is not clear how we
>can make the measurement of the crucial u0 operational.
>But I don't think this issue can be settled on purely formal grounds,
>because it has a real economic content. The question is whether it makes
>sense within the framework of the Marxian labor theory of value to
>attribute the change in the value of stocks through a period due to price
>changes to the expenditure of labor within that period. In my reading Marx
>is quite explicit and clear in viewing labor in production as adding value
>to the value of the raw materials it works with, which seems to me to
>correspond to the NI definition of the MELT.
>Duncan K. Foley
>Department of Economics
>Barnard College
>New York, NY 10027
>fax: (212)-854-8947
>e-mail: dkf2@columbia.edu