# [OPE-L:53] [OPE-L:283] Negative Value Added and the MELT

Duncan K. Foley (dkf2@columbia.edu)
Tue, 3 Nov 1998 12:09:30 -0500

In February, Andrew posted an example questioning how the New
Interpretation definition of the Monetary Expression of Labor Time would
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:

EXAMPLE #2: POSITIVE SURPLUS-LABOR BUT NEGATIVE "PROFIT"
=========================================================
Assume a two-sector capitalist economy, with the following input-output
relations:

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.

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 results.

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,

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
1.04 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

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
(212)-854-3790
fax: (212)-854-8947
e-mail: dkf2@columbia.edu