Perhaps the main reason that the trivial demonstrations of the preceding two
sections have not received attention until now is that theorists have been
interested in economies that are able to reproduce themselves physically. It
is therefore sometimes alleged that, if any physical surpluses are negative,
and especially if the money value of the "net product" is negative, the
economy is incapable of reproducing itself in the "long-run," and that such
cases are not worthy of theoretical consideration.
In response, five things may be noted. First, the appeal to physical
reproducibility is either an evasion of the issue at hand or the result of a
logical fallacy. Even were it true (which it is not, as I will show
presently) that, if an economy is physically sustainable, then simultaneist
surplus-labor and profit will both be positive, it does not follow that
surplus-labor is either necessary or sufficient for positive profit.
Likewise, if I am a man, then I am both male and adult. Yet not all males are
adults, nor are all adults males.
Second, when attempting to ascertain whether surplus-labor is necessary
and/or sufficient for profit to exist, it is very peculiar to exclude negative
physical surplus cases from consideration, because to excluding them is to
exclude the cases most likely to falsify the propositions in question.
Assume, for instance, that surplus-labor is extracted, and we wish to
ascertain whether this is sufficient for positive profit. If we then restrict
our investigation to cases in which all physical surpluses are positive, we
obviously exclude the vast majority of cases that common sense leads us to
believe would result in negative profit. It is rather like asking whether
massive heart failure is sufficient to kill someone, and then restricting the
investigation to victims who neither obtained medical treatment nor altered
their lifestyles. Similarly, if profit is positive, and we wish to ascertain
whether this could only be the case if surplus-labor is extracted, we exclude
the vast majority of likely negative surplus-labor cases if we then rule out
cases in which some physical surpluses are negative.
Third, the existence of a negative "net product" of some use-value is not as
restrictive a condition as is sometimes suggested (and a negative physical
surplus is even less restrictive). It is easily possible for some "net
products" to be negative even in very productive economies — a negative "net
product" does not mean that more of a use-value is consumed in its own
production than is produced, either directly (some aii of the A matrix exceeds
unity) or indirectly (the Hawkins-Simon conditions are violated). Instead,
more may be consumed in the production of other use-values, simply because
their scales of production are large. Imagine, for instance, that only 10/21
units of good A are needed to produce 1 unit of good A, and that 0.1 units of
good A are needed to produce 1 unit of good B. Good A is the only input into
both processes. Thus, the amount of A needed, directly and indirectly, to
produce a unit of A is only 10/21 and the maximum eigenvalue-profit-rate is
(10/21)^-1 - 1 = 110%. If 21 units of good A and 100 units of good B are
produced, then the "net product" of A equals 21 - (10/21)*21 = 0.1*100 = 1.
Yet if production of B is now increased by 20% to 120, although no more of A
is needed, directly or indirectly, to produce one unit of it, and although the
maximum eigenvalue-profit-rate is unchanged, the "net product" of A is now -1.
Fourth, to exclude negative physical surplus and negative "net product" cases
as unworthy of theoretical consideration is to deem all actual economies
unworthy of theoretical consideration. It is simply not the case that
economies are capable of sustaining themselves only if they produce
non-negative "net products" of all use-values. Indeed, every actual economy
produces a negative net product of some use-values, because some use-values
are used as inputs but, instead of being reproduced, they are used to produce
other, similar but not identical, use-values.**footnote 6** For instance, 386
computers have been used to produce 486 computers, and 486 computers have been
used to produce 586 computers.
As we have seen, when they claim that surplus-labor is sufficient for
positive profit, simultaneists rely crucially on the postulate of either a
positive "net product" of each use-value or a positive price of the "net
product" vector. Since this postulate is violated in every actual economy, it
follows that this claim does not apply to the real world.
It is impossible, moreover, for simultaneists to construct comparable theorems
to cover real-world situations. The key obstacle is that simultaneous
valuation is impossible if some inputs are not reproduced as outputs. To
compute the aggregate price of the "net product," and thus simultaneist
"profit," of a period, one takes the gross price of the outputs and subtracts
the replacement cost of the inputs, i.e., the vector of inputs pre-multiplied
by their end-of-period prices. Yet inputs that have been used up without
being reproduced do not have end-of-period prices, so this is impossible. One
could, of course, use their prices when they were committed to production, but
then one would not be valuing inputs and outputs simultaneously.
At best, one may attempt to estimate the inputs' end-of-period prices by
trying to establish an equivalence between inputs and outputs of the form x
commodity A = y commodity A'. What, however, is the basis of this
equivalence, the common factor or "third thing" of which A and A' are members?
Physically, they are heterogeneous, and irreducibly so — no abstract "Corn"
or "Car," etc. exists. Nor does abstract "utility" exist; many physical
things have multiple uses.**footnote 7** For instance, an electronic journal
may be much more useful than a print journal as a way of storing information,
slightly less useful as a way of reading that information, and considerably
less useful as a fly-swatter. (Note that print journals are indeed inputs
into electronic journals, as footnotes make clear.)
In addition to its conceptual inadmissibility, this attempted homogenization
of heterogeneous use-values yields arbitrary results. Undoubtedly estimates
of this sort are practical and necessary for some purposes, but even slightly
different estimates may lead to differences in the size and, more importantly
for present purposes, also the sign of the price of the "net product." One
estimate may tell us that quasi-simultaneist "profit" is positive, while a
slightly different one may tell us that it is negative. The truth of a
theorem that surplus-labor is necessary and/or sufficient for positive
"profit" would then depend on the idiosyncracies of the estimators.
V. Reproducibility Without "Reproducibility"
Fifth, even if we ignore non-reproduced inputs, it is very probable that
actual economies, even highly productive ones that do reproduce themselves
over time, fail to satisfy simultaneist definitions of "reproducibility"
(e.g., Roemer (1981)). To satisfy such definitions, they must produce
non-negative physical surpluses in each and every period. All that is
required for reproducibility in reality is that non-negative surpluses of all
use-values are produced over some expanse of time longer than one period (and
that initial reserve stocks be of sufficient size). For instance, assume a
two-good economy in which the physical surpluses of goods A and B are -3 and
4, respectively, in period 1, and 4 and -3 in period 2. Over these two
periods, 1 more unit of each use-value has been produced than has been used up
as means of production or wage good. Given an initial stock of A of at least
3 units, there are no technological barriers to its expanded reproduction.
Since the length of a "period" is arbitrary, one may of course lengthen the
period and thereby include such cases among those in which all physical
surpluses are non-negative in every period. Yet, once one does so,
simultaneist theorems that surplus-labor is necessary and sufficient for
positive profit will be false. Prices may change during the lengthened
"period" in such a way that, for instance, even though surplus-labor is
extracted in both "sub-periods," simultaneist "profit" may be negative in each
of them and therefore negative in the lengthened period as a whole.
This is demonstrated in Table 1. In order to apply to all simultaneist
interpretations, the wage rate is assumed to be zero; in this case, their
definitions of surplus-labor are identical. If one were to assume a very low
real wage consisting of equal amounts of both use-values, the same qualitative
results would obtain. Table 1 also assumes that technical coefficients are
unchanged over the two days, so that the 2% variations in each sector's daily
output are due to changes in activity levels alone.
------------------------------
Table 1
POSITIVE SURPLUS-LABOR BUT NEGATIVE SIMULTANEIST PROFIT
(with equalized wage rate and equalized 2-day profit rate, and positive
physical surpluses and balanced expanded reproduction over two days)
PHYSICAL QUANTITIES
===================
Inputs
Sec- --------------- Living
Day tor Good 1 Good 2 Labor Output__
1 10,100 10,100 1.01 20,201.01
1 2 9,900 9,900 0.99 19,800.99
tot. 20,000 20,000 2.00
1 9,900 9,900 0.99 19,800.99
2 2 10,100 10,100 1.01 20,201.01
tot. 20,000 20,000 2.00
1 20,000 20,000 2.00 40,002.00
1&2 2 20,000 20,000 2.00 40,002.00
tot. 40,000 40,000 4.00
PRICES AND PROFITS
==================
Costs
Sec- Unit ------------------------ Total
Day tor Price Good 1 Good 2 Total Price Profit
1 0.99 9,999 10,201 20,200 19,999.00 -201.00
1 2 1.01 9,801 9,999 19,800 19,999.00 199.00
tot. 19,800 20,200 40,000 39,998.00 -2.00
1 1.01 9,801 9,999 19,800 19,999.00 199.00
2 2 0.99 10,201 9,999 20,200 19,999.00 -201.00
tot. 19,800 20,200 40,000 39,998.00 -2.00
1 19,998 20,002 40,000 39,998.00 -2.00
1+2 2 20,002 19,998 40,000 39,998.00 -2.00
tot. 40,000 40,000 80,000 79,996.00 -4.00
NOTES: Equalized wage rate = 0. "Total Price" and "Profit"
figures rounded to two decimal places.
-------------------------------
Examining the lengthened period, Day 1+2, we seem to have an example of
strictly positive physical surpluses — 40,002 units of each good are produced,
while only 40,000 units are used up in production. Surplus-labor (equal to
living labor because wages are zero) is likewise positive, over the whole
period, and in each sector on each day. Yet each sector's profit for Day 1+2
is negative, because the cost of its inputs exceeds the total price of its
outputs. For convenience, the prices of the two goods are measured in units
of a third asset, not produced in this economy, but qualitatively identical
results, including equalized two-day profit rates, can also be obtained with
numéraire prices.
If valuation is simultaneous, however, i.e., if input prices equal output
prices, how can the cost of inputs possibly exceed the price of outputs when
physical surpluses positive? The solution to this riddle lies in the slight
(2%) variations in each sector's price and activity levels over the two
sub-periods, the latter of which causes a 2% physical deficit of good 2 on Day
1, and a 2% physical deficit of good 1 on Day 2. Because, on each day, the
size of one sector's deficit is about equal to the other's surplus, and
because the unit price of the deficit sector is
slightly (2%) higher than that of the surplus sector, the deficit is worth
more than the surplus. Profit is thus negative on each day.
It is also worth noting the plethora of equilibrium conditions packed into
this example. The wage rate is equalized across workers. Techniques of
production are not changing, and it is consistent with the example to assume
that all firms in a sector use the same technique. Over the two-day period,
the two sectors grow at the same rate, both in the sense that there is
balanced expanded reproduction of both use-values and, very importantly, in
the sense that profit rates are equal. By any reasonable definition,
everything is in equilibrium except that prices are slightly non-stationary.
Hence, if one construes a "period" to be of some reasonable length of time,
say two days or hours or minutes, then the extraction of surplus-labor is
insufficient for simultaneist "profit" to exist, even when (a) "daily"
physical deficits are very small in percentage terms, (b) physical deficits
are non-existent over two "days," and (c) profit rates are equal. The
theorems that claim the opposite are therefore true only if a non-negative
surplus of each use-value is produced in each and every period, no matter how
short one takes a period to be. (A "period" in this context can be no longer
than the length of time during which prices remain constant; but they can
change from one instant to the next.) This is the only way to rescue the
formal validity of these theorems. The shorter the length of a period,
however, the less likely it is that all physical surpluses will be positive.
For very short periods, it is almost inconceivable that this is the case.
Many factories and offices shut down overnight, but night in one part of the
world is midday in another. Some business is therefore always using up some
input that its supplier is not reproducing at that moment. Hence, if the
theorems in question are valid, they are irrelevant, because their key premise
is never true, while if they are relevant, they are false.
Table 2 presents a similar example. It shows that "surplus-labor" (according
to the standard, simultaneous dual-system definition) is zero, but
simultaneist "profit" is positive. The unit "value" of each commodity,
according to the interpretation in question, is 1, so the top set of figures
represent both physical and "value" magnitudes. Again, wage rates are equal,
techniques are not changing, the two sectors grow at the same rate (zero) in
physical terms, and their (positive) two-day profit rates are equal (1%).
This economy can also sustain itself ad infinitum, both in a physical sense —
two-day surpluses of both use-values are non-negative — and because the
capitalists are making profits. Even in this tableau, in which the economy is
in simple reproduction and everything is in equilibrium except that relative
prices vary modestly, the simultaneous dual-system interpretation implies that
surplus-labor is unnecessary for profit to be positive.
------------------------------
Table 2
ZERO SURPLUS-LABOR BUT POSITIVE SIMULTANEIST PROFIT
(with equalized wage rate and equalized 2-day
profit rate, and non-negative physical surpluses
and simple reproduction over two days)
PHYSICAL AND "VALUE" QUANTITIES
===============================
Wage Bundles
Sec- --------------- Living Surplus-
Day tor Good 1 Good 2 Labor Labor Output
1 29,997 29,997 59,994 0 59,994
1 2 9,999 9,999 19,998 0 19,998
tot. 39,996 39,996 79,992 0
1 9,999 9,999 19,998 0 19,998
2 2 29,997 29,997 59,994 0 59,994
tot. 39,996 39,996 79,992 0
1 39,996 39,996 79,992 0 79,992
1+2 2 39,996 39,996 79,992 0 79,992
tot. 79,992 79,992 159,984 0
PRICES AND PROFITS
==================
Wage Costs
Sec- Unit ----------------------- Total
Day tor Price Good 1 Good 2 Total Price Profit
10401/
1 9999 31,203 29,997 61,200 62,406 1206
1 2 1 10,401 9,999 20,400 19,998 -402
tot. 41,604 39,996 81,600 82,404 804
9601/
1 9999 9,601 9,999 19,600 19,202 -398
2 2 1 28,803 29,997 58,800 59,994 1194
tot. 38,404 39,996 78,400 79,196 796
1 40,804 39,996 80,800 81,608 808
1+2 2 39,204 39,996 79,200 79,992 792
tot. 80,008 79,992 160,000 161,600 1,600
-----------------------------------------
NOTES:
6. I am indebted to Alan Freeman for emphasizing this crucial point, and
for the example in the next sentence.
7. I am indebted to Karl Marx (Capital, vol. I, first section of Chap. 1)
for emphasizing these crucial points, but not for the example in the next
sentence.