2 Numeration of value and two
measures
2.1 Statement of the
problem
Numeration of value is such a fundamental concept in economics that it
hardly discussed. However, we focused on this concept in our examination
of the Marxian labor theory of value.
The most important previous criticism of the Marxian labor theory of
value has focused on the transformation problem. It was first raised in
1896 by Böhm-Bawerk as follows: in volume 1 of Capital , Marx
asserted the labor theory of value, but in volume 3 of Capital ,
he asserted the production price theory, which differs from the
statements made in volume 1. Subsequently, Bortkiewicz returned to the
problem algebraically, and Sweezy took it up in 1942. Then, Steedman,
Samuelson, Neumann, and Morishima, among others, examined the problem in
the 1970s. As a result, the problem has been debated for more than a
century, resulting in a highly mathematical argument that became very
difficult to settle.
After Bortkiewicz, the discussion focused on how the internal
inconsistency within Marxian theory could be resolved. The two theories
of Marx espouse inconsistent logic, leading to a serious discrepancy
that emerges when value is transformed into a price. In Marx’s
calculations, adding a general rate of profit to the cost price results
in a production price. However, in these calculations, the rate of
profit is not proportional to the quantity of labor inputs. The points
of dispute in the transformation problem are (1) whether surplus value
can be transformed into profit, and (2) whether value can be transformed
into prices. Both are difficult to resolve. Despite sufficient arguments
provided by econometrics, the transformation has only been proven in the
simple Leontief economic model and evidence for a general transformation
was not provided (Morishima1973).
In the 1980s, new approaches, such as the so-called New Interpretation
(NI), Simultaneous Single-System Interpretation (SSSI), and Temporal
Single-System Interpretation (TSSI), appeared11Such arguments
have been relatively accepted in the West, in contrast, not so much
known in Japan., and arguments over the transformation problem
entered a new phase. The dual system of value and prices was
self-evident in a conventional reading of Marx, but the NI, SSSI, and
TSSI criticize the dual system, taking a single system instead. Then,
based on the monetary expression of labor-time’ (Foley2000:21, Kliman
2007: 25), they considered that the relation between money and labor
time ‘preserves the rigorous quantitative relation between paid and
unpaid labor on the one hand and the aggregate wage bill and aggregate
gross profit on the other’ (Foley2000), in an attempt to make sense of
Marx by interpretation. They, however, abolished the transformation
problem; they only put a supposition in the definition that no problem
exists. Their approaches are criticized as a ‘contentless trick,’ or ‘ex
post accounting identities’ (Foley 2000). In any case, the controversy
surrounding the transformation problem, which has been rendered as a
question of internal inconsistency or interpretation, has not yielded a
true solution.
One of the known problems associated with the transformation problem is
the proof of exploitation. In the 1960s and1970s, Okishio proved
existence of exploitation mathematically, and Morishima named it the
‘fundamental Marxian theorem.’ Thereafter, the ‘generalized commodity
exploitation theorem’ was proved by Bowles–Gintis and Roemer. Their
studies, which belong to so-called analytical Marxism, do not solve the
internal inconsistency of Marxian theory despite exploring the existence
of exploitation and origin of profit. They concluded that not only labor
but also goods input into production are exploited. This can be
understood as a criticism against Marxian theory if construed as saying
that it is impossible to regard labor as special. However, the
conclusion that commodities are exploited is not acceptable for our
common belief.
According to their arguments, even if workers yield zero surplus labor,
profit can still be positive , because of exploitation of inputs
resources (Bowles and Gintis1981: 19). Because this is a refutation of
Marxian theory, Kliman, a proponent of the TSSI, strongly criticized
it.22Kliman insisted that the standard fundamental Marxian
theorem is disproved on the grounds that even if surplus labor of
workers is zero, profit can be positive (Kliman 2007: 179). However,
it is not proved. Something unknown may be the source of the profit.
However, if something unknown serves as the source of profit, what could
it be? This is an unresolved issue.
We posit that this failure to reach a comprehensive answer reflects
another unrecognized problem underlying the transformation problem. How
does a prenumerated value turn into a numerical figure? The conversion
mechanism has not been identified, a gaping hole at the center of the
transformation problem. Accordingly, all arguments developed based on
the transformation suffer the same central weakness, and their
mathematical solution becomes difficult. Unlike past discussions, we
return to the fundamental principle of numeration of value.
Since the NI, SSSI, and TSSI are hermeneutics to make sense of Marx’s
theory, their arguments are useless for examining the numeration of
value. Thus, our discussion continues without using their claims. The
analysis presented in this study is therefore able to show that the NI,
SSSI, and TSSI suffer from the same error as Marx.
2.2 Value measured by labor time and
money
First, let us consider a problem of the past arguments. To numerate
value we need a measurement. Two approaches exist when discussing how to
measure value. One approach considers that value is measured by the
amount of labor. Especially, Marx insisted that measurement of value is
labor time. He asked in the first section of volume 1 of Capitalhow the magnitude of this value to be measured. Then he answered that
‘plainly, by the quantity of the value-creating substance, the labour,
contained in the article’ (Marx 2014[1867: 28]). It is ‘the labour
time socially necessary for its production’, which is ‘that required to
produce an article under the normal conditions of production, and with
the average degree of skill and intensity prevalent at the time’ (Marx
2014[1867: 28]).
The other approach discusses numerical value as measured by money, that
is, price. Prices are determined by the market, and this approach
therefore focuses on the demand side, i.e., at the sale. Since this
measurement is in fact widely used, particularly in mainstream
economics, we hereafter describe it as the numerical value. Although
Marx used the first approach, he also treated production prices as being
measured by money in volume 3 of Capital .
Thus, we present the following question. If adopted measures differ,
like those used for money and labor time, are the values they produce in
fact comparable? To discuss this question, a necessary prerequisite is
to find out at what point in time each approach determines values. Value
measured by labor time is determined at production, whereas price is
determined in the market. However, in economics, there is no consensus
regarding the answer to this question because classical economics
emphasizes the supply side in the determination of value, and
neoclassical economics emphasizes the demand side.
The issue is further complicated by economics’ split into the classical
school and neoclassical school that occurred after the publication of
volume 1 of Capital . In the 1870s, a marginal revolution occurred
in economics through the work of Jevons, Menger, and Walras. The earlier
classical school studied the value of property from the production side;
in contrast, the new neoclassical economics school, presenting the
concept of utility anew, shifted emphasis to the demand side. At that
time, a dispute arose concerning whether prices are determined at the
supply side or demand side. Marshall ended this dispute, concluding that
‘as a general rule, the shorter the period which we are considering, the
greater must be the share of our attention which is given to the
influence of demand on value; and the longer the period, the more
important will be the influence of cost of production on value‘
(Marshall 1907: 350). By this conclusion, the classical school sees
value as determined by labor, and the neoclassical school sees prices as
determined by markets—a situation that has led these schools to work
in isolation. As a result, the theories of value and prices run parallel
and never cross.
Marshall’s assertion, i.e., approving both theories, is a gray-area
conclusion that offers tacit evidence that value is the same whether
measured at the supply or demand side. However, the question remains: at
what point in time are prices actually determined? This question has a
long history, originating with the distinction between natural price and
market price made by Adam Smith.
Substantial value is determined at production, next it is evaluated as a
price in the market. It is common that even if superior products are
produced, they are not adequately evaluated in the market. Marx used the
term ‘salto mortale’ to express the difficulty of predicting exchange
value (Marx 2014 [1867]: 71). It implies that we do not know a price
before a sale is made. Such examples show that a price is determined
only in the market. This empirical fact, however, is not proved in
economics.
Behind this problem, there are unique causal relations. (1) Substantial
value is determined at production, and (2) numerical value is determined
at a market: according to this, (1) is a cause, and (2) is a result.
Next, (3) added value at production is calculated after (2) and can be
known numerically. Then added value is determined by knowing that the
ex-post calculation can be traced back to the point of the cause, which
can be found at the past production point. We refer to this as the
retroactive causal recognition of added value. That is, both value and
prices of commodities are determined in the normal order of causality,
but the recognition of added value is not; this in fact goes backward in
terms of its causality. This retroactive causal recognition forces the
discussion to contend with the issue of determining the exact moment of
price determination. Of course, the present does not really affect the
past. It only appears to do so.
An important problem about this process can be found in Marxian price
theory. In volume 3 of Capital , Marx argued ‘the conversion of
surplus-value into profit’ and formulized ‘the value of every
commodity.’ Then he developed his price theory such that adding a
general rate of profit to a cost price turns into the production price.
However, although the formulas: C = c + v + s and C = k + s (Marx 2014
[1894]: 19) look like adequate, they have a problem about causality.
The reason is because added value as numerical data never emerges before
the ex-post calculation. Profit is always measured by money, and added
value also does not emerge except for as money. Marx’s explanation
involves predetermining the effect in causality by putting ex-post added
value before the effect (price). Marx’s production price constructed by
using this inadequate logic is impossible.
Nevertheless, Marx’s predetermination of the effect in causality has
been accepted by economists. One reason is that the retroactive causal
recognition disturbs our inference of the flow of time. The other is
that economics basically argues correlation rather than causation.
However, since production price of Marx’s arguments does not exist at
the point of production, causation cannot be ignorable. Anyway, it is
impossible to predetermine the effect without a time machine. Marshal’s
assertion may be adequate as an argument of determinants of value, but
it should not be regarded as evidence for the point of price
determination. That is, what point of time value is determined is
different according to the measurements; value measured by labor time is
determined at production, and value measured by money at exchange.
Let us return to the question mentioned above: if the measures adopted
differ, are the resulting values the same? We indicate here that they
too differ; different measures yield different values. For example, to
increase monetary value, we can improve the quality of goods to increase
their value, or we can simply raise the selling price. This shows that
the origin of monetary added value can be traced to two places:
production and sale. Therefore, the monetary value contains monetary
profits. On the other hand, value as measured by labor time cannot
contain monetary profits. That is, although value is substantially the
same in the two measures, their contents differ. Numeration of value is
not simply a matter of conversion. This is the issue that this study
adduces.
2.3 Process of transforming value into numerical
units
These two approaches have differing measures of value. Why does this
difference arise? To answer this question, we first construct a
principle of numeration of value. Prenumerated value is an idea.
Numeration of value cannot be separated from the process of exchange; it
is impossible to numerate a value without an exchange taking place. For
example, the manufacturing industry usually sells products to wholesale
stores, which is one form of exchange. When value is numerated through
this type of sale, the value that emerges not only arises in production
but also in the act of exchange itself. One viewpoint holds that the
manufacturing industry’s total profit was accrued by the manufacturing
process itself. However, this assertion does not hold. Substantial value
is created at production and profit is added through evaluation at
exchange; this is the process of numeration of value in the
manufacturing industry.
Here we must be cautious as the word ‘profit’ is being used in two
different senses. Profit usually refers to ex-post profits, which is the
sum of the added value at production and profits at exchange. In
contrast, profits at exchange are prenumerical profits, and being
numerated, they comprise a part of what we generally call profit.
It is difficult to recognize that profits are only added at exchange;
merely observing reality does not fully reveal the mechanism. We can,
however, reason it out by delving below observable reality. First, we
can increase ex-post profits by efforts at the place of sale, even in
the manufacturing industry. This fact proves that profit can be added at
exchange.
Second, we can reason that exchange creates profit from the fact that
commerce gains profit only by selling. The profit made from commerce
(i.e., wholesalers selling to retailers, and retailers selling to the
public, neither of which sets of transactions involve manufacturing and
thus exclude the surplus value added in the manufacturing process)
indicates that the selling price is higher than the cost price.
Furthermore, the manufacturing industry also obtains its profits through
sales, as the act of selling is the same for commercial and
manufacturing industries. If profits are negative, the manufacturing
industry will stop making transactions with a wholesale store to sell
directly to customers.
Third, ex-post profits fluctuate according to supply and demand. This
fact proves that value is not directly converted into prices. Such
fluctuations increase or decrease monetarily and do not exist at the
point of production. Both classical and neoclassical economics call this
element ‘profit.’ Sale prices in the manufacturing industry may also
fluctuate by market. Accordingly, the manufacturing industry also has
profits arising at exchange.
Judging from these facts and circumstances, profit in the manufacturing
industry is added at exchange. The manufacturing industry does not exist
to simply produce, but to exchange. This implies that a process of
numeration involves profit. Numeration of value is not the mere
conversion of measurements or units of measure. Although Marx claimed
that value emerges by exchanging equivalent values, equivalent figures
nonetheless include profit at exchange.
This new principle of numeration of value can explain why values differ
between the two approaches mentioned above. Numerical values consider
added value and profit at exchange; on the other hand, values measured
by labor time cannot consider profit at exchange. Therefore, the two
approaches’ measures of value encompass different factors.
Without understanding this, economists including Marx thought that since
value is unitary, value must be the same whether measured by labor time
or money. This lack of comprehension does not affect neoclassical
economics because neoclassical economics treats mainly market prices on
the framework of supply and demand concepts. In contrast, serious
problems exist in the Marxian labor theory of value.
The Marxian labor theory of value cannot incorporate profit at exchange.
Marx briefly examined the assertion of Condilac to represent the
circulation of commodities as a source of surplus value, and denied it
(Marx 2014[1867: 110]). And by overlooking profit, Marx mistakenly
constructed his theory. Since value of Marx excludes profit at exchange,
it does not match the price obtained at exchange, i.e., market price.
Whereas Marx’s definition of value differs from ours, so long as he
defines value apart from a price and theorizes the transformation of
value into a price, in the process to transform he never evades the lack
of the element. Even if you adopt the monetary expression of labor-time
(MELT), it cannot salvage the Marxian theory.
One further troublesome problem arises: it is impossible to numerically
correct for profit overlooked at exchange. In the manufacturing
industry, value is generated through two processes (value + profit) that
numerically emerge in monism. Value and profit are unified and
inseparable. We refer to this as ‘indivisibility of value and profit.’
This particular phenomenon comes into prominence when converting value
into prices. This indivisibility means that Marx’s surplus value is in
fact numerically uncertain, and mathematics cannot be used to argue
value before exchange.
In Marxian theory, the existence of surplus value can be confirmed by
examining the ex-post profits remaining in the hands of capitalists.
However, if value is generated in two places, you cannot determine the
ratio of value originating at production or exchange. When profits
emerging at exchange are large, it is likely that surplus value is zero
or negative.
The process of changing from dualism to monism is very difficult to
recognize. Since value and profit emerge in a state of numerical
unification, it is easy to assume that value alone is numerically
emerging. In such a view, profit at exchange disappears and the
transaction is seen as one of equivalent exchange. However, the
transaction nevertheless contains unobservable profit. Therefore, Marx
failed to recognize the phenomenon of numeration of value.
The Marxian labor theory of value was originated in classical economics.
Furthermore, Ricardo probably considered that production alone creates
the entire value of goods.33Ricardo stated the following in a
note: ‘Mr. Malthus appears to think that it is a part of my doctrine,
that the cost and value of a thing should be the same; it is, if he
means by cost, “cost of production” including profits’ (Ricardo, pp.
80). This suggests that Ricardo’s concept of value includes profits.
However, we can interpret Ricardo’s overall insistence that production
costs are just costs and do not include profits. He did not, however,
pursue the resources of surplus value; therefore, overlooking
unobservable profit at exchange does greatly reduce the significance of
his theory.
In Ricardo’s theory, goods have value equal to the value of their labor
inputs; in short, value equals wages. Consequently, it is theoretically
indefinite who creates the portion of value exceeding wages, i.e.,
profit. To revise Ricardo’s indefiniteness, Marx distinguished
labor-power from labor, and constructed a theory where capitalists buy
labor-power at the same value of the means of subsistence, which they
use to produce more value than they pay (Marx 2014[1867: 120]). This
is the basis of the process of increasing value, in which labor creates
all surplus value. In other words, while pinpointing the source of value
theoretically, Marx eliminated unobservable profit arising at exchange.
Thus, Marx considered that production value is the sole value.
2.4 Value created by sales
We will now discuss profit arising at exchange. Profit most certainly
arises at exchange; in other words, a sale also numerically creates
value. However, what is the nature of the numerical value created by a
sale? Where does it come from? To search for its origins, we explore a
situation where the numerical value from sale is larger than the value
at production and confirm its existence through examination of extreme
examples. Here for the sake of simplicity, we omit wholesale and retail
stores.
Early in the Industrial Revolution, workers long earned low wages, as
Marx indicated, before wages finally began to increase from the 1850s
onward. Therefore, no explicit proof exists that the high rate of profit
of the Industrial Revolution era depended on labor exploitation because
profits were earned in both low- and higher-wage times. In that era,
obtaining a high rate of profit would be easy because industrially
manufactured commodities enjoyed overwhelming predominance in
competition with conventional handiwork commodities, whereas competition
between factories remained rather low. The high rate of profit is often
attributed to increased efficiency through the division of work, as
mentioned by Adam Smith. However, generally speaking, even if
innovations in industrial technology occurred, when prices decrease in
line with cost savings attributable to increased efficiency, the overall
rate of profit should not increase. Innovations in industrial technology
occurred; moreover, in such a situation, when they competed with the
conventional manufacturing system, a high rate of profit was realized.
This high rate of profit is obtained by winning in the competition at
sale, and it indicates that value numerically arising at the moment of
sale is large.
When markets mature, advertisements are required for companies to
increase sales. Advertising not only stimulates demand but also
increases the rate of profit as it avoids a decline in price due to
excessive competition between companies. Therefore, this indicates that
as prices increase as an effect of advertising, advertisements can be
said to create numerical value at sale. Moreover, in a mature market, it
becomes difficult to make profit simply by producing excellent products
given that competition among companies often takes the form of lowering
prices. Consequently, to avoid falling into this price-cutting cycle,
some other form of differentiation is needed, such as adding an idea or
responding to various customer needs. Product differentiation can also
therefore be used to avoid price-based competition and thus ensure that
sales produce constant value. Thus, corporate efforts to increase
profits in a mature market often focus on increasing the numerical value
arising at the point of sale rather than on reducing costs.
ICT (Information and Communication Technology) companies such as
Microsoft and Apple sometimes realize a substantial rate of profit
through monopolizing an operating system used on a majority of personal
computers or by creating original products that their competitors cannot
produce. Their sizable rates of profit are realized by obtaining large
profit at sale. This, in turn, can be traced back to having the power to
dominate prices in a market, not because value as labor embodied in a
product through the Chinese factory is overwhelmingly large. According
to conventional wisdom, such a high rate of profit is based on
outstanding technology. However, if rivals can easily copy an
innovator’s new technology, the business falls into excessive
competition and the rate of profit will drop. To determine the dominance
of price controls, the competitive edge conferred by patent protection
must be considered. Thus, the substantial rate of profit in ICT
companies can be traced to value numerically created by sales. We can
refer to the technological developments made by ICT companies as
innovation; their value is not created solely through technology but
also by them maintaining their dominant positions through their ability
to control prices.
As we have indicated, several phenomena exist that we should explain
with introducing the concept of value numerically created by sale. The
fact that profit rates can increase when competition is not strong is
proof that labor is not the source of all value. Although value created
by sales is numerically unknowable, it most certainly exists, while the
unobservable nature of profit at exchange led Marx to overlook it in his
theory.
Marx understood that value does not always coincide with price.
According to the Marxian theory, real market is in disequilibrium, and a
market price deviates from value. It does not justify his theory. The
value of Marx is not monetarily numeral. If it is so, what should we use
as a criterion to assess the deviation?
It is interesting to explore the value numerically created by sales
because it has not been argued previously; furthermore, in this study,
we do not go far into this argument. The concept of value numerically
created by sales can contribute to renewaling the innovation study,
which no more takes value created at sales into account than Marx. When
this concept’s validity is accepted widely, Marx’s spell will be broken.
2.5 Defects in the exploitation
concept
The same problem exists in Marx’s exploitation concept as in his value
concept. Marx considered that exploitation occurs at production, but
exploitation occurs elsewhere as well. Since a sale also creates value,
exploitation can also arise at the point of sale. Consequently, a
phenomenon emerges that Marx entirely failed to consider.
A capitalist requires two types of people from whom to derive profit:
workers and consumers. A capitalist obtains profit from workers at
production. He also obtains profit from wholesale stores and retail
stores when selling products. Omitting the distribution industry for the
sake of simplicity, a capitalist obtains profit from unspecified
consumers. A capitalist thus obtains profit from two channels: workers
and consumers. A worker provides labor to a capitalist with whom he
contracts to provide his labor in exchange for wages, and by whom he is
exploited. A consumer purchases goods with the wages obtained by labor;
in doing so, he is exploited by paying excessive prices to retail stores
(for simplification, capitalists). In this way, a capitalist and a
worker-consumer ensure that transaction partners change, making a loop
and thus powering economic circulation. The specific value of each of
the exploitations is numerically unknowable.
Value created by sales is exploitation of consumption. Workers are
exploited in both labor and consumption. Because a capitalist and a
worker contract over employment, exploitation in this transaction can be
criticized as plunder from the result of labor. Exploitation at the
retail store, however, cannot be criticized as plunder. Instead,
consumers are ‘exploited’ through their voluntarily paying of excessive
prices (providing profit) to retail stores. At that time, consumers have
the freedom to choose: they can elect to buy products in pleasing stores
and consent to paying excessive prices, or not. Marx did not incorporate
such exploitation of consumption, claiming that exploitation only occurs
in the capital–labor relationship.
Exploitation of consumption suggests that exploitation occurs in
corporate transactions as well. The manufacturing industry exploits
wholesale stores, who in turn exploit retail stores. Both wholesale and
retail stores perform commercial transactions to obtain profit by
reselling. Therefore, we consider it unsuitable to apply the
exploitation concept, which implies plunder, to these transactions.
The high rates of profit that IT entrepreneurs seek are also derived
from exploitation of consumption. Successful innovation requires
substantial exploitation of consumption. No matter how high the rate of
profit, nobody will criticize innovation because it creates new value
and generates new demand.
The state of obtaining large profits at sale is also realized through
both monopoly and regulation. If monopolized goods are infrastructure
such as electricity or gas, or commodity necessities such as rice or
wheat, no matter how expensive they become, people have to buy them. It
is not desirable for excessive payments to be extracted where no
substitutes exist. This example of exploitation of consumption shows
that exploitation may also occur in a national monopolistic undertaking
or through governmental regulations. Marx overlooked such exploitation
of consumption, suggesting that his exploitation concept lacked
effectiveness as a criticism of capitalism.
Regarding the fundamental Marxian theorem, Okishio and Morishima
accepted the Marxian theory’s exploitation concept that only labor is
exploited, and created a formula based on this premise. Distinguishing
explicitly between the value accounting system and the price accounting
system, Morishima sought to prove the existence of exploitation.
However, just before the conclusion, he asked, ‘What conditions are
necessary and sufficient for the existence of a set of non-negative
prices and a wage rate yielding positive profits in every industry?’
(Morishima 1973: 53). He demonstrated that this would occur if and only
if a ‘real-wage rate’ is given such that the rate of exploitation is
positive. However, this is not a necessary and sufficient condition.
Even if the rate of exploitation (in production) is negative, profits
are still positive when the rate of exploitation of consumption is
positive. That is, since exploitation occurs at both production and
consumption, their argument is wrong in its premise.
After Okishio and Morishima, Bowles and Gintis presented ‘the peanut
theory of value and energy theory of value’ (Bowles and Gintis 1981: 19)
as an appendix of their paper; that is the ‘generalized commodity
exploitation theorem.’ Their argument states that not only labor but
goods that serve as inputs to production, for example, peanuts and
energy, are also exploited because all inputs resources may have the
same form of equation as that of labor-power (Bowles and Gintis1981:
19). Additionally, Roemer (1982) presented ‘a general theorem of
exploitation and class.’ Their assertions can be understood to imply
that labor is not the only source of value. In this point, they moved
forward from Okishio and Morishima’s conclusion. However, the conclusion
that goods such as peanuts and energy are exploited is too strange for
our common sense to accept.
Their conclusion stemmed from their method to convert input into output
without understanding the mechanism of profit at exchange or
exploitation at consumption. It is true that there may be no difference
analytically between labor and the other raw materials; however, they
have no evidence of the exploitation of peanuts. Although their process
of reasoning to the problem will be appreciated, their conclusion should
be revised. It is labor and consumption that are exploited, while
production and sales create value.
2.6 Failure of the transformation
concept
This study has already provided the answer to the error of the Marxian
value theory. Labor is not the sole origin of surplus value; that is,
sales, too, create surplus value. This is the crucial problem. If so,
discussions of the transformation problem do not have much meaning, but
we examine it to settle the disputations.
In past discussion of the transformation problem, one focus has been on
the fact that Marx’s theory is inconsistent regarding the rate of profit
for each segment of industry. In Marx’s theory, the profit rates for
each segment of industry do not correspond and the profit rate is not
proportional to the amount of labor inputs. This is an evident error of
Marx. Samuelson provided a case in which Marx’s calculation is
consistent, one where the organic composition of capital is equal. This
is a singular case, and therefore it is not realistic. Then he instead
considered what might be called the case of ‘equal internal compositions
of (constant) capitals’ (Samuelson 1971). In such cases, value and price
is consistent; does it prove the accuracy of Marx’s procedure?
Discussions of internal inconsistency cannot resolve the issue,
revealing this process’ own limitations.44Steedman’s joint
production (Steedman 1977: 150) is a similar example. Accordingly, we
approach this issue from a different angle.
With regard to the transformation problem, after Bortkiewicz, economists
have approached the problem by considering Marxian theory as a dual
system: one in terms of value and the other in terms of prices. The
value calculation in the dual system, however, as we have repeated
above, contains no profit at exchange; it is erroneous. Although Marx
sought a concrete criterion of value, in numeration of value, an
abstract element is added, and the numerated economy cannot be discussed
by materialism.
Furthermore, the second element of the dual system, the production price
calculation is impossible. The production price theory, which Marx
developed in volume 3 of Capital , has misunderstandings by the
retroactive causal recognition . Cost prices can be calculated by adding
up costs. From the Marx’s formulas (Marx 2014 [1894]: 19), merely
adding profit onto costs yields the price. Then, Marx insisted
‘equalisation of the general rate of profit through competition’ (Marx
2014 [1894]: 126) , predetermined the general rate of profit and
totaled it. However, ex-post profit cannot be causally added like costs.
It may be possible to calculate an average rate of profit using past
data on profits, but current prices are determined by the market. We
refer to this flaw as the causal impossibility of adding up costs.
Steedman (1977), a Neo-Ricardian, putting a physical system before the
value system and price system, takes the physical quantities approach.
It is an argument without reference to value. This lets him abandon the
transformation problem as a pseudo problem. This approach is based on
Sraffa’s (1960) framework. In Sraffa’s model,55Sraffa models the
special case on the supposition: an annual cycle of production with an
annual market (Sraffa 1960: 10). His model is simultaneous determinism
mathematically realized under this condition; it also predetermines
the cause substantially because in his model the rate of profit is
determined earlier than the real point of determination. physical
data determine the rate of profit and relative price. This approach,
however, is just mathematical determinism, and the model abstracts both
a numeration principle and causal relations; that is, it abstracts the
both defects of the Marxian value theory and production price theory.
Therefore, it will seem to indicate that Marx was right, but in fact, it
predetermines the rate of profit under special conditions and does not
reflect reality. Using this framework, Sraffian economists examine input
and output as the physical system. However, this does not hold, if not
on the condition of Sraffa.
As we have argued, the value system is erroneous and the production
price system is impossible. The physical system cannot rescue the
defects of the dual system. Therefore, transformation is impossible, and
the transformation concept itself is flawed. Marx’s so-called production
price does not exist. Even if you take a macroscopic view, aggregate
value never includes profit at exchange and aggregate production price
is impossible. Therefore, Marx’s two propositions about aggregate
equalities also fail to hold too. Since in the conventional dual system
approach to the transformation problem, both underlying premises are
erroneous, and the disputants notice none of them, the approach would
never produce valid results. Despite the many discourses in the history
of the dispute over the transformation problem, a reexamination will not
be productive.
After all, value can be numerated neither by labor time nor by totaling
costs. Price must be derived from a market exogenously. Although
classical economists (including Marx) have long argued value as
economics, strictly speaking, it is impossible because of adding up
costs.
Not noticing these errors, the NI, SSSI, and TSSI radically criticized
the dual system approach and physicalism (Kliman 2007: 157). They
emphasize their ability to interpret Marxian theory in a manner that
renders it logically consistent and elaborate to interpret as the single
system. We, however, have indicated the existence of dual defects in the
value theory and the production price theory. Consequently, internal
inconsistency is a logical outcome. We cannot make sense out of their
effort to interpret.
In brief, both the Marxian value and price theories predetermine value
and price in causality at the point of production. Such predetermination
is incompatible with profit at exchange in numeration. Therefore, value
and price calculations become inconsistent in that theory. To resolve
it, the NI construes variable-capital value as the actual sum of money
wages (Foley1982, Duménil1983). Then, as inconsistencies still remain,
the SSSI applies the same method of determination also to constant
capital (Moseley2000). Nevertheless, inconsistencies continue to remain,
thus the TSSI advances the supposition that the valuation is temporal,
with value and price being determined interdependently (Kliman 2007: 2).
In such ways, the proponents after the NI devised artificial methods to
solve the internal inconsistency of Marxian theory. However, such
‘Band-Aid’ approaches never resolved (or interpreted) the real problem.
2.7 Impossibility of measuring labor
time
Previous arguments in economics assumed that value could be determined
no matter what scales of measurement were used. However, this assumption
does not hold because price does not emerge before exchange by money.
For example, the price of a McDonald’s Big Mac can be used to compare
the purchasing power of each country’s currency. However, despite this
ability, the economy cannot be numerated by the Big Mac. Only items
already used as money somewhere in the world (such as gold, silver,
rice, wheat, shells, stones, and cloth) can numerate value in a society.
Since measurement units of labor time are not used anywhere in the world
to numerate value, these units remain an abstraction.
Nevertheless, such a measure has been accepted consistently, partly
because such a measure of labor time is useful to decide wages for
factory workers, who perform limited and specific tasks. However, it
only determines wages, not the product’s value.
Numeration of value is the fact that we have numerated in the past,
i.e., determined a price. Numeration is practice, and there is no price
before practice. In addition, no measures except money can let price
emerge.
In mainstream economics, GDP encompasses only economic activity that
appears as prices. Domestic labor, such as household labor, is not
contained in GDP because no money changes hands. Furthermore, the
self-consumptive element of agricultural products is not contained in
GDP by usual calculation methods; therefore, a special imputation
calculation is required. The economy is the movement of money, no more
than a locus of past trading.
Nevertheless, a black box exists in the process between value and price.
Numeration of value is more profound than we think. This problem
overlaps what Marx argued as reification. Marx considered the mystery of
value as follows: the social relationship of labor is perceived to be
its exchange value, as the fetishism of commodities (Marx 2014
[1867]: 46). However, this explanation seems to drive the problem
out of the falsifiable world, indicating that it cannot be proved or
disproved; therefore, another approach is needed. We shall examine this
point in the following section.