Advances in Systems Science and Application (2016) Vol.16 No.3 1-10

on Mutual Coincidence of Return on Capital
Measuring Principles by Adam Smith and Karl Marx
(A Critique of “Capital in the Twenty-First Century”

by Thomas Piketty)
S.Baizakov1,Y.Utembayev2,A.R. Oinarov3 and J.Forrest4

1 Scientific Supervisor, JSC "Economic Research Institute"; Astana, Kazakhstan;
2 Independent expert, Astana, Kazakhstan;

3 OinarovAzamat, Chairman of the Board of the JSC "Kazakhstan Center for
Public-Private Partnership", Astana, Kazakhstan;

4 Jeffrey Forrest, School of Business, Slippery Rock University, Philadelphia, USA

Annotation
In his book “Capital in the XXI Century” by Thomas Piketty justified the two
basic laws of capitalism. On the basis of these economic laws Thomas Piketty
concluded destabilizing role of accumulated national capital. Based on his critical
analysis this paper studied alternative ways of identification and knowledge of the
objective laws’ system that would become the tools of detection imbalances in the
economy and assessing the impact of the regulatory impacts on the development
of a market economy. Develop an appropriate model for the analysis of regulatory
impacts.
Keywords Capital, Profitability, Scientific and technological Potential, Law, Macroe-
conomics, Balance, Effect Methods
Thomas Piketty, author of the bestselling book “Capital in the Twenty-First Cen-
tury”, has paid serious attention to the methods of measuring economic growth,
including the method of measurement of nominal GDP, defining its by multipli-
cation of return on capital by its volume. He correctly noted that “the concepts
of inflation and growth are not always very well defined. The decomposition of
the nominal growth (the only kind that can be observed with the naked eye, as
it were) into a real component and inflation component is in part arbitrary and
has been the source of numerous controversies” [1].

Speaking about the effects of accumulation and return on capital’s decrease, he
notes, “...on the basis of historical experience, the most likely outcome is that the
volume effect will outweigh the price effect, which means that the accumulation
effect will outweigh the decrease in the return on capital.”[1]. At the same time, he
pays attention to that in agriculture there is a reverse process: “... capital (such
as farmland in the case in point), it is inevitable that beyond a certain point, the
price effect will outweigh the volume effect... There is no better illustration of the
maxim “Too much capital kills the return on capital” than the relative value of
land and land rents in the New World and the World” [1].

In general in the Piketty’s book, the principle of two-dimensional measurement



2 S.Baizakov, Y.Utembayev, A.R.Oinarov, J.Forrest:on Mutual Coincidence ...

of economic growth was successfully used to analyze the price effect, as a form of
the capital’s cost in its form of goods, and volume effect, as a form of the capital’s
cost of in its form of money. The same principle is used for two-dimensional mea-
surement of the two fundamental economic laws of capitalism (in the terminology
of the author).

However, deeper analysis shows that these laws have no any relation to the fact
that the “the volume effect is will outweigh the price effect, which means that the
accumulation effect will outweigh the decrease in the return on capital”. Moreover
it hasn’t related to“...farmland in the case in point it is inevitable that beyond a
certain point, the price effect will outweigh the volume effect”. Pikettydoes his
findings on the basis of historical retrospective in some combination of it with the
dynamics of economic laws. The reason for these inconsistencies and inaccuracies
has often derived from an outdated theoretical basis of establishment of analytical
toolsthat are being used now in the practice of market economies institutions and
management agents’ regulatory impact assessment.

In our opinion, the main factor that has a destabilizing effect on the sustain-
ability of the market economy is the outdated persistence of a one-dimensional
measure of return on capital, which is recommended by Adam Smith as a tool to
assess the true value of goods and money[2].

So, up to this day the principle of a one-dimensional measure of return on
capital by Adam Smith has existed in the theoretical basis of current models of
balanced economic growth. As an example, the traditional formula of the GDP
deflator (inflation) - pb, can be taken for, which has the known form as follows:

pb =
NGDP

RGDP
(A)

where NGDP-is nominal GDP, which by its content is the final product in money
terms.

The theoretical basis of the formula (A) is the Adam Smith’s principle of a
one-dimensional measure of return on capital. According to this formula, if nom-
inal GDP (NGDP) grows faster than real GDP (RGDP) in the long term, what is
happening in some developing countries nowadays, then the GDP deflator (pb) as
an indicator of inflation, fueled by the national currencies devaluation may tend
to infinity (pb −→ ∞).

This is not the only example, which defines the Adam Smith’s principle of
one-sidedness of return on capital’s measurement and its limitation as a balanced
growth’s theoretical base models. Thus, in the equation of monetarism, by re-
placing pb*RGDP onto NGDP, we have got:

NGDP = V ∗M

where M - money supply, V - velocity of money.



Advances in Systems Science and Application (2016) Vol.16 No.3 3

Since V (velocity of circulation) according to the monetarism model is a con-
stant, and taken M (money supply) tending to infinity, then nominal GDP (NGDP)
may also tend to infinity. Even though Thomas Piketty properly finds out the
formula (A)’s limit to assess the balanced economic growth, he himself falls into
the formula’s trap. For instance, in his analysis of the real growth rate’s measure-
ment tools ThomasPikettyhas failed to go beyond the limits of the Adam Smith’s
principle of a one-dimensional measure of return on capital.

His artistic success in the establishment of two economic laws of national income
and the national capital, could not spread further towards the correct breakdown
of “nominal growth into real and inflationary components”, and towards the e-
limination of errors in evaluation methods for growth rateand inflation. In short,
Thomas Piketty diagnosedproperly the market economy disease, but was not able
to determine the treatment methods.

Identification and knowledge of the market economy development laws is need-
ed to make key management decisions and adjustments of previously taken ones.
Otherwise, inaccurate directions and contradictory readings of analytical tools
result in the destabilizing and social inequalities that are listed in the Thomas
Piketty’sbook.

As already mentioned, the theoretical basis of all actual current market equi-
librium and balanced growth’s models, including Piketty’s economic equilibrium
model, up to this day is founded on the Adam Smith’s one-sided principle of return
on capital’s measurement. Adam Smith’s one-sided approach consists in reducing
the economic growth’stwo-dimensional,by working time and national currency,
measurement system into the one-dimensional system measured by money.

For Adam Smith, “the annual cost of the product” is identified with “the cost
that is newly established during the year[3]. More precisely, he was correct that
the value of the annual product can be reduced to the same components of the
newly created during the year value. Adam Smith and his modern followers are
right in establishing the value of the final product by deducting material resources
spent costs from the “cost of the ready product”. From a mathematical point of
view these transactions by A.Smith and his followers are perfect.

However, economy development indicators, both by the Adam Smith’s theory
and by the Karl Marx’s theory, are measured in the first place by working time.
By both theories the price of the working time is the base measure for productive
forces of labour and capital . Thus, Adam Smith specifically states that “Labour
measures the value, not only of that part of price which resolves itself into labour,
but of that which resolves itself into rent, and of that which resolves itself into
profit”[2]. Then he gives a specific example:“In the price of corn, for example, one
part pays the rent of the landlord, another pays the wages or maintenance of the
labourers and labouring cattle employed in producing it, and the third pays the



4 S.Baizakov, Y.Utembayev, A.R.Oinarov, J.Forrest:on Mutual Coincidence ...

profit of the farmer. These three parts seem either immediately or ultimately to
make up the whole price of corn. A fourth part, it may perhaps be thought is
necessary for replacing the stock of the farmer, or for compensating the wear and
tear of his labouring cattle, and other instruments of husbandry. But it must be
considered, that the price of any instrument of husbandry, such as a labouring
horse, is itself made up of the same time parts; the rent of the land upon which
he is reared, the labourof tending and rearing him, and the profits of the farmer,
who advances both the rent of this land, and the wages of this labour. Though
the price of the corn, therefore, may pay the price as well as the maintenance of
the horse, the whole price still resolves itself, either immediately or ultimately,
into the same three parts of rent, labour, and profit.”[Ibid, p.105].

This approach of Adam Smith is static, and focused on the short term and for
a momentary effect when the scientific and technological potential of the country
has no time to be updated, or when its impact on the real economy can be ig-
nored. Karl Marx’s approach is focused on long-term development and the market
economy sustainable development. But his approach does not replace the Adam
Smith’s principle of return on capital, but summarizes and complements it.

A commodity, according to Marx, is in development, its dividing onto “the
goods and money is the law of the expression of the product as a commodity”
[3]. It is this law Thomas Piketty did not consider by partly remaining within
the framework of the Adam Smith’s principle of a one-dimensional measurement.
He failed to take into account that goods and money were developing and trans-
forming into capital, which became a form of its product or its form of money.

In the third volume of “Capital” which explores the development and self-
development of capital in general Karl Marx introduces two-dimensional mea-
surement of capital in its form of money and capital in the form of its goods.
These measures or economic growth measurement “rulers” are being presented by
working time in form of man-hours and money in form of the national currency
of each country.

Marx’s summary with respect to the Adam Smith’s one-dimensional approach
is the following: “He does not distinguish the dual nature of labour itself, i.e.does
not distinguish between labour,as a cost of wage creating value, and labour, as
a specific and useful labour creating commodities (use-value). The total amount
of goods produced in a year i.e. an entire annual product is a product of useful
labour active during the past year; all these products exist only due to the fac-
t that publicly employedlabourwas consumed in diversified extensive system of
various kinds of usefullabour. That is the only reason the cost of the means of
production has been consumed during manufacturing but kept in the total cost
of manufactured commodities, preserved as reappearing in a new kind. Conse-
quently, the entire annual product is a result of the useful labour expended during



Advances in Systems Science and Application (2016) Vol.16 No.3 5

the year. But only a part of the annual cost of the product has being created
newly; this part is the newly created cost for the year, which embodies the sum
of labour,spent during the year” [3].

Our studies done based oneconomic science latest achievements, in particular
the Nobel Prize Leonid Kantorovich and TjallingKoopmans’ duality principle,
show that Adam Smith is partly right in saying that “the cost of the annual prod-
uct”,according to that principle, can be reduced to “the newly created cost for the
year.”

The Adam Smith’s principle of return on capital allows to estimate the cost
of capital in its form of money; while Karl Marx is right in saying that the total
costs of producing a particular product, as capital, in the form of its goods are
consumed in the production of the final product “capital plus income” [4]. Both
of these indicators are not just theoretical, but also have a crucial practical sig-
nificance.

In accordance with the principle of duality, they form the basis for the two-
dimensional measurement of the balanced economic growth. Thus, the newly
created value for the year by Adam Smith is an exact expression of the cost of
capital in its form of money. The practical implementation of this concept is
found in the nominal GDP, which is the cost of the final product. And the cost of
the annual product by Karl Marx is an exact expression of the cost of capital in
its form of goods. The practical implementation of this concept is in real GDP,
which is to represent the volume of actually produced final product.

The conclusion is that to eliminate errors in the measurement of inflation and
real growth,which is possible by adding the Adam Smith’s one-dimensional ap-
proach with the Karl Marx’s approach based on assessmentof the labour’ total
costs, that are objectively necessary for the production of the given structure’s
final product amount. Therefore, the rationale of the new market equilibrium
equation can start from that point where ThomasPikettystopped his theoretical
research of two-dimensional measurement: of the national income ĺCby money,
and of the national capital ĺC by working time, man-years.

In this case, the duality theory allows you to take advantage of the two-
dimensional measurement criterion. Firstly, the cost of the working time is mea-
sured by estimating the product’s direct and full labour-intensity of economic
activities. Second, the cost of the final product (nominal GDP) and resources to-
tal costs for the production of nominal GDP are set in monetary terms. According
to the duality principle, solutions for interlinked problems identified on the basis
of the industries intersectional balance report will meet following criteria [5-7]:

L = t ∗X = T ∗ Y (B)

where t - is direct line and T- product fulllabour-intensity, L - the entire fund
of working time, in man-years, Y- final product value (nominal GDP) and X-



6 S.Baizakov, Y.Utembayev, A.R.Oinarov, J.Forrest:on Mutual Coincidence ...

resources full costs for the nominal GDP production.
Fourthly, we introduce the extension transformation below:
The tool for solving the contradictory problem is extension transformation. By

using certain transformations, an unfeasible problem can be transformed a feasible
one. We only introduce the general concept and the basic types of transformation.

In the formula (B), each component of the full labour-intensity Tof the final
product value Y is determined by the scalar multiplication of the product’s direct
labour-intensity components t by components of each column of the full costs
technology matrixB = (E - A)-1, which serves as a carrier of scientific and tech-
nological progress and, therefore, the true value of goods and services.

At the national level we have the equalities t = L / X and T = L / Y. From
here we denote the level of scientific and technological potential (STP) as c and
get as follows:

c =
t

T
=

Y

X
(C)

STP ratio of the country c with its growth (+,-) is determined either by the
magnitude of the margin, which is correlated with changes in the prices of goods
and services, or by the amount of rent which changingrate is correlated with the
intensity of productive resources utilization.

In any case, the effect of volume, which represents the level of scientific and
technological potential of the country, is measured by the difference between the
growth in labour productivity, defined by value of the final product and used in
its resources production, as they have both utilized the very same equal fund of
working time:

c

c
=

Y/L

Y/L
− X/L

X/L
.

The new equation of market equilibrium derives from the basis of adding the
Adam Smith’sprinciple of return on capital to the principle based on the ratio of
direct and fulllabour-intensity, as determined by the Karl Marx’s theory of capi-
tal’s labour value.

Thus, on one hand, the new equation ofthe balanced economic growth of nom-
inal value of the final product (NGDP = Y) defined by the formula:

NGDP = c ∗X.

In this formula the level of national income is measured by the value of nominal
GDP. It is determined by multiplying the level of scientific and technological
potential (STP) of the country c by a volume of domestic capital X. Here, the
scientific and technological potential (STP) of the country c represents coefficient
of national capital efficiency. This equation is the analog of the first fundamental



Advances in Systems Science and Application (2016) Vol.16 No.3 7

law of market economy development, defined on the basis of the principle of
duality.

On the other hand, multiplying both sides of the GDP deflator equation by the
purchasing power of the national currency (not to be mixed up with purchasing
power parity) pp, we have got as follows:

pp ∗NGDP = pp ∗ pb ∗RGDP

Hence we have a qualitatively new equation of balanced economic growth, which
determines the actual volume of the final product RQ:

RQ = pp ∗NGDP = pp ∗ pb ∗RGDP (D)

where NGDP, as well as previously, represents nominal GDP, which determines
the cost of the final product, and its multiplication by the level of the true value
of money represents the real final product.

Since the pp * pb is equal to c = NGDP / Xas by definition the value of money
pp = RGDP / X, while the GDP deflator pb = NGDP / RGDP, then the pur-
chasing power of money (not to be mixed up with the parity of purchasing power
of money) is defined by formula:

pp =
c

pb
,

where the value of the ccoefficient, which represents the level of scientific and
technological potential of the country, is determined by the ratio of direct labour-
intensity to its full labour-intensity (t / T).

This ratio is determined due to the principle of duality solution for interlinked
problems, based on the data of given reports on the industries intersectional bal-
ance of the country; and it is equal to the ratio of the value of the final product
cost used in the country to the total consumption of resources used for its pro-
duction (Y / X).

To change economic policy, aimed at establishing a real growth index of prices
of goods and services, and the level of depreciation of the national currency, is
doable due to the system of economic laws and regulations, which are derived
from combining the Adam Smith’s principle of one-dimensional measure of return
on capital to the Karl Marx’sprinciple of two-dimensional measurement of return
on labourand capital.

The main ones, which are caused by the definition of the true cost of price
indices of goods and services by the purchasing power of money, are as follows:

1) The law on determining overall impact of the takenincentives on innovative
investmentsinto the economy and on scientific and technological improvement of
the production process, including the strength of competition c(t):

c(t) = NGDP/X(t) ̸= 1,



8 S.Baizakov, Y.Utembayev, A.R.Oinarov, J.Forrest:on Mutual Coincidence ...

Though on the basis of return on equity ratio by Adam Smith an STP co-
efficient: c (t) = pp ∗ pb = 1,because by definition, the value of money pp =
RGDP/NGDP , and the GDP deflator pb = NGDP/RGDP .

2) The basic law on determiningreal purchasing power of money, as the ratio
of the scientific and technological potential of the country to the GDP deflator
pp(t):

pp (t) = c (t) /pb (t) .

3) The law on determining prices of goods and services pc(t) = 1/pp(t):

pc (t) = 1/pp (t) = NGDP (t) /(c (t) ∗RGDP (t)).

4) Leading law on determining real growth of the final product on the basis of
nominal GDP growthRQ(t):

RQ (t) = pp (t) ∗NGDP (t) .

5) The control law on determining real growth of the economy, on the basis of
real GDP growth RQ(t):

RQ (t) = c (t) ∗RGDP (t) .

6) The law on defininga GDP deflator, the general price deflation of goods and
services pb(t):

pb (t) = c (t) /pp (t) = NGDP (t) /RGDP (t) .

7) The law on determining net benefits of promoting scientific and technological
advances and competition (±△c (t)):

±△c (t)% = (c (t) /c (t− 1))%− 100%.

Since any incentives on scientific and technological improvements have certain
expenses of costs of labour, capital and materials then their return is associated
with risks, and return on these funds can be a value greater than 100 and less
than 100. However, where the competitive environment is developed there the
contribution of science and technology potential into the development of the real
economy, as a rule, would be positive.

The exceptions are those developed countries where sources of reduction of
material resources through scientific and technological advances have been ex-
hausted; and those countries trying to maintainthe efficiency of their economies
at the expense of reducing their national currenciespurchasing value. However,
these attempts are easily detected by a tool developed with the help of a system
of laws to promote competition in the market economy.



Advances in Systems Science and Application (2016) Vol.16 No.3 9

The path to sustainable economic growth goes through the open labour mar-
ket, focused on the final product production. Thus, last five - six years the actual
“restoration” of the old world monetary and financial system by transferring pri-
vate risk to the global (system-wide) level, and by the public debt exponential
increase in a number of leading countries and the money supply, makes the issue
of transition to a new world economic order more difficult.

The problem of transition from the current crisis and unstable state of the world
economy to a sustainable growth mode should be investigated in the system, as
shown above, in the unity of the macroeconomic, sectoral and microeconomic as-
pects of market economy development based on feedbacks that exist between the
various regulatedagents, and of patterns of the long-term economic development
countries of the world.

This approach significantly expands the understanding of the causes of the glob-
al financial crisis, allowing to realise mechanisms of modern economy reproduction
and to develop reliable tools for its sustainable development. Thus, the history
of economic thought tells that objective laws of market economy can justify new,
adequate to the new world economic order, models of economic governance, by
which it will be able to ensure the unity of the three product types: nominal, real
and final.

By and large, the core to ensure the unity of three GDP growth rates is the
final product, the real value of which is determined by the equation (D) under the
influence of the real purchasing power of the national currency at nominal GDP
and the rate of scientific and technological potentialat the real GDP.

According to this model of balanced economic growth the procedure of targeting
nominal GDP is implemented instead of inflation targeting’monetary policy.This
is the Tate-Shafarevich group: XE/K . Here it is as a subscript: AX .

References

[1] Piketty and Thomas(2014),Capital in the twenty-first century,The Belknap
Press of Harvard University Press.

[2] Smith and Adam(2007),An Inquiry intothe Nature and Causes of the Wealth
of Nations,Moscow EKSMO.

[3] Marx and Karl(1978),Capital,Critique of Political Economy:The Process of
Circulation of Capital,vol.IV, 648 p.

[4] Marx and Karl(1975),Capital,Critique of Political Economy:The Process of
Capitalist Production as a Whole, vol.III, part 1.

[5] Y. Hasanli, S. Bayzakov, V. Valiyev and G. Sarsembaeva. (2011), “Modeling



10 S.Baizakov, Y.Utembayev, A.R.Oinarov, J.Forrest:on Mutual Coincidence ...

of the multiplicative effects of opening of the work places on the bases of
‘Intersectoral labor balance’ (on example of Azerbaijan and Kazakhstan)”,
EcomodAzKz_Full Pape eng.

[6] S. Baizakov(2014), “Model of the labour market, based on the final product”,
science and innovation, No.12, pp.31-34.

[7] S. Baizakov(2015), “Declaration on Market Laws of Economic Development
of World Countries”, VEO of Russia, No.195, pp.143-156.

Corresponding author
Sailau Baizakov can be contacted at: baizakov37@mail.ru