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Editors
Stanković, M.
Nikolić, V.
PaKSoM 2020
2nd Virtual International Conference
Path to a Knowledge Society-Managing Risks and
Innovation
Proceedings
Publishers
Research and Development Center “IRC ALFATEC”, Niš, Serbia
Complex System Research Centre, Niš, Serbia
Serbia, Niš, November 16-17, 2020
Proceedings of
2nd Virtual International Conference
Path to a Knowledge Society-Managing Risks and Innovation
Serbia, Niš, November 16-17, 2020
Editors:
Prof. Dr. Miomir Stanković and Prof. Dr. Vesna Nikolić
Technical Editor:
Dr. Lazar Z. Velimirović
Published by:
Research and Development Center “IRC ALFATEC”, Niš, Serbia, and
Complex System Research Centre, Niš, Serbia
Printed by:
Blue Copy, Niš, Serbia
Number of copies printed: 100
The publishing year: 2020
Printing of this edition has been financially supported by
Serbian Ministry of Education, Science and Technological Development
ISBN 978-86-80616-06-3
PaKSoM 2020
2nd Virtual International Conference
Path to a Knowledge Society-Managing Risks
and Innovation
Organizer:
Research and Development Center “IRC ALFATEC”
Co-organizers:
Mathematical Institute of the Serbian Academy of Sciences and Arts
Complex System Research Centre
Supported by:
Serbian Ministry of Education, Science and Technological Development
PaKSoM 2020
ISBN: 978-86-80616-06-3 195
Impact Factor of Capital to the
Economy and Tax System
Constantinos Challoumis
Greece, National Kapodistrian University of Athens
challoumis_constantinos@yahoo.com
Abstract— This paper is about the capital of the
enterprises to the tax system. We have an analysis
of the impact factor of tax revenues of countries
subject to the capital of companies on the tax
system. From the view of the level of influence of
the enterprises which participate in controlled
transactions of transfer pricing to the global tax
revenue, it is plausible to identify the impact factor
of capital, when there exists that factor with the
case in which that factor has omitted. Then the
impact factor of capital in combination with the
tax revenues is determined through the Q.E.
method and the R.B.Q. model. Therefore, is
clarified the behavior of the tax system subject to
the capital of the tax system.
Keywords - capital, tax system, the Cycle of
Money
I. INTRODUCTION
This work aims to clarify the impact of
capital on the tax system and public policy. The
theoretical background is based on the cycle of
money: The theory shows that to an economy the
taxes return to the society, basically to the case
of the education and the health system. But, the
main rule is that the authorities should keep the
taxes as low as is plausible. Moreover, if
something is plausible to be offered by medium
or small economic units, and enterprises, the
government should protect them by very low
taxes and at the same time to put higher taxes on
the bigger companies. But, for the case of the big
companies that their purposes are not covered by
small companies, should be put low taxes. Also,
factories and high technology companies should
have low tax [2], [14]. Then, the main concept is
to have an economy, with the best allocation of
production. In that way, an economy achieves its
higher level. Additionally, this theory shows that
with the best allocation of production units and
of taxes the money is cycled in the economy and
is not lost from the economy, as it achieves the
maximum use of the same amount of money in
an economy [29]. The cycle of money is based
on the way that money reused in the economy
and the way that is an economy is structured. To
this theory, the controlled transactions, and the
system are directly connected. Then, the purpose
of this paper is to clarify the behavior of the
capital with applied tax.
The applied methodology is based on the
Q.E. method and the R.B.Q. model. This means
that the initial hypothesis of the model is tested
by a type of Monte Carlo approach, meaning that
a program is used for the compilation of the
theory instead of using an empirical method [11].
The results comply with the existing
bibliography. The originality of the paper is that
using a compilation is determined the behavior of
capital to the case of low taxes and the case of
high taxes and showed the impact of high taxes
on the capital, according to the theory of the
cycle of money. The results show that the taxes
should be higher to the companies which proceed
to tax avoidance, therefore to controlled
transactions, and lower to the companies which
proceed to uncontrolled transactions [5], [15].
The results confirm the initial hypothesis of the
theory of the cycle of money, in which the
controlled transactions and tax avoidance reduce
the cycle of money, making the countries’
economies weaker [17].
The theory of the cycle of money shows that
to an economy the taxes return to the society,
basically to the case of the education and the
health system. But, the main rule is that the
authorities should keep the taxes as low as is
plausible. Moreover, if something is plausible to
be offered by medium or small economic units,
196
and enterprises, the government should protect
them by very low taxes and at the same time to
put higher taxes on the bigger companies.
Cycle of money
liquidity
savings
investements
consumption education
health
Controlled transactions
taxes
Figure 1: Cycle of money (author’s source)
But, for the case of the big companies that
their purposes are not covered by small
companies, should be put low taxes. Also,
factories and high technology companies should
have low taxes [8], [16]. Then, the main concept
is to have an economy, with the best allocation of
production. In that way, an economy achieves its
higher level. Additionally, the theory of the cycle
of money shows that with the best allocation of
production units and of taxes the money is cycled
in the economy and is not lost from the economy,
as achieves the maximum use of the same
amount of money in an economy [4], [17].
II. METHODOLOGY
In this paper, we determine how the capital
affects the economy and more precisely the tax
income of the governments. For this reason, we
compile capital in a simulation based on the
R.B.Q model, to determine if the theory of the
cycle of money complies with the rule that local
companies should have lower taxes than the
companies of controlled transactions1. The
quantification analysis of the capital of the tax
system
1
with the tax revenue from a global view
is done by the application of the Q.E. method [6].
On that ground of this method is determined the
behavior analysis of mathematical equations.
Thence, there we clarify two levels to the
analysis of the Q.E. method which are:
The analysis of the behavior of the model
stands on the scrutiny of the structural
characteristics of each model accordingly
allowing with that way the extraction of general
1
Controlled transections are the transections which happen
between companies that control their transactions with such
way to have profits and control of their losses.
conclusions about the model which is under
examination.
The frequency analysis behavior scrutinizes
the behavior of the dependent variables, but from
the view of the number of appearances of a
variable than another, estimating the impact that
one independent variable has with one or more
other independent variables.
Thereupon, using the previous two axes of
the Q.E. method is plausible to extract
conclusions about the behavior of mathematical
equations and the way that some factors react to
changes. Consequently, it is plausible the
transformation of quality data to quantity data.
This method is applied for this study for
controlled transactions and more precisely in the
variables of the impact factor of the tax revenue.
The mechanism of Q.E. is based on the
dependent variables which are modified for the
generator. Thereupon, the generator produces
values for the dependent variables. The extracted
values of the generator permit the creation of
magnitudes, which are the base for comparisons,
and the scrutiny of mathematical equations.
Thus, it is plausible to quantify qualitative data.
In our analysis, this method is used for
clarification of the behavior of the impact factor
of the global tax revenue [21]. Then is followed
the R.B.Q methodology, which means that the
first step defined the hypothesis, the theoretical,
and the mathematical background [23]. As the
second step is to set a compilation of the
equations (the tree steps referred to before) to
clarify the behavior of the model. As the third
step is to set the econometric procedure to
conclude the appropriate conclusions for the
hypothesis. Finally compared the result of
programming compilation with the
mathematical, theoretical, and econometric
results to establish that comply between
them [29].
The determination of capital of tax system is
established by the impact factor of capital which
shows the level of influence of capital in the
business plan of the enterprises. To clarify the
way that capital affects global tax revenues, we
proceed with the following diversion:
The first application of Q.E. methodology is
applied to all the factors of the global tax
revenue, 𝒔. In that case, it is plausible to obtain
197
the behavior of the global tax revenue using the
completed form of the Eq. (1).
In the second application of Q.E.
methodology are applied all the factors except
the factor which is under review. Thereupon, in
that case, is avoided the factor of the capital of
the tax system, 𝒔.
This methodology is illustrated below:
Global tax revenue
All factors of tax
revenue
All factors of tax
revenue except from
risks of tax system
Figure 2: Steps of Q.E. application (author’s source)
The previous scheme is shown the
methodology followed by the Q.E. method to
determine the behavior of the global tax revenue
in the case that there exists the capital in the
controlled transactions of the transfer pricing and
the case that we have an absence of the impact
factor of capital [11].
III. LITERATURE REVIEW
The profits and losses are related to the case
of the taxes and consequently with the case of the
taxes to the education machine in the economy.
Because of the controlled transactions, the tax
avoidance of the huge organizations, and the
global controlled transactions affect the taxing
machine, in keeping with the principle of the
cycle of money. Then the case of taxes to the
education machine is an exception from the
overall taxes. Therefore, the behavior of the
companies and the implied taxes from the
government outline the frame of this research.
Some necessary theoretical historical past is
presented. Then, the contracts of groups and the
agreements of corporations with the government
are very vital for their income and losses. The
modifications in the contracts must be included
in the agreements. This is vital for the procedure
as the changes that corporations make plausibly
could affect their courting with the government
[25], [27]. The tax authorities should make
periodic inspections. Therefore the
comparability evaluation needs the periodic
specification of contracts. This evaluation is
about the assessment of the listed targets that the
government places with the real records which
give the enterprises. The arm’s length precept
method wishes the periodic inspections of the
agencies which participate in managed
transactions. The cost-sharing pends on the
periodic check of agencies that are examined
parties. The organizations of managed
transactions face taxation troubles that are related
to their activities. Hence, the companies of
controlled transactions have to follow the arm’s
length precept of the authorities. The
comparability evaluation has as a goal to make
clear the tax duties of the companies they comply
with the tax requirements of the government.
Since the ok settlement of the corporations of
managed transactions is that which maximizes
the fees in financial environments with a high tax
rate and at the same time maximizes their profits
in tax environments with a low tax rate [3]. The
impact factor of tax revenues of countries which
are tax heaves, 𝒔 is determined as that:
kl
sr c t i
. (1)
Therefore are countries that receive products
are taxed in different countries. This allocation of
profits between profits and losses permits the
enterprises which participate in controlled
transactions of the transfer pricing activities to
maximize their utility [8], [13]. But,
contemporaneously the tax revenue from the
global view is declined. Then, the loss of tax
income from some countries is more than the
profits that make the countries which are tax
heavens. Thereupon, the symbol of 𝒔 the impact
factor of tax revenue from a global view, and
there are some coefficients which are 𝒌, 𝒍, 𝒓, 𝒕, i,
and 𝒄. Thus, the symbol of 𝒌 is about the impact
factor of capital, 𝒍 is the impact factor about the
liability of the authorities on the tax system. The
interpretation of the liability is about how
unbalanced it is the tax system. The parameter of
r is about the risk, the t is about how much trust
is the tax system (bureaucracy). The symbol of 𝒊
examines the case of intangibles (the intangibles
which are charged to the subsidiaries) of the tax
system. Additionally, the symbol of c is about the
cost of enterprises. The symbols with the “~” are
accordingly the same thing but from the view of
198
the uncontrolled transactions
2
. Thus, the
numerator is proportional to the income of taxes,
as the investments and the stable tax
environments, with liability, enhance the tax
income. On the other hand, the denominator is
inverted proportional to the tax income, as the
risk, the cost, and the unbalance of taxation cause
less tax income. Moreover, for 𝒔
̃ we have that:
kl
sr c t i
. (2)
Equation, Eq. (3) determines the aggregate
impact factor of tax revenues, which is
symbolized by 𝒔
̂, and is defined by the next
equation:
ˆs s s
. (3)
Based on the prior equations we could
proceed to the identification of the behavior of
the impact factors of tax revenues in the case of
tax heavens and the case of the non-tax heavens.
Consequently, using the prior equations is
plausible to examine the controlled and
uncontrolled transactions. Then, 𝒔 is a factor that
allows the comparison between the controlled
with the uncontrolled transactions. Thence can
have a standalone behavior analysis of controlled
transactions and a combined behavior analysis
between the controlled transactions with the
uncontrolled transactions. The next section is
analyzed the impact factor of tax revenues with
the rest impact factors.
IV. RESULTS
The capital of the tax system is in interaction
with the impact factor of tax revenues. This
behavioral analysis is determined by the model
which explains the behavior of the impact factor
of tax revenues with the existence and with the
avoidance of the impact factor of capital. All the
necessary equations have referred to the previous
sections, except from one condition. Then, for
the application of the Q.E. method, we use the
following condition, which is:
t l i r k c
. (3)
Therefore, it is plausible to proceed to a
quantitative analysis using Eqs. (1), (2), and (4).
The examination of tangibles with the capital is
2
Uncontrolled transactions are the transactions which
happen between companies free of control and allocation of
profits and losses.
important for the transfer pricing theory. The
examination of capital is used many times from
the enterprises of controlled transactions to reach
the arm’s length principle
3
[5]. Compiling
according to the prior equations:
%Q.E. method for the determination of capital (Compile to
Matlab)
q=0;
while q<10
q=q+1;
count=0;
counts=1;
counts51=1;
while count<10
if rand()<9
t=0.8*rand();
end
if rand()<9
l=0.7*rand();
end
if rand()<9
i=0.6*rand();
end
if rand()<9
r=0.5*rand();
end
if rand()<9
k=0.4*rand();
end
if rand()<9
c=0.3*rand();
end
s=(k+l)/(r+c+t+i);
s5=(l)/(r+c+t+i); % without capital
s_tilda=0.3;
count=count+1
if s<0.3 %it is one limit for comparison above than this
we think s_tilda, but is not the same one as s_tilda
%and it is used as meter to compare all the
different
%counts1,counts2,....
counts=counts+1;
else
counts1=counts1+1;
end
if s5<0.3
counts51=counts51+1;
else
counts53=counts53+1;
end
%to the first compile must omit; tec
end
tec=[count,counts51,t,l,i,r,k,c,s,s5,s_tilda;tec];
end
3
As arm’s length principle is determined the compliance
between controlled transactions with the uncontrolled
transactions. The arm’s length principle is used as index that
companies of controlled transactions comply with the tax
requirements of the tax authorities.
199
Therefore, applying the Q.E. method and
choosing the appropriate values for the
coefficients of global tax revenue, we have that:
TABLE I. COMPILING COEFFICIENTS (AUTHOR’S
SIMULATION)
Factors
Values of s
Values of s’
k
0.4
-
i
0.6
0.6
l
0.7
0.7
r
0.5
0.5
c
0.3
0.3
t
0.8
0.8
fs
< 0.3
< 0.3
fsi
< 0.3
< 0.3
Thereupon, using the previous factors can
determine the behavior of the model through the
generator of the Q.E. method. The factors of the
prior table have as an upper limit the 1 and as a
lower limit the 0. But, 𝒔 and 𝒔
̃ are plausible to
receive values greater than one as their
mathematical structure allows this. After 461
iterations extracted the next diagrams:
Figure 3: (a) Impact factors of 𝒔 and 𝒔′, (b) frequencies of 𝒔
and 𝒔′ (author’s source)
In the prior figure, we used the 𝒔
̃, which here
is the same for the case that we have the capital
and in the case that we have avoided the capital.
Then with 𝒔 (blue line) is symbolized the case
that we have the impact factor of 𝒌 which
symbolizes the capital of the enterprises in the
environment of the tax system. With 𝒔′ (red line)
is symbolized the case that we have avoided the
capital, 𝒌. The global tax revenue is higher in the
case that has the capital (blue line) than in the
case that the impact factor of capital is avoided
(red line). As we expected the absence of capital
declines the global tax revenues. The reason for
the diminished global tax revenues in the case of
𝒔′ is because the capital makes the companies of
controlled transactions enforce and extend their
activities. Should be notified that for the
comparative analysis we used 𝒔
̃ as constant to be
able to compare 𝒔 with 𝒔′. Additionally, from the
diagram (b) of figure 3, we obtain that the
frequency of the 𝒇𝒔 (black line) is lower than the
frequency of 𝒇𝒔′ (blue line). Thereupon, the
companies with high capital expenditures, which
participate in controlled transactions of transfer
pricing, decreased comparing them with the case
that we do not have capital [blue line of diagram
(b)]. The interpretation of this economic situation
is that the requirements for capital make the
companies of controlled transactions stop their
activities. But, at the same time, the global tax
revenue increased when the capital is increased.
The companies of controlled transactions prefer
to have profits without growing their capital.
Then, the number of controlled transactions is
less when there are requirements for capital,
because the existence of capital increases the
global tax revenue. We conclude that the
increased requirements for capital for the scope
of transfer pricing make the companies prefer
uncontrolled transactions, instead of controlled
transactions.
V. CONCLUSIONS
We conclude that the capital is increased
when the global revenue is increased, and on the
other hand when we have limited capital the
global income is decreased, as we expected. At
the same time the companies, because they lose
money from the needs of capital, prefer to
proceed to controlled transactions. Then, the
global tax revenue is decreased from
uncontrolled transactions. Therefore, the
authorities should have higher taxes on the
companies which make controlled transactions,
and lower taxes for the local enterprises and the
companies which make uncontrolled
transactions. Then, in that way, the aggregate tax
income will be higher for the governments.
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