Entrepreneurship and Innovation in the Polish Industry
JAN ZWOLAK
Faculty of Economic Sciences
Pope John Paul II State School of Higher Education in Biała Podlaska
21-500 Biała Podlaska, ul. Sidorska 95/97
POLAND
Abstract:- Entrepreneurship is a process in which goals or tasks are set at one’s own initiative, whereby no
efforts are spared to ensure their efficient and effective implementation. The concept of entrepreneurship is
associated with innovation as entailing ongoing research and the introduction of rational changes and novel
ideas. The aim of the research is to determine the regression interdependencies between the number of
enterprises (entrepreneurship) and process and product innovation expenditure (innovators' activity) and the
number of inventions (inventors' activity), and in the second regression model: also the number of enterprises
(entrepreneurship) and process and product innovative expenditure (innovators' activity) and the number of
patents (inventors' activities) generated within the Polish industry in the years 2015-2017. The hypothesis is
that patents (inventors' activities) get reinforced with process and product innovation expenditures (innovators’
activities) employed in the process of growth of the number of enterprises (entrepreneurship) in industry, as
well as the overall efficiency of expenditures and technologies (patents) in the Polish industry over the course
of the researched years. Conducted studies have confirmed the above hypothesis. In addition, the research
carried out has shown that patents (inventors 'activities) have supplemented the share (elasticity) of process and
product innovation (innovators' activities) by 10% in the increase in the number of enterprises
(entrepreneurship) as observed in industry. This share is transferred from the supply element to that of demand.
Key-Words:- entrepreneurship, process and product innovative expenditure, inventions and patents, growth
model, power regression model, industry, Poland.
Received: May 18, 2021. Revised: December 19, 2021. Accepted: January 5, 2022. Published: January 7, 2022.
1 Introduction
Readiness to undertake innovation in production or
services is related to its propensity. It is consequent
to a conscious pursuit of changes in the production
process or concerning the nature of the product
(active innovation), while it may also be forced by
the environment or market competition (passive
innovation).
Propensity to innovation is also associated with
readiness to accept risks and tensions that
accompany the course of process or product
changes, with the simultaneous need to undertake
investments, and to introduce a product or service
onto the market [1]. Propensity to innovation is an
indispensable, yet insufficient condition for
innovation. It depends on many factors, such as the
size of the enterprise, the level of competition on the
market and the structure of economy organization.
The transfer of innovation is related to the
process as a result of which the range of invention
implementation (patent) in the economy is
expanding. We are rather dealing here with a
diffusion of innovation. It involves extending the
use of innovation within one enterprise (the use of
an invention in an enterprise). The nature of this
application can be gradual and it may occur between
enterprises representing a similar type of production
or services rendered (horizontal transfer) or between
different types of production or services rendered
(diagonal transfer). The transfer of innovation can
be measured with the number of enterprises
(entrepreneurship) that have applied the new
invention (patent), the value of production or
innovative services in absolute amounts, based on
the new invention, or the share of the value of
production or innovative services in production or in
services of a given type. These categories, such as
enterprise (entrepreneurship), process and product
innovation (activities of innovators) and inventions
(and patents) (activities of inventors) are the subject
of the study in this article.
The above-mentioned issues have not been
sufficiently developed in the understanding of
relationships (relations) occurring between these
categories in the industry of given economies at the
macroeconomic level. The presentation of this
research constitutes a contribution to the
development of the theory (growth model) of
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regression interdependencies occurring between
these categories in the Polish industry.
The aim of the research is to determine the
regression relationships between the number of
enterprises (entrepreneurship) and the expenditure
on process and product innovation (innovators'
activity) as well as the number of inventions
(inventors' activity), and in the second regression
model: also between the number of enterprises
(entrepreneurship) and expenditure on process and
product innovation (innovators' activity) and the
number of patents (inventors' activities) in the
industry in Poland in the years 2015-2017.
Constituting the foundation of the research is the
hypothesis that patents (inventors' activities) are
reinforced with the expenditures on process and
product innovation (activities of innovators) in the
course of the process of increasing the number of
enterprises (entrepreneurship) in industry and with
the overall efficiency of inputs and technologies
(patents) observed in the Polish industry in the
researched years.
Section 2 presents a selection of theoretical and
empirical literature. Section 3 describes the applied
methodology. Section 4 contains variable
parameters and their respective analysis. Section 5
presents the results and the discussion. Finally,
section 6 features the final conclusion.
2 Literature Review
The research conducted by [2] Hughes and Mina
(2010) indicates that patent in enterprises is an
increasingly important factor in the environment of
financial support. Patents also have been proven to
limit competitive access [3]. In a highly competitive
environment, a patent plays the role of a strategic
instrument [4]. In order to capitalise on the higher
value, competitive markets are needed to develop
the dynamic capability of enterprises, which is what
innovation provides [5]. The patent serves the
markets of highly profitable economies [6]. The
quality of patents itself ought to be patented (high-
quality patents). This, in turn, implicates the
increase in the responsibility for creating new
products and new ventures [7].
The information on the grant should be known
prior to the patent being issued [8]. At the same
time, business methods should be separated from
patents [9].
Innovations in business models are also
distinguished: R&D is separated from the
production in enterprises [10]. In order to stimulate
the development of business methods, existing
patents are reviewed with respect to the possible
improvements that can be effectuated in relation
thereto [11]. Patents serve the desired purpose of
catalysing innovation [12]. Product innovation leads
to product differentiation (range) and to the
introduction of a variety of goods and services [13].
A patent as a source of innovation constitutes the
development of the technology market for the
benefit of the national economy. A significant
proportion of patents on the market serve to increase
the benefits of this market [14]. Market motivation
plays an important role in shaping the investment in
new technologies [15].
Patents promote innovation. This is the exclusive
right to implement innovation [16]. The level of
activity of a given idea shifts the technological
environment. At the same time, the asymmetry of
knowledge can be better placed [17].
Wherever legal coercion limits capacity and
patent law could be adapted, there is one common
feature applicable to those two circumstances the
incentive approach [18]. The reallocation of
activities to sectors where an intense increase in
knowledge is noted causes changes in the structure.
The same is applicable to the sector for activities
showing a greater demand for knowledge [19]. The
horizontal transfer of innovation affects all sectors
to the same extent. The result is that no new sectors
are created. A new sector springs up wherever the
level of high technologies increases, thus creating a
new direction of growth [20]. Owning technology
allows competitive entry onto a new market
segment or an entry onto an entirely new market
[21]. New individuals can strengthen the
competition and improve long-term performance
with the help of Schumpeter competition [22, 23].
In most cases, launching an activity is facilitated
by patents as a key collective property and
entrepreneurship development tool. The patent
business plan helps focus on the technology base,
effective management, information protection and
an efficient task delivery [24]. R&D expenditure
management increases the patent-measured
efficiency [25]. All models suggest a directional role
for R&D spending (elasticity 0.37-0.48) [26].
Patents also increment the value of the enterprise,
either through their sales or by means of
entrepreneurial growth [27]. The increase in the
number of patents in an enterprise is associated with
its higher market price as a signal of the quality of
the enterprise in question [28]. It serves as a
protection mechanism for the intellectual capital of
an enterprise; for the most part, it functions as a
patent system [29]. Useful models indicate
irrelevant patents and an alternative short-time
protection of this invention, as well as the lower cost
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of its protection [30]. This leads to harmonisation of
growth and ensures positive structural changes in
industry [31]. The industry has the greatest potential
for implementing innovations. It boosts the
efficiency of innovation and integrates the
remaining sectors of the economy. It determines the
implementation of innovations therein and creates
an environment of innovation application [32].
The goal of business incubators is
entrepreneurship, creative work, commercialisation
of research and undertaking profitable projects
[33].The actual implementation of technologies
(patents) does not only initiate business
(entrepreneurship) but it also significantly
contributes to the national economic growth [34].
Competition can affect the implementation of
various technical patent standards within the same
industry [35]. Joining patents for technology
substitution can limit competition and discourage
innovation [36]. Combined innovation adopts a
central position in the economic growth [37]. Small
countries (like, for instance, Estonia) should
increase its public R&D and innovation expenditure,
as well as its spending on public science and
technology universities, together with their
international patenting [38].
Intellectual property theory explains that patents
protect the newly created knowledge. From an
economic point of view, it follows that innovation
implies new ways of undertaking entrepreneurship.
On the other hand, the theory of excessive
entrepreneurship indicates the need for the existence
of generated knowledge to ensure the growth in
entrepreneurship within newly created enterprises,
since a start-up is favoured by new investments
[39]. The comparative advantage is correlated with
industry technologies [40]. The praxeological model
shows that patents understood as a patent system are
necessary for the indispensable for innovation.
However, it does not explain the complex
relationship of the patent system with science and
innovation. Every model not only the
praxeological one is simplified and requires
empirical verification. An extended patent renewal
model can be used to understand the empirical
regularity of the data [41].
3 Research Methodology
The model whose source is R&D and the patent
system is referred to as the supply model. It is also a
curvilinear model of the innovation process (Figure
1):
Fig. 1: Elements of the innovation process growth model
In this model, one can distinguish the endogenous
growth model due to the role it plays in the field of
innovation. We can distinguish the activity of the
inventor (patent) and, separately, the activity of the
innovator [42]. We are dealing here with a two-way
relationship between R&D expenditure and
innovation. There is also the interdependency
between innovation and economic growth. Each of
those three variables has the potential to function
separately in a relationship [43]. The growth model
of entrepreneurship (enterprises) is a function of
inventions (patents) (inventors' activities) and
innovative process and product expenditures
(innovators' activities). It follows that the subject of
the study is the growth model (figure 2).
Fig. 2: Elements of the economic growth model with the separation of the activities performed by inventors and
innovators
innovators'
activities
(innovation
commercialisation)
entrepreneurship
(enterprise)
economic
growth
patent
(technology)
entrepreneurship
(enterprise)
R +D
invention
growth
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This model provides a general model for the
endogenous growth of balance that separates the
invention from innovation, whereby the excess of
knowledge is estimated simultaneously between
these two activities. The economic growth provides
a dynamic complement to these activities. The
process of economic growth serves to mutually
enhance the separate activities and knowledge as
well as its commercialisation.
The theory of entrepreneurship of the saving
formula indicates that the more the indicator of cost
intensity of the sold value of industry decreases, the
stronger the increase of the cost advantage of
innovative value sold. This indicates entrepreneurial
rationalisation of the composition of the elements of
the economic system or the industry sector in
question. This rationalisation is the primary phase
relative to the main phase of entrepreneurial and
economic activity. The growth rate [44] within the
extreme range, within the scope of process and
product innovation expenditure as well as the
spending employed for inventions and patents per
enterprise, indicates the degree of activity of
innovation commercialisation and the degree to
which the knowledge necessitated by innovation is
created within the industry.
The comparison of the marginal categories with
the average values in individual examinations of
independent variables, and their respective
correlation, indicates the possibilities of their
balancing in conducted entrepreneurship within
industry. This constitutes the economic value of
entrepreneurship [45].
4 Data and Empirical Analysis
The highest internal variability is shown by the set
of enterprises in industry in the years 2015-2017
(95%). The average set of enterprises is over 1.7
times smaller than the centre number of their range
0.5 (xn + x1) (Table 1).
Process and product innovation outlays show a
lower internal variability in the set by over 10
percentage points than the internal variability of
industrial enterprises. And their mean of the set is
over 1.7 times lesser than the value of the mid
range. It can be assumed that the distributions of the
compared sets are similar.
On the other hand, the set of the number of
inventions in the analysed years indicates that the
variability is lower by over 16 percentage points
compared to the set of the number of enterprises in
industry. The average of the set is over 1.9 times
smaller than the number of the centre range of
inventions.
In contrast, the average of patents is 2.3 times
smaller than the number of their centre range. The
internal variability of the set of the number of
patents is similar to the set of the number of
industrial enterprises. The patent variable and the
enterprise variable have similar set distributions.
The chronologically discussed variables shown
in Table 1 indicate a decrease in the mean in each of
the sets of variables relative to their centre range.
This relationship is a common feature of the studied
variables.
Table 1. Parameters of the features of innovative variables within the industry in Poland in the years 2015-2017
Item
Specification
Symbol
Measurement
unit
Arithmetic
average
Range
min. – max.
Coefficient of
variation %
1.
Number of enterprises
Y1
number
7418.0
1031.3-24800.8
95
2.
Process and product
innovation outlays
X1
million PLN
1496.7
251.6-4944.5
84.7
3.
Number of inventions
X2
number
267.9
59.0-983.0
78.8
4.
Number of patents
X3
number
177.3
21.0-811.0
93.3
Source: Statistical yearbook of voivodships. Central Statistical Office in Warsaw 2016 - 2018. Author's own
calculations.
The randomness study of the distribution of the
random component was carried out with the help of
a graphical analysis and the test of the number of
series, at a significance level of 0.05. The graphic
analysis and the test of the number of series verify
the hypothesis and confirm the accuracy of the
selection of the analytical form of the models (Table
2). The random component normality examination
was performed using the Kolomogorov-Liliefors
test. The compared values calculated with critical
values at the significance level of 0.05 do not defy
the hypothesis that the distribution of random
components is normal. Autocorrelation was tested
using the Durin-Watson test, and no autocorrelation
of the random component was found at a
significance level of 0.05. The verification of the
homoscedasticity hypothesis of random components
was performed by means of the Godfeld-Quandt
test. At a significance level of 0.05, the critical
values of the F Snedecor distribution are greater
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than the calculated ones, however, there are no
grounds to reject the hypothesis of homoscedasticity
of random components.
5 Results and Discussion
Marginal theory can be treated as a borderline case
analysis of the inventor's and innovator's activity in
relation to entrepreneurship (enterprises) in the
Polish industry in the years 2015-2017. The subject
of the study are growth models expressed by Cobb-
Douglas-type curvilinear power regression. They
have been included in tabular arrangement (in two
respective models) in Table 2.
Table 2. Power regressions of the number of enterprises (Y1) against process and product innovation
expenditures (X1) and the number of inventions (X2) and the number of patents (X3) in industry in Poland in
the years 2015-2017
a
Regression
coefficient
(parameter)
Standard Error
T-Test
R2 Adjusted
X1
X2
a
X1
X2
a
X1
X2
1.1032
(3.0138)*
0.727
O.431
0.48
0.15
0.18
2.26
4.77
2.37
0.84
X1
X3
a
X1
X3
a
X1
X3
1.4931
(4.4509)*
0.798
0.295
0.50
0.12
0.11
2.99
6.70
2.58
0.85
Source: Statistical yearbook of voivodships. Central Statistical Office in Warsaw 2016 - 2018. Author's own
calculations.
* free logarithmised term
The range of the significance level of the parameters: 0.00 – 0.02
The data presented in Table 2 show the
regression dependence of the number of enterprises
(entrepreneurship) (Y1) on the process and product
innovation expenditures (activities of innovators)
(X1) and the number of inventions (activities of
inventors) (X2); and in the second model Y1, the
dependence is measured against X1 (activities of
innovators) and the number of patents (activities of
inventors) (X3) in the Polish industry in the years
2015-2017. In both models, the variability in the
number of enterprises (entrepreneurship) is
explained by the outlays on process and product
innovation, the number of inventions and the
number of patents generated within the industry:
84% and 85%, respectively. An explanation of high
variability has thus been obtained. The volatility is
not explained by the participation of other variables
that are not the subject of the study. The strength of
the relationship between all variables expressed with
the multiple correlation coefficient (R) amounts to
92% for both models. Regression coefficients
(parameters) in both models have standard errors
lower than 50% of their absolute values. The t-test
values are several times higher than the absolute
values of the regression coefficients, whereby the
level of significance of the regression coefficients in
both models ranges from 0.00 to 0.02. A statistical
evaluation of the regression coefficients indicates
the possibility of their use in the econometric
analysis of the enterprise (entrepreneurship) and
industrial innovation in Poland in the years 2015-
2017.
Regression coefficients (parameters) which
determine the elasticity of the number of enterprises
(entrepreneurship) relative to the value of process
and product innovation expenditure (innovators
'activities) as well as the number of inventions and
the number of patents (innovators' activities) in the
industry in the years 2015-2017, are referred to as
elasticity coefficients. The elasticity coefficients
indicate by how many percentage points the
dependent variable (Y1) changes (increases or
decreases) when factor Xj increases by 1%, with the
relative stability of the remaining factors. The
elasticity of enterprises (entrepreneurship) (Table 2)
is higher in relation to innovative process and
product expenditure (innovators 'activities) (0.727)
than the number of inventions (inventors' activities)
(0.431).
This also applies to the second model, whereby
the elasticity of enterprises (entrepreneurship) is,
however, at its highest in relation to the innovative
process and product expenditure (innovators
'activities) (0.798) against the number of patents
(inventors' activities). Patents, due to their earlier
verification by the patent system, encompass a
greater number of original inventions, hence they
get strengthened with the expenditure on process
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and product innovation in the process of growth in
industry. As evidenced by a comparison of the sum
of elasticity in the models, the elasticity of
enterprises (entrepreneurship) is higher in the first
model by 0.065. However, upon comparing the
elasticity of enterprises with respect to innovative
process and product outlays, the elasticity is higher
for these enterprises in the second model (0.071).
This proves that patents (inventors' activities)
significantly increase the activity of innovators in
the process of entrepreneurship growth in industry.
Comparison of the overall efficiency parameters
(constant terms) in the models prior to their
delogarithmising shows that the constant term in the
second model is 35.3% higher. This indicates that
the overall efficiency of the number of enterprises
(entrepreneurship) shaped by the activities of
innovators and the activities of inventors in the
second model increases entrepreneurship by over
a third of its growth (35.3%). Research shows that
patents (inventors' activities) boost the activity of
innovators, and simultaneously, the overall
effectiveness of entrepreneurship shaped by these
activities of innovation. Patents, therefore,
significantly complement each other in the overall
growth of the product of innovation, which
contributes to the stable growth of entrepreneurship
and innovation in industry.
The combined incrementation in process and
product innovation expenditure (activity of
innovators) as well as the number of inventions and
the number of patents (activity of inventors) by 10%
increases the number of enterprises
(entrepreneurship) by about 11%, in both models.
This is more than a proportional augmentation of the
number of enterprises (entrepreneurship). The sum
of 100% elasticity indicates that the proportion of
process and product innovation outlays (activity of
innovators) as well as that of the number of
inventions and the number of patents (activity of
inventors) in the first model is 63% and 37%
respectively, and in the second one: 73% and 27%.
Comparing these shares shows that 10% of the
proportion of patents (inventors' activities) is
transferred onto the process and product innovation
expenditures (innovators' activities) in the increase
in the number of enterprises (entrepreneurship) in
the second model. This proportion is significant as
the number of enterprises (entrepreneurship) shifts
its character from supply (patents) to that of
demand.
Cobb-Douglas regression analysis allows for a
determination of the relationship between the
number of enterprises (entrepreneurship) (Y1), the
average (X/Y1) and the marginal (dX/dY1) values
and the amount of the input of factor X. These
relationships have been included in Tables 3, 4, 5
and 6.
Table 3. Marginal and average process and product innovation expenditure in the Polish industry in the years
2015 - 2017
Number of
enterprises
(Y1)
Innovative process and
product expenditures
(X1) million PLN
Innovative process and product expenditures per enterprise:
average PLN million
marginal PLN million
4010.93
720.90
0.1797
0.1307
5773.85
1189.90
0.2061
0.1498
7351.55
1658.90
0.2257
0.1640
8810.29
2127.90
0.2415
0.1756
10183.07
2596.90
0.2550
0.1854
11489.40
3065.90
0.2668
0.1940
12742.06
3534.90
0.2774
0.2017
13950.02
4003.90
0.2870
0.2087
15119.87
4472.90
0.2958
0.2151
16256.63
4941.90
0.3040
0.2210
Source: Author’s own calculations based on the data presented in tables 1 and 2.
The data presented in Table 3 shows that
marginal process and product innovation
expenditures (marginal activity of innovators) in
their middle range constitute 73% of the average
level centre. This means that the marginal value is
approaching the average value at a fast rate. The
marginal activity of innovators is growing above the
average, which is augmenting at a slower rate, while
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entrepreneurship is incrementing at an increasingly
faster pace. These interdependencies are
characterised by the first model presented in Table
2.
Table 4. Marginal and average process and product innovation expenditure in the Polish industry in the years
2015 - 2017 (second regression)
Number of
enterprises
(Y1)
Innovative process
and product
expenditures (X1)
million PLN
Innovative process and product expenditures per enterprise:
average PLN million
marginal PLN million
3911.99
720.90
0.1843
0.1471
5835.41
1189.90
0.2039
0.1627
7607.29
1658.90
0.2181
0.1740
9279.38
2127.90
0.2293
0.1830
10878.00
2596.90
0.2387
0.1905
12419.01
3065.90
0.2469
0.1970
13912.93
3534.90
0.2541
0.2028
15367.22
4003.90
0.2605
0.2079
16787.42
4472.90
0.2664
0.2126
18177.79
4941.90
0.2719
0.2169
Source: Author’s own calculations based on the data presented in tables 1 and 2.
As evidenced by the data presented in Table 4
(the second model), the marginal process and
product innovation expenditures (marginal activity
of innovators) in their middle range constitute 80%
of the average level centre. This means that the
marginal value is approaching the average one at an
even faster rate. The marginal activity of innovators
is growing at an even faster pace than the average
activity, which is incrementing more slowly, while
entrepreneurship is growing even faster. These
interdependencies are characterised by the
strengthening of innovators' activities with the
activities of inventors by means of patents (Table 2).
Table 5. Marginal and average inventions in the Polish industry in the years 2015 - 2017
Number of
enterprises (Y1)
Number of
inventions (X2)
Number of inventions per enterprise:
average number
marginal number
5334.22
151.40
0.0284
0.0122
6545.46
243.40
0.0372
0.0160
7515.43
335.40
0.0446
0.0192
8343.07
427.40
0.0512
0.0221
9074.39
519.40
0.0572
0.0247
9735.15
611.40
0.0628
0.0271
10341.43
703.40
0.0680
0.0293
10904.07
795.40
0.0729
0.0314
11430.78
887.40
0.0776
0.0335
11927.24
979.40
0.0821
0.0354
Source: Author’s own calculations based on the data presented in tables 1 and 2.
As indicated by the data presented in Table 5
(the first model), the marginal number of inventions
(marginal activity of inventors) in their middle
range constitutes 86% of the average level centre.
This means that the marginal number is approaching
the average one at the fastest rate. The marginal
activity of inventors is growing at the fastest pace,
surpassing the average one, which is growing at the
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slowest rate, while entrepreneurship is incrementing even faster.
Table 6. Marginal and average patents in the Polish industry in the years 2015 - 2017 (second regression)
Number of
enterprises (Y1)
Number of patents
(X3)
Number of inventions per enterprise:
average number
marginal number
5918.37
100.00
0.0169
0.0050
7027.39
179.00
0.0255
0.0075
7827.62
258.00
0.0330
0.0097
8469.41
337.00
0.0398
0.0117
9012.28
416.00
0.0462
0.0136
9486.60
495.00
0.0522
0.0154
9910.17
574.00
0.0579
0.0171
10294.41
653.00
0.0634
0.0187
10647.14
732.00
0.0688
0.0203
10973.96
811.00
0.0739
0.0218
Source: Author’s own calculations based on the data presented in tables 1 and 2.
As is to be concluded from the data presented in
Table 6 (the second model), the marginal number of
patents (marginal activity of inventors) in the centre
of their range constitutes 29.5% of the centre of the
level average. This, in turn, means that the marginal
number decreases, down to zero, which also causes
the average number to fall, albeit at a slower pace;
however, entrepreneurship (number of enterprises)
is incrementing, but its growth rate tends to zero.
This indicates the need to modernise these patents to
maintain the level of entrepreneurship in industry,
and even so as to increase it.
The above interdependencies are related to the
average growth rate of the categories subjected to
the study. The regularity of incidence of these
categories is expressed by the average growth rate
within their range, which indicates the nature of
changes occurring in these economic phenomena in
the industry (Table 7).
Table 7. Average growth rate of the number of enterprises (Y1) within the range of the value of process and
product innovation expenditure (X1) as well as the number of inventions (X2) and the number of patents (X3)
within the industry in Poland in the years 2015-2017; %
Specification
Table 3
Table 4
Table 5
Table 6
Number of enterprises (Y1)
16.82
18.61
9.35
7.10
Innovative process and product expenditure X1)
23.85
23.85
Number of inventions (X2)
23.05
Number of patents (X3)
26.18
Marginal process and product innovation
expenditure
6.01
4.41
Average process and product innovation
expenditure
6.01
4.41
Marginal number of inventions
12.53
Average number of inventions
12.53
Marginal number of patents
17.82
Average number of patents
17.82
Source: Author's own calculations based on the data presented in tables 3, 4, 5 and 6 with the help of dynamics
with a variable basis and a geometric mean.
The comparison of the data presented in Table 7
indicates that with the same average growth rate of
process and product innovation expenditure (23.8%)
(innovators' activity), the average growth rate of the
number of inventions is the same (23%) (inventors'
activity) while that of the number patents is faster
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Volume 19, 2022
by 3 percentage points (26%). This faster average
growth rate by 3 percentage points of the number of
patents causes the augmentation of the average
growth rate of the marginal and average number of
patents by over 5 percentage points. This implies a
better application of the number of patents in the
average industry enterprise over the studied period.
Patents as a synthetic (original) category are
characterised by better qualitative use within the
Polish industry.
At a relatively constant average growth rate of
innovators 'activity, one can present the regression
dependence of the increase in entrepreneurship
(number of enterprises) on the number of patents
(inventors' activities). The number of enterprises
(entrepreneurship) (Y1) can be expressed by a
single-factor Cobb-Douglas power function (Y1 = a
* X3b).
Y1 = f (X3)
(1)
The maximum number of enterprises
(entrepreneurship) is achieved when the subsequent
increase in patents (dX3) no longer brings an
augmentation in the number of enterprises
(entrepreneurship). This dependency is expressed by
the following formula:
dX3/dY1 = 0
(2)
The industry is interested in whether the cost
(expenditure expressed in monetary means) of
subsequent patents will bring an additional effect of
entrepreneurship (number of enterprises). This
answer can be obtained using the marginal calculus.
If the growth in entrepreneurship is presented as the
cost of the number of patents (PY1), similarly to the
cost of the number of patents (PX3), then the optimal
level of patent implementation can be determined. It
is equal to the next number of patents that brings an
increase in entrepreneurship (number of
enterprises), which in turn is equal to the cost value
of the number of patents. Further patent expansion
in the same market conditions is no longer justified
as it results in a decline in entrepreneurship (number
of enterprises). This interdependency can be
expressed as follows:
(dX3/dY1) * PY1 = PX3 (3)
The marginal calculus serves to optimise the
number of patents, and it is more complex, as the
effects of patents last for several years.
6 Conclusion
Entrepreneurship and innovation understood as a
process of creation and growth of enterprises
constitute an instrument of structural transformation
in the innovative economy. The theory of
cumulative changes serves well to elucidate the
process of establishing entrepreneurship with the
participation of innovations. It explains the
dependence of positive feedbacks in that a change of
one factor strengthens the impulses that stimulate
the change retroactively. There are two ways in
which innovation can be introduced to industry: the
market and the institutional type of introduction.
The research has confirmed the hypothesis that
patents as a result of the inventors' activities
strengthen themselves together with the process and
product innovation expenditures (activities of
innovators) over the course of the process of
increasing entrepreneurship (enterprises) of
industry, while also boosting the overall efficiency
of these expenditures and technologies (patents) in
the Polish industry over the researched period.
The conducted studies have shown that
entrepreneurship (the number of enterprises) relative
to innovative process and product inputs (innovators
'activities), as well as inventions and patents
(inventors' activities), increases more than
proportionally in the years studied. It turned out that
patents (inventors 'activities) supplemented the
share (elasticity) of innovative process and product
expenditures (innovators' activities) by 10% in the
increase in the number of enterprises
(entrepreneurship) that emerged in the industry.
This share is transferred from the supply type to the
demand one. This proves that these activities are
mutually complementary in the process of economic
growth.
Comparisons of the impact of inventions and
patents in separate models on the increase in
entrepreneurship (number of enterprises) show that
the formation of the marginal number category of
patents and inventions is different for the same
period of research. It has been explained that when
the marginal number of patents decreases, it causes
their average number to decrease, while the number
of enterprises (entrepreneurship) is on the rise,
although its growth rate tends to zero. Nonetheless,
the category of inventions does not specify this last
important interdependency. It is of high significance
as it explains that the wave of entrepreneurship
growth closes within the three years under review,
and thus the activity of innovators will be on the
decrease. This is consistent with the fluctuation in
Schumpeter's theory. The patent category as a
synthetic one describes precisely the variability of
entrepreneurship (number of enterprises). It
indicates the necessary secondary entrepreneurship
with the help of innovation (patents) in industry.
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The conducted research has shown that the
integration of knowledge and its commercialisation
are separate activities of inventors and innovators,
which strengthen themselves mutually in the process
of economic growth.
The empirical research undertaken in the future
will focus on the further exploration of the
interdependency of the categories of effects of
inventions and innovators and their optimisation, so
as to offer a superior explanation of the issue of
implementing innovation in industry.
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