Modern Economy, 2011, 2, 780-787
doi:10.4236/me.2011.25086 Published Online November 2011 (
Copyright © 2011 SciRes. ME
Labor Productivity vs. Minimum Wage Level
Mieczysław Dobija
Cracow University of Economics, Cracow, Poland
Received August 19, 2011; revised September 17, 2011; accepted October 29, 2011
Recognition of the abstract nature of capital has liberated some new possibilities for alternative human capi-
tal research. Human capital, that is to say the human ability of doing work, is under the authority of all fun-
damental laws established in respect of the general notion of capital as spontaneous, and possessing random
diffusion and limited growth. The phenomenon of human capital’s natural dispersion is a starting point for
the theory of minimum wage, which ought to be sufficient to counterbalance the natural thinning out of the
initial human capital of an employee. In practice, the legal minimum wage is fixed at different levels, and
sometimes it is very low. Labor productivity is one fundamental factor that enables the establishment of a
proper minimum wage level. Each human capital is vanquished by spontaneous and random diffusion, which
averages 8% of the initial capital. Therefore the 8% rule is applicable to each employee no matter how edu-
cated and experienced he or she is. The results show that the level and fairness of the legal minimum wages
is conditioned by labor productivity measured by ratio Q. This ratio should be at least 3.0 so the minimum
wage could set off spontaneous random diffusion of employee’s human capital.
Keywords: Capital, Human Capital, Minimum Wage, Constant Pay, Labor Productivity
1. Introduction
The considerations introduced in this paper belong to an
alternative research program of human capital. This re-
search differs from T. Shultz’s and G. Becker’s well-
known program coined under the popular title, “Invest-
ing in People”, as described by M. Blaug [1, pp. 303-
321]. The new program is anchored in a deeper under-
standing of capital, which is discerned as the abstract
“ability to do work.” The potential growth of capital is
determined by the discovered constant p. The kernel of
this research program [Lakatos’ hard core] is a model of
capital that discloses factors causing changes of the ini-
tial capital. In addition to the hard core there is the triad,
“capital-labor-money,” where labor is the transfer of
capital to objects of work, and money is the pay receiv-
ables for work done. Therefore, a labor-driven economy
is the central focus of the research program.
The model of capital at moment t [2] identifies factors
that influence an initial value of capital. Among the fac-
tors are ratios s and p, where s measures the spontaneous
diffusion of initial capital, and p denotes the economic
constant of potential growth. The most important rela-
tionship shows that p = Ε(s) = 0.08 [1/year].
Initial capital C0 and time t are the essential factors of
the compound interest formula Ct = C0ert. But a true
challenge is the theory of the rate (r). As stated by M.
Dobija [2] the rate of growth of the initial capital has a
three-factor structure. Namely, r = ps + m, so the ini-
tial capital C0 is influenced by the three subsequent fac-
tors and flow of time t as follows:
ee ee)
tstmt psmt
()0.081/ yearpEs
The variables are defined as follows:
t—is the coordinating (calendar) time measured by
chosen cyclical movements, particularly of the Earth;
ept—is the factor of natural potential growth deter-
mined by the economic constant p = 0.08; the p also
serves as the capitalization rate;
e–st—discount factor, s, is the rate of spontaneous
and random diffusion of the initial capital; s is a central
part of discount rates.
emt—is an inflow of capital by human labor and
management, which can offset the natural diffusion of
capital and can save the potential for growth changing it
to profit.
Let us note that the variables s and m represent active
work of the natural forces (–s) and the active outer work
that can restrain the dispersion (m). Instead, the constant
p symbolizes a potential. The potential p can yield fruit,
provided the diffusion s is counterbalanced by the work
The powerful forces determining our reality become
visible in the model of the initial capital changes. Both
thermodynamic principles are present here. The first
thermodynamic principle is present since the model con-
tains initial capital C0. This means that the initial capital
can only be changed or transferred but never created.
The Second Law is also present since capital constantly
diffuses; the initial value spontaneously and randomly
The third force that has its part in the game is the
natural potential for growth. It is the setup of the Earth
and the Sun that guarantees essential potential for growth
(p = 8%). Thanks to this potential, human capital grows,
originating labor resources. Subsequently, human labor
can prevent diffusion by wise, productive labor, setting
off dispersion forces and causing that potential growth p
to become real economic value1. The model shows,
among others, that economy is a non-zero sum game, and
the added value can achieve an average rate of 8%. This
value concentrates in different resources, both material
(goods, soil, devices) and immaterial as intellectual and
institutional resources (laws and procedures, among oth-
Much research has been done to measure the value of
the constant p. This constant manifests in many fields of
economic investigation, and is known on the capital mar-
ket as the risk premium. A significant research on the
subject has been done by B. Kurek [3], who also de-
scribed related issues in a recent book “Deterministic
Risk Premium Hypothesis” [4, p. 124]. The author found
that a good estimator of the constant p is a properly de-
fined ROA. Examining financial statements of compa-
nies belonging to the S & P 1500 over a 20-year period,
the author showed that the average value of ROA = 8%,
28% so the p as a priori value is 8%. Financial state-
ments show values at the end of the year so the initial
capital compounded at a rate of 0.08 should yield e0.08 =
1.08328, that is to say 8.33%. The author established the
confidence interval (8.25; 8.89). Many authors still ex-
amine the constant p in the field of employees’ human
capital and their compensations. The human capital
model and derived compensation models are suitable for
testing the fundamental relationship: p = E(s) = 0.08 [1/
year]. For testing, a simple econometric model is suitable.
Namely Wa = AWh + B, where Wa is the real pay, and Wh
= s × H(T, p) is the pay calculated in line with the human
capital model. The variables H(T, p) and T denote re-
spectively: H(T, p)—employee’s human capital, and T
years of professional work.
Human capital is discerned as an employee’s ability to
do work. Models of human capital are derived from the
general model, and then compensation models stem from
the model of human capital. The most important conclu-
sion stemming from the model of capital concerns an
amount of fair constant pay. An employee as a living
creature has to waste some capital since heat engines
working in his body [5, pp. 157-158] have to disperse
some energy. To keep balance, the constant pay has to
counterbalance this loss. Therefore the constant pay
should not be less than 8% of the employee’s human
capital (s × H(T, p)). Then the employee’s human capital
is maintained, whereas less pay leads to the depreciation
of the employee’s human capital. In human capital cal-
culations, both the diffusion rate s is assumed as 8% and
the deterministic constant p = .08 as the capitalization
Research has shown that countries have different per-
centages of consistency regarding the legal minimum pay
for employees’ human capital. Western democratic coun-
tries have constant pay consistent with the 8% rule. This
means the natural diffusion of the employee’s human
capital (ratio s) is set off by basic constant pay. If the
constant pay (W) is s × H(T, p), where H(T, p) is the em-
ployee’s human capital, where T = years of professional
work then it is a fair pay that preserves the employee’s
human capital. This is not the case in many other coun-
tries, where consistency is not 100% and sometimes is as
low as 50%. The migration of the labor force (human
capital) in searching for better work and living condi-
tions is a natural phenomenon. Poland and Ukraine,
whose degree of consistency does not exceed 80% and
50%, respectively, are good examples.
It seems an important reason, for a low minimum
wage is weak labor productivity of an economy. Al-
though low labor productivity is not the only reason for
the inconsistency of the minimum wage, with the pay
level equal to p = E(s) = 8% of an employee’s human
capital (proper Gini’s coefficient can show other reason),
it is a fundamental condition. The research presented
here proposes that to attain the desired level of constant
pay, the macroeconomic ratio of labor productivity Q
ought to be sufficiently high. The Q is the ratio of labor
productivity [6,7] roughly determined as the quotient of
real GDP to total compensation. The searched level of
labor productivity is computed from a regression curve
showing the percentage of consistency between real pay
Wa and theoretical pay Wh = s × H(T, p) as a function of
1A farmer’s crop does not spoil and it yields economic value since the
farmer harvests it in the proper time.
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2. A Capital Theory of Minimum Wage
From the human capital point of view, the minimum
wage is assigned to a sufficiently mature individual with
the least ability to do work. It is usually an individual
aged 17 or 18, who has just completed mandatory educa-
tion but has not done professional work. On the one hand,
the individual’s ability to work (human capital) can be
computed in line with the general model. In the next step
we calculate its human capital’s annual diffusion. On the
other hand, in most states the legal minimum wage is
established as mandatory law. The two abovementioned
amounts are compared and assessed.
Thus, in the case of minimum pay, the receiver—an
employee—is an individual without professional educa-
tion and experience. The source of human capital is only
the stream of outlays on expenses of an employee’s par-
ents and society. In this case, the human capital model
H(T, p) = K(p), where H(T, p)—denotes the human capi-
tal of a person with T = 0 years of professional work; and
p = 0.08 is the economic constant which serves as the
capitalization rate. K(p)—denotes the capitalized cost of
living (future value) through the period, ending at the
moment mandatory education is completed.
To illustrate how the model works we apply human
capital calculations for computing a fair minimal pay in
the case of the USA. Let us assume a child is born in an
American family (2 + 2 persons). This child would die
soon if the parents and society did not care for it (The
Second Law and dispersion rate s). Fortunately, they do
this, and the inflow of capital (ratio m) offsets the s at
least. Therefore, the human capital of the child can grow
at rate p = 8%. In the course of life, human capital is
funded by outlays for costs of living2 estimated at $ 500
per person per month. Parents’ labor is not included.
We calculate the human capital at the end of the 17th
year of life (6 + 10 + 1) and then compute an adequate
fair pay resulting from human capital theory (HCT). The
issues are presented in Table 1. Thus, the legal pay
meets the theoretical one. The above calculations au-
thorize the conclusion that the current minimum pay in
the USA is (on average) fixed at a fair level, and the
percentage of consistency between practice and theory is
close to 100%.
It is a canon that Western democratic and capitalistic
countries execute the 8% rule, and so employees’ human
capital is preserved. One can say that it is an essence of
adult democratic capitalism. In contrast to Western de-
mocratic countries, many other countries apply legal
minimum pay beneath the 8% theoretical level. This
causes a migration of the labor force to countries with a
Table 1. Computation of human capital and the minimum
wage for the USA.
Monthly cost of living (rough estimation) $ 500
Future value of stream of outlays: $ 6000
for 17 years capitalized at the rate of 8% $ 202,501
Fair annual pay is equal to annual
diffusion of employee’s human capital (s
0.08 × $ 202,501 = $ 16,200
Monthly pay $ 16,200/12 = $ 1350
per month
Hourly pay $1,350/176 hour = $ 7.670
per hour
Current legal minimum pay in the USA $7.25
Current social security rate paid by
employer 6.2%
Hourly cost of labor $ 7.25 × 1.062 = $ 7.70
Percentage of consistency between legal
and HCT* pay
$ 7.70/$7.674 = 1.003
*HCT—human capital theory.
higher degree of consistency, because compensation less
than 8% of employee’s human capital means its depre-
ciation. However, the legal minimum payment of less
than 8% of employee’s human capital is not only an
agenda of a bad policy and the policymakers fault but
also a sort of real economic boundaries. One of them is
too low labor productivity.
In the body of Table 2 are data illustrating a situation
affecting a significant part of the labor force in Ukraine,
where the consistency of legal minimum pay with fair
pay computed on the basis of human capital theory does
not exceed 50% through the past five years. All numbers
in the body of Table 2 are expressed in the Ukrainian
national currency unit Hrn or Hrn per period.
Data presented in Table 2 show a difficult economic
situation for numerous groups of young employees start-
ing their first job and workers paid on a minimum wage
level. Since the minimum wage is the pillar of all com-
pensations one can conclude that most compensations do
not preserve human capital. As a result, Ukraine loses a
significant part of the labor force through migrations
motivated by the desire to earn more. In addition, the
Ukrainian population has significantly declined because
human capital is not preserved, so people do not see a
good future. E. Libanova [8] called this state of affairs a
“demographic collapse.”
The above considerations show that the simplest
model of employees’ human capital Ht is Ht = K(p),
where K(p) is the capitalized cost of living at the capi-
talization rate p = 0.08. The fair pay that preserves the
capital Ht is W = s × Ht. Indeed, the present value of the
tream of pays W yields Ht if the discount rate is equal to
2Cost of living denotes the minimal outlays needed for a child to grow
along with social standards developing its personal human capital. s
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Table 2. Ukrainian minimum wages in comparison to pay computed in line with HCT* (data are publicly available).
Years 2006 2007 2008 2009 2010 2011
Cost of living (4-person family) 400 440 500 780 870 997
Value of human capital H 162001 178201 224700 350532 390980 448055
Yearly cost of labor (0.08 × H) 12 960 14 256 17 976 28 042 31 278 35844
Monthly cost of labor (MCL) 1 080 1 188 1 498 2 339 2 606 2987
Legal minimum wages (LMW) 400.0 440.0 545.0 744.0 888.0 960.0
Monthly (LMW) increased by
pension charge 36.6% (LMCL) 400 × 1.366 = 546 440 × 1.366 = 601545 × 1.366 = 728744 × 1.366 = 1 016888 × 1.366 = 1 213 960 × 1.366 = 1 311
Ratio of LMCL to MCL 51% 50% 49% 44% 46% 44%
*HCT—human capital theory.
rate s, which represents random and natural diffusion of
capital, that is to say a decline of the initial capital.
/()1 1
close to zero random factor.
The above proof may be illustrated by simple but sig-
nificant calculations. In the case of the USA a couple
with two children who earn the minimum wage have a
monthly revenue of 2 × $ 7.70 × 176 hours = $ 2,710.4.
Let as assume that health care for a four-person family
requires 9% of the total. In addition, they pay 20% for
pension funds capitalized at a modest rate of 3%. Thus,
the couple have a residual income of $ 1,924.4, which,
divided by 4, yields $ 481 per person. Since the pays will
grow together with professional experience, an amount
of $ 500 is accessible as their cost of living. Moreover, at
the age of 65 years, a pension fund for the parents will
amount to 0.2 × 2710.4 × 12 × 100,4 = $ 653,075. The
amount for one person is then $ 326,538. Thus, if the
pension payments are preserved by a right policy, fair
money for older age is also guaranteed.
3. The Theory of Constant Pay Preserving
Employee’s Human Capital
The 8% rule is applicable to each employee no matter
how educated and experienced he or she is. Each capital
is vanquished by spontaneous and random diffusion,
which averages 8% of the initial capital. Therefore, a
constant part of compensation should exist, and its
amount ought to be able to counterbalance the effect of
dispersion. Such a level of constant pay is subordinated
to the 8% rule, and is called fair. The 8% rule has been
tested many times in numerous empirical researches,
which show that pays lower than 8% of employees’
capital trigger workers’ protests. In addition, their re-
quests for a pay rise halts at a level close to 8%. Re-
search shows that irrespective of the country or place,
employees expect compensation equal to at least 8% of
their human capital. The constant p = 0.08 determines a
border, since this value allows employees’ to keep their
human capital intact. If the percentage is higher, the em-
ployees feel safer and they have a greater possibility of
Research in Poland and the Ukraine has confirmed this
opinion. Author M. Dobija [9], among others, examined
compensation in a chosen institution and other compa-
nies as well as the salaries of some professionals, such as
school and academic teachers, nurses, and physicians. W.
Kozioł [10] examined compensations in companies and
universities. The author has shown that the constant pay
was close to 8% of human capital, whereas the average
percentage of compensations paid in the Polish compa-
nies examined was 10.1% in respect of employees’ hu-
man capital. Similarly, J. Renkas [11] found that this
percentage was 9.1% in the Ukrainian company exam-
ined, so the 8% rule also applied. J. Barburski [12] ex-
amined a set of companies and showed that the average
percentage of compensation over 8% (premium pay) was
1.74; in other words 21.75% of the constant pay. I. Ci-
eślak [13] in Poland and J. Renkas in Ukraine examined
the expectations of unemployed people searching for
work through employment offices. Both researches have
shown that expectations of constant pay have averaged
8% with respect to employee’s human capital.
Generally, an employee also has capital from profess-
sional education and experience. Considering not only
the cost of living K(t, p) capitalized through t years, but
also capital originating from a professional education E(t,
p), the employee’s human capital can be expressed as Ht
= K(t, p) + E(t, p). This is human capital on the threshold
of a professional career. When years of employment T
are taken into account, then employee capital increases
through experience. Quantifying experience by a semi
learning curve Q(T), the typical model of employee capi-
tal is as follows:
 
(),, 1 ()HTK t pEt pQT 
where: T—years of employment, w - learning parameters
of the employee, Q(T)—coefficient of experience ideal-
izing an idea of a learning curve.
The above model can be reshaped to an additive form
as follows;
 
() ,,()
where: D(T)—denotes capital from experience.
 
() (),,(0)()DTHTKtpEt pHQT 
Perceiving a human being as a triad: “body-mind-
spirit,” the above model gains one more factor, namely
“creativity capital”. The last is measured as the present
value of a stream of earnings exceeding fair pay stem-
ming from employee’s human capital. Thus, the entire
model of human capital is as follows:
() ()
where: R—denotes creativity capital. The above model
illustrates that the intellectual capital I(T) of an employee
is as follows:
() ()()
Having determined models of an employee’s capital,
one can prove that the minimum basic pay, which pre-
serves initial capital, is determined by the 8% rule. By
applying the IRR concept to employee’s human capital
over a one-year period, we get the equation:
 
()1 1HTrWHT 
where: r—the expected rate of return on capital, W
market pay received by the employee during one year in
the form of wages and fringe benefits. By finding vari-
able W, we can derive an adequate earning model:
()1 ()
 
 
Here ΔD(T) measures the annual increase of em-
ployee’s experience. The last factor ΔD(T) is significant
at the start of a professional career, and it tends to zero if
T grows.
Thus, the basic wage is determined by the employee’s
capital and rate of return. This amount is decreased by
the experience the employee got in the last year. The
above model confirms Sunder’s [14, p. 36] opinion that
experience is a “by-product of doing a job”, and thus an
employer is justified in modifying an employee’s earn-
ings in the short run. It is an interesting phenomenon that
earnings can be lower in some cases, because of non-
monetary benefits in terms of experience the employee
gains during the course of a year. An employer may be
aware of the resources, opportunities, and benefits en-
joyed by an employee as well as on-the-job-training op-
portunities. According to the above model, the experi-
ence gained is capitalized, increasing the earnings poten-
tial in the subsequent period. Factor ΔD(T) diminishes
quickly in time; it affects the first years of employment.
Since it quickly disappears, the general basic wage
model stemming from human capital measurement can
be limited to formula W = r × H(T, p).
Now, the essential question is about the size of rate r.
The answer is that the rate of return should be equal to
constant p = E(s) = 0.08. Then the employee’s human
capital does not deteriorate. To prove this, let us compute
the present value (PV) of a stream of wages. PV = pH(T,
p)/s pH(T, p)/p = H(T, p) since p = E(s). Thus the for-
mula W = p × H(T, p) estimates the fair basic pay. In
other words, the basic pay is sufficient to cover all natu-
ral depreciation of the employee’s capital. Consequently,
under average conditions, this pay allows a couple to
cover the costs of living and the education of their two
children. This means a couple have the resources needed
to cover the cost of living and the cost of education of a
four-person family, and their two children can attain the
parent’s level of professional education.
Fair constant pay is a stabilizing factor of socio-eco-
nomic life. The correct amount of this pay enables re-
sponsible family planning and is an essential variable of
home economics equilibrium. This pay is paid inde-
pendently from company performance, whereas other
parts of compensation (premium pay) depend strongly on
profitability and other ratios measuring company per-
4. Labor Productivity Ratio Q as a Factor of
Production Function
A deeper economic sense of the ratio Q can be explained
by the production function arising in the analytical ap-
proach rather than an econometric one as discussed in
earlier papers [15,16]. Reservations about the economet-
ric production function result from observations of the
features pertaining to a money-goods economy, in which
production factors are measured in money units; there-
fore, the value of production outlays (labor costs, use of
materials, etc.) is defined as an amount in a uniform unit
of measurement. These production factors are summed
up in the product according to the principles of cost cal-
culation and common sense; therefore it is the grand total
of product components as a result of combining produc-
tion factors that could become the starting point for de-
fining production function.
Taking into account the above fact, and applying a
natural approach based on the calculus of costs, we ar-
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rive at a production function with seven specified argu-
ments. As a result, the structure of the arguments speci-
fies all the significant variables, and the basic analytical
formula of the function does not require an estimation of
parameters. Production function expressed analytically
may be a tool of economic analysis using differential
calculus; or it may provide numerous non-linear models
describing the behavior of a selected variable. The value
of production in the historical prices of outlays may be
expressed as follows:
1/ 1PKZK Kr 
where: P—denotes yearly production in market prices, K
all costs of manufacturing and managing, and Z—annual
income. Thus Z/K denotes cost profitability. This ratio
can be introduced as a function of the ROA. The quotient
w = K/A, where A is the book value of assets is known as
the turnover ratio. Thus K = wA, and Z/K = Z/wA =
Production cost K can be divided into two parts; cost
of labor W and other costs M. Therefore K = W + M = W
+ zA, where z is the turnover ratio calculated in relation
to other costs M. Hence, we obtain product P, expressed
in market prices, as follows:
1PWzA r 
where: P denotes value of products in real market prices,
z—index of annual assets’ turnover.
After reshaping, the value of production becomes:
1/1PW zAWr 
Because the variable W is related to human capital, we
apply W = u × H, where: u is the rate of remuneration of
human capital and H is the total value of human capital
of all employees.
In the next step we attain the formula:
1/ 1PW zAuHr 
Then, using approximation (1 + x ex), the production
function is described by the following formula:
e1e 1
zA zA
uH uH
 
 
Here Q is the labor productivity. Thus the labor pro-
ductivity Q is a dimensionless variable (multiplier) and
as a function of several variables, it synthesizes all in-
fluences of material, labor factors, and skilled manage-
ment. Q therefore depends upon the capacity to generate
market value (ROA), technical equipment for the work
(A/H), assets rotation (z and w), and the degree of remu-
neration for labor (u).
In macroeconomic interpretation P can be replaced by
real GDP, so that it forms the relationship: GDP = W × Q.
Here the factors that influence GDP are divided into two
groups. The first, represented by W, involves labor and
demand created by labor costs. The second is Q showing
how efficiently one dollar of pay is changed into GDP.
Of course the least value of Q is 1. The more the Q is
greater than 1, the better. An increase of the productivity
ratio Q means an increase in the society’s wealth. Q = 1
means that the prehistoric individual gathers food neces-
sary for survival, and this alone constitutes the wage.
Then products equal earnings, and Q = 1. These days,
that index is usually higher than one; for example, in the
USA it approximates 3.5.
There is one defect hidden in the Q. This number can-
not be computed simply by dividing real GDP by an em-
pirical number of the total compensations W. As a matter
of fact, total compensations are the sum of the private
sector pays and the public sector pays. But compensation
in the public sector has its source in taxes. This is not
right since labor is self financing as explained in [17].
Therefore, empirical data need some corrections done
while calculating the Q for a group of states (Table 3).
As labor share like factor the Q is pretty stable.
It is important to discern the wide applications of the
ratio Q both macroeconomically as discussed in [17] and
microeconomically as presented by J. Barburski [18], W.
Kozioł [19], M. Dobija [20], and others. Ratio Q is, after
all, an important ratio for evaluating company perform-
ance. It serves, among others, to determine the right fund
for premium pay consistent with company economic
5. The Empirical Relationship between
Labor Productivity (the Ratio Q) and
Minimum Wage Level
There is no question about the positive relationship be-
tween the ratio Q and employees’ earnings. Instead, an
Table 3. The ratio Q for a group of states.
Country 2006 2007 2008 2009 2010
USA 3.458 3.470 3.560 3.500 3.452
Japan 3.069 3.093 3.186 3.433 3.279
UK 3.204 3.517 3.444 3.082 3.095
Switzerland 3.534 3.645 3.748 3.650 3.509
Germany 2.498 3.380 3.389 3.276 3.169
Czech Republic1.873 2.204 2.355 2.210 2.134
Poland 1.881 1.992 1.854 1.869 1.903
China 1.415 1.512 1.685 1.762 1.768
Source: M. Dobija [7] for years 2006-2009.
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interesting question is, what minimum level of the Q still
guarantees the preservation of employees’ human capital?
An answer to this question requires an examination of
pays and of the Q using a representative sample for the
world. Here the agenda in narrowed to minimum wages
only and to the European group of states together with
the USA. Therefore, the issues can give an orientation
rather than an exact answer for every country of the
world. Table 4 includes sample data, which enables the
application of a regression relationship (conditional
mean) between variables Con and Q.
6. Conclusions
The presented empirical study concerned mainly mini-
mum wages. Assuming that the legal minimum wage
does influence the level of all compensation, and it is an
indicator of a country’s economy, the presented research
authorizes some conclusions. The most general reflection
suggests that the level of preservation of employees’
human capital depends among others on labor productiv-
ity. Therefore, an increase in rising labor productivity is
a constant task of management and the state authorities.
It is not an easy task since each real growth of GDP is a
reason to request more pay, as happened in Poland in
2007, or increasing the budget sector. The effects are
apparent in Table 3. Therefore, Poland still has a re-
markable gap compared to countries with a Q of not less
than 3.0. The earning migration trend still continues,
although it has declined slightly compared to ten years
ago. Poland needs to increase the Q to about 1 in order to
become a member of the welfare states. On the other
hand, the Polish situation is much better than that of
Ukraine, which is still in a state of stagnation.
The data from columns 5 and 6 allow for the determi-
nation of a conditional relationship between the variables
Con and Q according to regression curve: F(q) = E
(ConQ = q). In order to avoid a mistake by applying
linear regression or a personal choice sort of curve, we
use the nonparametric approach. We use an estimator of
the conditional mean as introduced in papers [21,22].
The estimator is the function as follows:
con, ,
qn i
Productivity in the private sector, which operates in a
free market environment, is driven by market forces and
market competitions. A public sector that is too large and
does not have proper control of productivity is undoubt-
edly a reason for general low productivity as measured
by the ratio Q. Therefore, comprehensive control of the
public sector and deep reform, in particular, as discussed
in [23] are ways of attaining better preservation of em-
ployees’ human capital. This reform requires an under-
The functions of weight φ(q, qi, σqn) are the density
function of the normal distribution. Having determined a
suitable estimator of the conditional mean we find that
90% of consistency between the legal minimum pay and
the constant pay determined by HCT is achieved at the Q
2.7, while the Q 3.2 guarantees a consistency close to
Table 4. Sample of data for establishing the relationship between variables Con and Q.
Country Legal Minimum Wage Cost of Labor* Pay in line with HCT#Con§ Labor Productivity Ratio Q
1 2 3 4 5 6
1. USA $ 1,276 $ 1,355 $ 1,350 100% 3,452
2. France € 1,365 € 1,837 € 1,947 101% 3,070
3. Germany € 1,467 € 1,687 € 1,700 100% 3,169
… Data are available for request from the author …
27 Czech Rep. 8000 Krn 9440 Krn 11,000 Krn 86% 2134
28 Poland 1386 zł 1636 zł 2097 zł 78% 1903
29 Ukraine 915 Hrn 1234 Hrn 2741 Hrn 46% 1455
*Legal Minimum Wage increased by pension payment charging employer; #HCT—Human Capital Theory; §The quotient of column 3 to column 4 expressed as
percentage. a
standing and application of labor self-financing as well
as a limitation of total pays in the public sector according
to the size of the Q. We can conclude that labor produc-
tivity measured by ratio Q is significant factor influence-
ing level of the minimum wage. Nevertheless it is not
exclusive factor. The mentioned Gini’s coefficient of
earnings distribution as well the too large public sector
are also essential factors.
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