Теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива
The purpose of the research is to test a possibility of using the theory of utility function in economics theory [1] for aggregating different kinds of variables such as economic benefit and ecological damages of industrial activities. An example of coal fuel combustion for electricity generation [2...
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The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
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| author | Matsuki, Y. Bidyuk, P. I. |
| author_facet | Matsuki, Y. Bidyuk, P. I. |
| author_institution_txt_mv | [
{
"author": "Y. Matsuki",
"institution": null
},
{
"author": "P. I. Bidyuk",
"institution": null
}
] |
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| description | The purpose of the research is to test a possibility of using the theory of utility function in economics theory [1] for aggregating different kinds of variables such as economic benefit and ecological damages of industrial activities. An example of coal fuel combustion for electricity generation [2, 3] is selected for this test, which produces both economic benefit and human health damages. Several mathematical models for the utility function are tested with the data of the volume of combustions and the amount of air pollutions of twenty seven Oblasts of Ukraine by the regression analysis [4]. Consistent results are obtained upon the theory and the statistical data analysis. It is concluded that the prices take important role to give the weighting factor through the aggregation process of various indicators (independent variables) because in this theory the prices make up the total budget, which gives the constraints for maximizing the utility with given values such as number and volume of the indicators. |
| first_indexed | 2025-07-17T10:18:50Z |
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© Y. Matsuki, P.I. Bidyuk, 2013
Системні дослідження та інформаційні технології, 2013, № 3 19
TIДC
ПРОБЛЕМИ ПРИЙНЯТТЯ РІШЕНЬ І
УПРАВЛІННЯ В ЕКОНОМІЧНИХ, ТЕХНІЧНИХ,
ЕКОЛОГІЧНИХ І СОЦІАЛЬНИХ СИСТЕМАХ
UDC 519.004.942
THEORY, ALGORITHM AND CONDITION
FOR AGGREGATING ECONOMIC BENEFIT AND HEALTH
DAMAGES OF COAL FUEL COMBUSTION
Y. MATSUKI, P.I. BIDYUK
The purpose of the research is to test a possibility of using the theory of utility func-
tion in economics theory [1] for aggregating different kinds of variables such as
economic benefit and ecological damages of industrial activities. An example of
coal fuel combustion for electricity generation [2, 3] is selected for this test, which
produces both economic benefit and human health damages. Several mathematical
models for the utility function are tested with the data of the volume of combustions
and the amount of air pollutions of twenty seven Oblasts of Ukraine by the regres-
sion analysis [4]. Consistent results are obtained upon the theory and the statistical
data analysis. It is concluded that the prices take important role to give the weighting
factor through the aggregation process of various indicators (independent variables)
because in this theory the prices make up the total budget, which gives the con-
straints for maximizing the utility with given values such as number and volume of
the indicators.
INTRODUCTION
Utility function is a theory to indicate the level of wellness of human and/or soci-
ety, ,iX where ,,...,2,1 ni = such as foods, cloth, and utility such as electricity,
gas, water, and resources. Human and/or society wishes higher level of utility,
),,......,,( 321 nXXXXU but the constraints are given by the total budget, ,I to-
gether with the prices
ixP for having different kinds of wellness iX respectively,
where
i
n
i
x XPI
i∑
=
=
1
. (1)
Under this constraint, the condition for obtaining the maximum utility is to
be found, using the Lagrangean Multiplier Technique, as shown bellow.
At first, the Lagrangean is defined as the follow.
)(),....,,(
1
321 ∑
=
−+=
n
i
ixn XPIXXXXUL
i
λ . (2)
Here, λ is an unknown variable, which is called “Lagrangean multiplier”.
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2013, № 3 20
The first order condition to get the maximum utility, ),...,,,( 321 nXXXXU ,
is partial derivatives of L by each of nXXXX ,...,,, 321 and λ are equal
to zero, i.e.
0=−∂
∂=∂
∂
ix
ii
PX
U
X
L λ .
0
1
=−=∂
∂ ∑
=
n
i
ix XPIL
iλ . (4)
For example, by dividing i-th equation by )1( +i -th equation of the above
(1)–(4), we get the following:
,
j
i
X
X
j
i
P
P
X
U
X
U
=
∂
∂
∂
∂
(5)
where .ji ≠
The above equation (5) means that the marginal rate of substitution (the ratio
of these two partial derivatives of utility function by iX and jX ) should be equal
to the ratio of the prices of these iX and jX in order to get the maximum
utility [1]. In other words, although people wish to possess the higher/bigger
utility, the maximum utility is always constrained by the budget and the prices,
and the maximum utility is obtained only where and/or when the marginal rate of
substitution,
j
i
X
U
X
U
∂
∂
∂
∂
and the ratio of the corresponding two prices,
j
i
X
X
P
P
i.e. the
slope of the budget line, are equal. This point is the equilibrium to give people the
maximum utility, which is given under the budget constraint. In other words, the
utility is at the maximum, and there is enough amount of budget. Therefore, it is
expected that if the economy of a region stays for a considerably long time-
period, it is reasonable for analysts to think that the utility of the market is at the
maximum equilibrium.
METHOD
The mathematical model of the utility function needs to be found. At first, the
following three models are assumed, and then empirical analysis is made for test-
ing the fitting of each model to the statistical data:
• Linear model:
.
1
i
n
i
i XCU ∑
=
= (6)
• Non-linear model (Cobb-Douglas function [1]):
.
1
∏
=
=
n
i
C
i
iXU (7)
Theory, algorithm and condition for aggregating economic benefit and health damages …
Системні дослідження та інформаційні технології, 2013, № 3 21
• Logarithmic model:
,Log
1
∑
=
=
n
i
ii XCU (8)
where
.1
1
=∑
=
n
i
iC (9)
Here, iC is a weighting factor to combine various wellness, ,iX to make up
a utility ,U but it can be also translated as preference or probability to make the
weights of different options of the wellness or resources.
In order to make the statistical test, the variable included in the equations
(6)–(8) are not enough, but each of these models needs to be transformed to the
linear equations, with the Lagrangean multiplier technique as shown bellow, with
which each wellness, iX , can be mathematically indicated as the function of the
total budget, ,I and the prices of various wellness, ,,...,,,
31 ns xxxx PPPP which
are available in the actual statistical database. Then, the linear regression analysis
can be carried out for the statistical tests.
For the linear model, i
n
i
i XCU ∑
=
=
1
, the Lagrangean is:
.)(
1
iXi
n
i
i XPIXCL
i∑∑ −+=
=
λ (10)
Given the budget constraint, the first order condition for maximizing the utility,
i
n
i
i XC∑
=1
is that the partial derivatives of L by each of nXXXX ,...,,, 321 and
λ are equal to zero, i.e.
,0=−=∂
∂
iXi
i
PCX
L λ (11)
,0
1
=−=∂
∂ ∑
=
i
n
i
x XPIL
iλ (12)
where .,...,2,1 ni =
From (11)
.
λ
i
X
C
P
i
= (13)
From (12)
.
1
i
n
i
X XPI
i∑
=
= (14)
Then, replace
jXP of (14) by (13) to get:
,
1
1
∑
−
=
+=
n
i
j
j
iX X
C
XPI
i λ
(15)
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2013, № 3 22
where .ji ≠
From (13)
.1
i
X
C
P
i=
λ
(16)
Then, replace
λ
1 of (15) by (16) to get:
.
1
1
j
n
j i
j
X
i X
C
C
P
IX
i
∑
−
=
−= (17)
With the same procedure to get (17) from (6), for the non-linear model,
∏
=
=
n
i
C
i
iXU
1
and for the logarithmic model, ,Log
1
∑
=
=
n
i
ii XCU the following
equation is obtained for both of these two models:
.
1
∑
=
=
n
j
j
i
X
i
C
C
P
IX
i
(18)
The next step is to test which model statistically fits in the actual data, upon
(17) and (18).
RESULTS
The economic benefit and the health damages of coal fuel combustion are in-
cluded together in the models of utility function, and they are empirically ana-
lyzed together with the data taken from the National Statistics of Ukraine for 27
Oblasts (Provinces) in 2010 and 2011. From this database, the volume of coal
combustion (tons/year) is taken as the surrogate of the economic benefit from the
activity of coal combustion, and the emission volumes (tons/year) of Nitrogen
oxides and Sulfur compounds from stationary sources, as well as the greenhouse
gas emission volume, are selected as the surrogates for health damages of the coal
combustion. The prices of these indicators (variables) are set as follows:
• The price of coal combustion: 100 US dollars per ton as the price
of coal per ton [5].
• The price of health damage by the emission of Nitrogen oxides and Sulfur
compounds are calculated by multiplying the price of one person’s life who is
dying by the air pollution [2] by the calculated number of long-term mortalities
from the nitrate and the sulfate respectively [2] and then divided by the volume of
the emission of the Nitrogen oxides and Sulfur compounds respectively from the
reference power station, the Tripylska Power Station [2]. Those values are shown
in Table 1.
• The price of the greenhouse gas emission, 22 US dollars/ton (CO2 equiva-
lent) is taken from the average price of the carbon tax of France, 25 US dol-
lars/ton, Ireland, 20 US dollars/ton, and Norway, 21 US dollars/ton [6].
Theory, algorithm and condition for aggregating economic benefit and health damages …
Системні дослідження та інформаційні технології, 2013, № 3 23
T a b l e 1 . Values used for calculating the price of health damages from the air
pollutions
Value Description Reference
Value of life, LV 18000
US dollars
The value of one person’s death
within his or her life time after one
year exposure to the air pollutions
[2]
page 27
by Nitro
gen oxides
emission
992
persons/year Number of
the deaths,
ND by Sulfur
compounds
emission
2504 per-
sons/year
Calculated number of the long-term
mortalities (deaths) in all territory
of Ukraine from the emission for
one year at the Tripylska Power
Station.
[2]
Page 28
Table 7
Nitrogen
oxides
11108
tons/year Emission
volume, VE Sulfur
compounds
40909
tons/year
Emission from Tripylska Power
Station for one year
[2]
Page 25
Table 3
by Nitro
gen oxides
emission
4097
US dollars/tonPrice of
health dam-
age, PH by Sulfur
compounds
emission
436
US dollars/ton
Calculated by:
EDHH VNVP /=
The descriptive statistics of the variables selected for this statistical test are
shown in Table 2, the correlations between these selected variables are shown in
Table 3, and the results of the statistical tests are shown in Table 4 for the linear
model, the non-linear model, and the logarithmic model. In Table 2, the total
budget is calculated by the equation (1), given that the statistical data is consid-
ered at the equilibrium that makes up the maximum utility.
T a b l e 2 . Descriptive statistics of the variables for coal combustion and the
health damages
Parameter Budget
(US$)
Coal
combustion
(tons)
Sulfur
compounds
emission (tons)
Nitrogen
oxides
emission (tons)
Greenhouse gas
emission (CO2
equivalent tons)
Mean 482149,6 2559,024 46,5441 11,9628 7,287157
Median 94856,79 158,2500 4,0085 4,0875 2,928500
Maximum 5917803, 30150,90 381,4940 94,5760 61,47900
Minimum 4590,271 9,5000 0,1610 0,3000 0,400000
Std. Dev. 1014658. 6082,066 86,4365 19,4452 11,75112
Skewness 3,6936 3,6329 2,5260 2,7623 3,618079
Kurtosis 18,0194 16,3432 9,2654 10,5239 16,75077
Obs. 54 54 54 54 54
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2013, № 3 24
T a b l e 3 . Correlations between the variables
Parameter Budget Coal
combustion
Nitrogen
oxides
emission
Sulfur
compounds
emission
Green-
house gas
emission
Budget 1
Coal combustion 0,9520 1
Nitrogen oxides emission 0,9452 0,9536 1
Sulfur compounds emission 0,9201 0,9532 0,9379 1
Greenhouse gas emission 0,9299 0,9718 0,9346 0,9138 1
T a b l e 4 . Statistical test on the coal combustion and health damages by the air
pollutions
Model Dependent
Variable
Independent
Variable
Coefficient
T-
Statistics
R2 AIC Schwartz
Interception –966,0035 –5,5818
Budget/price 0,1018 2,1769
Nitrogen emission 20,2686 0,7418
Sulfur emission 20,3609 4,1017
Linear
model, 1
Coal com-
bustion
Greenhouse
gas emission 253,0772 6,8217
0,9744 16,7648 16,9490
Interception 2,1496 1,9381
Budget/price 0,0275 2,8428
Coal combustion 0,0006 0,7418
Sulfur emission 0,0656 2,3111
Linear
model, 2
Nitrogen
oxides
emission
Greenhouse
gas emission 0,2913 1,0949
0,9323 6,2464 6,4305
Interception 10,5520 1,9965
Budget/price 0,0006 0,1102
Coal combustion 0,0126 4,1017
Nitrogen emission 1,4972 2,3111
Linear
model, 3
Sulfur
compounds
emission
Greenhouse
gas emission –2,0155 –1,6078
0,9219 9,3734 9,5576
Interception 2,4176 4,8033
Budget/price 5,51E–06 0,1857
Nitrogen emission 0,0820 1,0949
Sulfur emission –0,0249 –1,6078
Linear
model, 4
Green-
house gas
emission
Coal combustion 0,0019 6,8217
0,9479 4,9782 5,1623
Interception –192,2655 –0,6776 Non-
linear/log
model, 1
Coal com-
bustion Budget/price 0,5706 22,4198 0,9062 17,9524 18,0260
Interception 3,2290 3,3380 Non-
linear/log
model, 2
Nitrogen
oxides
emission Budget/price 0,07421 20,8767 0,8934 6,5897 6,6634
Interception 8,7513 1,6968 Non-
linear/log
model, 3
Sulfur
compounds
emission Budget/price 0,0341 16,9434 0,8466 9,9371 10,0108
Interception 2,0946 3,1806 Non-
linear/log
model, 4
Green-
house gas
emission Budget/price 0,0002 18,2312 0,8647 5,8208 5,8944
Theory, algorithm and condition for aggregating economic benefit and health damages …
Системні дослідження та інформаційні технології, 2013, № 3 25
The values of R2 show that both the linear model and the non-linear model
including the logarithmic model well fit in the given database, while the values of
R2 of the linear models indicate better fitting than the non-linear/logarithmic
models’. However, the signs, i.e., + and –, of the coefficients of the linear models
don’t represent signs of the coefficients of the equation (17). To remove this prob-
lem and to give the negative signs to the coefficients of the linear model, the fol-
lowing operations are made:
Upon this result, it is observed that the order of magnitude of the prices dif-
fer from 22 US dollars/ton to 4097 US dollars, and the volumes (tons) of combus-
tion and the emissions differ from 7 tons/year to 2559 tons/year. From this obser-
vation, it is assumed that the order of magnitude of one variable or one price
should not be so different from each other. In order to check this assumption, two
sub-systems of the dataset are created, i.e., the coal combustion volume, the nitro-
gen oxides emission as one set, and the coal combustion volume, the sulfur com-
pounds emission, and the greenhouse gas emission as another one set. The de-
scriptive statistics of the variables of each group is shown in Table 5, the
correlations of the set of the variables in each group are shown in Table 6 and
Table 7, and the results of the regression analysis are shown in Table 8 for the
coal combustion and nitrogen oxides emission, and in Table 9 for the coal
combustion, sulfur compounds emission and greenhouse gas combustion.
T a b l e 5 . Descriptive statistics of the variables for coal combustion and the
health damages
Parameter
Total Budget for coal
combustion
and nitrogen oxides emission (US$)
Total Budget for coal combustion,
sulfur compounds
and greenhouse gas emission (US$)
Mean 304913,8 276356,0
Median 58034,36 20271,43
Maximum 3389568 3180226
Minimum 2998,500 1264,000
Std. Dev. 684600,9 644479,6
Skewness 3,5428 3,5756
Kurtosis 15,7033 15,9646
Obs. 54 54
T a b l e 6 . Correlations between budget, coal combustion and nitrogen oxides
emission
Parameter Budget Coal combustion Nitrogen oxides emission
Budget 1
Coal combustion 0,9994 1
Nitrogen oxides emission 0,9636 0,9536 1
T a b l e 7 . Correlations between budget, coal combustion, sulfur compounds
emission and greenhouse gas emission
Variable Budget Coal
combustion
Sulfur com-
pounds emission
Greenhouse
gas emission
Budget 1
Coal combustion 0,9998 1
Sulfur compounds emission 0,9584 0,9532 1
Greenhouse gas emission 0,9710 0,9718 0,9138 1
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2013, № 3 26
T a b l e 8 . Statistical test on the coal combustion and nitrogen emission
Model Dependent
Variable
Independent-
Variable Coefficient T-
Statistics R2 AIC Schwartz
Interception 0,0002 2,0042
Budget/price 1,0000 19564952Linear
model
Coal
combustion Nitrogen
emission – 40,9701 – 2276781
1,0000 –11,6920 –11,5815
Interception – 148,2003 – 4,6194Non-
linear
model
Coal
combustion Budget/price 0,8879 205,7971
0,9988 13,6157 13,6894
Interception 5,90E–06 2,0042
Budget/price 1,0000 2562759Linear
model
Nitrogen
emission Coal
combustion – 0,0244 – 2276781
1,0000 –19,1177 –19,0072
Interception 3,6173 4,6195 Non-
linear
model
Nitrogen
emission Budget/price 0,1121 25,9916
0,9285 6,1900 6,2637
T a b l e 9 . Statistical test on the coal combustion, sulfur compounds emission
and greenhouse gas emission
Model Dependent
Variable
Independent
Variable Coefficient
T-
Statistics
R2 AIC Schwartz
Interception 5,51E– 06 0,0715
Budget/price 1,0000 20896952
Sulfur emission – 4,3600 –2074635
Linear
model
Coal
combustion
Greenhouse
gas emission – 0,2200 –11923,23
1,0000 –12,9160 –12,7686
Interception – 48,5881 –3,0200Non-
linear
model
Coal
combustion Budget/price 0,9436 408,0275
0,9997 12,2477 12,3214
Interception 1,26E-06 0,0715
Budget/price 1,0000 2231241
Coal
combustion – 0,2294 –2074635
Linear
model
Sulfur
emission
Greenhouse
gas emission – 0,0505 –11939,86
1,0000 –15,8609 –15,7136
Interception 11,0232 2,983100Non-
linear
model
Sulfur
emission Budget/price 0,0560 24,1998
0,9184 9,3056 9,3792
Interception 2,59E-05 0,074005
Budget/price 1,0001 11928,81
Coal
combustion – 4,5459 –11923,23
Linear
model
Greenhouse
gas
emission
Sulfur emission –19,8203 –11939,86
1,0000 –9,8875 –9,7402
Interception 2,3946 5,688897Non-
linear
model
Greenhouse
gas
emission Budget/price 0,0004 29,26192
0,9427 4,9609 5,0345
Theory, algorithm and condition for aggregating economic benefit and health damages …
Системні дослідження та інформаційні технології, 2013, № 3 27
As a result after dividing the database into two groups, according to the size
of the values of the prices, the results of the regression analysis upon each of two
groups in Table 8 and Table 9 show good fitting of the linear model, because all
the coefficients of terms for the budget/price are close to 1,0 and the sign of each
coefficient from the second term is negative, which satisfy the form of equation
(17), while the values of T-statistics of the coefficients show enough statistical
significance. The values of R2, Akaike Information Criterion, and Schwarz Crite-
rion also show statistical well-fitting of the model to each of two databases.
For the non-linear and the logarithmic models, the sum of the calculated co-
efficients of “budget/price” over the different variables are close to 1,0 in both
groups in Table 8 and Table 9, and this result is consistent to the equation (18).
The Akaike Information Criterion and Shwartz Criterion don’t show statistical
well-fitting.
The next step is to estimate the weighting factors, as shown in the equation
(17) and (18) as the coefficient iC , where ....,,2,1 ni = For this purpose, the statis-
tically obtained values for the coefficient of the equation (17) and (18) are used.
The coefficients of the linear model are obtained as shown bellow.
When
,ij
i
j
C
C
α= (19)
where ijα is the observed value of the coefficient that is obtained by the linear
regression analysis, as shown in Table 8 and Table 9.
From (17) and (19),
,
1
1
j
n
j
ij
X
i X
P
IX
i
∑
−
=
−= α (20)
where
.
1
1
1 ∑
∑
=
−
= =
n
j
ij
i
n
j
j
C
C
α (21)
From (9)
.1
1
11
=+= ∑∑
−
==
n
j
ji
n
i
i CCC (22)
Then, from (21) and (22),
,
1 1
1
∑
−
=
=
− n
j
ij
i
i
C
C
α (23)
,1
1
1
∑
−
=
=−
n
j
ijii CC α (24)
.11
1
1
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+∑
−
=
n
j
ijiC α (25)
Y. Matsuki, P.I. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2013, № 3 28
Therefore
.
1
1
1
1
∑
−
=
+
= n
j
ij
iC
α
(26)
With the equation (26), the following utility functions, (27) from Table 8 and
(28) from Table 9, are obtained:
,9762,00238,0 nitrogencoal XXU += (27)
.0394,07814,01792,0 greenhousesulfurcoal XXXU ++= (28)
For non-liner and logarithmic models, the observed coefficient iβ of
“budget/price” in Table 8 and Table 9 is given in the equation (29). As observed
in Table 8 and Table 9, each sum of the observed coefficients is close to 1,0, and
this result indicates the equation (30). With (29) and (30), the observed coefficient
iβ is equal to the normalized coefficient iC of the equation (7) and (8):
,1
1
1
=∑
∑=
=
n
i
n
j
j
i
C
C
(29)
.
1
in
j
j
i
C
C β=
∑
=
(30)
Thus, the following utility functions are obtained, (31) from Table 8 and (32)
from Table 9:
,1121,0
nitrogen
8879,0
coal XXU = (31)
.0004,0
greenhouse
05601,0
sulfur
9436,0
coal XXXU = (32)
For the logarithmic model, the following functions are obtained, (33) from
Table 8 and (34) from Table 9.
,log1121,0log8879,0 nitrogencoal XXU += (33)
.log0004,0log05601,0log9436,0 greenhousesulfurcoal XXXU ++= (34)
CONCLUSIONS AND RECOMMENDATIONS
It has been demonstrated that the theory of utility function can be used for aggre-
gating various indicators, including both the economic benefits and health
damages. For this process, the prices take important role to give the weighting
factors for aggregating various indicators (independent variables) because the
prices make up the total budget, which gives the constraints for maximizing the
utility with given values such as number and volume of the indicators in this
theory of utility function.
Theory, algorithm and condition for aggregating economic benefit and health damages …
Системні дослідження та інформаційні технології, 2013, № 3 29
When the orders of magnitudes of the selected indicators or the values of the
prices of those indicators are close to each other, for example within the order of
100, both linear and non-linear/logarithmic models can explain the weighting
and/or preference of the various indicators in the database of coal combustion and
health damages in 27 Oblasts (Provinces) of Ukraine. Therefore, for constructing
the larger system with more number of the indicators (variables), it is necessary to
select the indicators, which have the closer orders of magnitudes in the prices.
Further research and analysis are needed for more variety of indicators and
for larger system, which includes the indicators of social, ecological and eco-
nomic impacts of the industrial activities.
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3. Мацукі Й. Оцінка зовнішніх витрат як зведеного показника сталого промисло-
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тексти: У 2 ч. / Міжнар. рада з науки (ICSU) [та ін.]; наук. кер. М.З. Згу-
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Received 08.02.2012
From the Editorial Board: the article corresponds completely to submitted manu-
script.
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| id | journaliasakpiua-article-43890 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2025-07-17T10:18:50Z |
| publishDate | 2013 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/75/ab01db1dc000cc0e55694827e985a375.pdf |
| spelling | journaliasakpiua-article-438902018-03-30T15:16:01Z Theory, algorithm and condition for aggregating economic benefit and health damagesof coal fuel combustion Теория, алгоритм и условия агрегирования экономической выгоды и вреда здоровью при сжигании угольного топлива Теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива Matsuki, Y. Bidyuk, P. I. The purpose of the research is to test a possibility of using the theory of utility function in economics theory [1] for aggregating different kinds of variables such as economic benefit and ecological damages of industrial activities. An example of coal fuel combustion for electricity generation [2, 3] is selected for this test, which produces both economic benefit and human health damages. Several mathematical models for the utility function are tested with the data of the volume of combustions and the amount of air pollutions of twenty seven Oblasts of Ukraine by the regression analysis [4]. Consistent results are obtained upon the theory and the statistical data analysis. It is concluded that the prices take important role to give the weighting factor through the aggregation process of various indicators (independent variables) because in this theory the prices make up the total budget, which gives the constraints for maximizing the utility with given values such as number and volume of the indicators. Целью исследования является проверка возможности применения в экономической теории концепции функции полезности для агрегирования разных переменных, таких как экономическая выгода и экологический вред промышленной деятельности. Для данной проверки выбран пример сжигания угольного топлива для выработки электроэнергии, являющегося источником как экономической выгоды, так и вреда здоровью человека. С помощью регрессионного анализа на основании данных объема сжигаемого материала и уровня загрязненности воздуха двадцати семи областей проведено тестирование нескольких математических моделей функции полезности. Полученные результаты согласуются с теорией и анализом статистических данных. Авторы пришли к выводу, что в процессе агрегирования различных индикаторов (независимых переменных) большое значение для коэффициента взвешивания имеют цены, поскольку в этой теории они определяют общий бюджет, устанавливающий ограничения для максимизации полезности при данных параметрах, таких как количество и величина индикаторов. Метою дослідження є перевірка можливості застосування в економічній теорії концепції функції корисності для агрегування різних змінних, таких як економічна вигода та екологічна шкода промислової діяльності. Для цієї перевірки обрано приклад спалювання вугільного палива для вироблення електроенергії, яке є джерелом як економічної вигоди, так і шкоди здоров’ю людини. За допомогою регресійного аналізу на підставі даних обсягу спалюваного матеріалу та рівня забрудненості повітря двадцяти семи областей проведено тестування декількох математичних моделей функції корисності. Отримані результати узгоджуються з теорією та аналізом статистичних даних. Автори дійшли висновку, що у процесі агрегування різноманітних індикаторів (незалежних змінних) важливе значення для коефіцієнта зважування мають ціни, оскільки у цій теорії вони визначають загальний бюджет, який встановлює обмеження для максимізації корисності за цих параметрів, таких як кількість та величина індикаторів. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2013-09-25 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/43890 System research and information technologies; No. 3 (2013); 19-29 Системные исследования и информационные технологии; № 3 (2013); 19-29 Системні дослідження та інформаційні технології; № 3 (2013); 19-29 2308-8893 1681-6048 uk https://journal.iasa.kpi.ua/article/view/43890/40172 Copyright (c) 2021 System research and information technologies |
| spellingShingle | Matsuki, Y. Bidyuk, P. I. Теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива |
| title | Теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива |
| title_alt | Theory, algorithm and condition for aggregating economic benefit and health damagesof coal fuel combustion Теория, алгоритм и условия агрегирования экономической выгоды и вреда здоровью при сжигании угольного топлива |
| title_full | Теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива |
| title_fullStr | Теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива |
| title_full_unstemmed | Теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива |
| title_short | Теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива |
| title_sort | теорія, алгоритм та умови агрегування економічної вигоди та шкоди здоров’ю під час спалювання вугільного палива |
| url | https://journal.iasa.kpi.ua/article/view/43890 |
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