Research Article Real National Income Average Growth Rate ...
Transcript of Research Article Real National Income Average Growth Rate ...
Research ArticleReal National Income Average Growth Rate A Novel EconomicGrowth and Social Fair Evaluation Index
Chien Wei Wu1 and Wei Zhan Hung2
1Department of Economics National Chi Nan University No 1 University Road Puli Nantou County 54561 Taiwan2Department of International Tourism and Recreation Hsing-Kuo University No 600 Section 3 Taijiang BoulevardAnnan District Tainan Taiwan
Correspondence should be addressed to Wei Zhan Hung steady 2006hotmailcom
Received 4 September 2014 Accepted 12 December 2014
Academic Editor Joao Ricardo Faria
Copyright copy 2015 C W Wu and W Z Hung This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
The purpose of this study is to propose a new economic index namely real national income average growth rate (RNIAGR)whichmeasures the performance of economic growth with consideration for income distributionThis study also develops anothernew economic index called five-scale real national income average growth rate (FSRNIAGR) which simplifies the calculation ofRNIAGRThe merits of these new indexes are discussed to justify their efficacy This paper also justifies the use of proposed indexby showing that this index can actually measure the ordering of social welfare To highlight the difference between this new indexand the traditional ones this paper compares the index with real economic growth rate using the data of Taiwan In addition thispaper shows that when the real growth stagnates or even declines this new index indicates that income distribution deteriorates
1 Introduction
In recent years an immense income disparity has become acommon phenomenon across borders For example accord-ing to a report published by the Organization for EconomicCooperation and Development (OECD) in 2011 the averageincome of the richest 10 of the population is about ninetimes that of the poorest 10 across theOECD up from seventimes in 1985 Hence income distribution has been a centralconcern for both academics and policy makers in developedcountries as well as developing countries As pointed out byRobert Shiller one of the winners of the Nobel Prize forEconomics in 2013 ldquoThemost important problem that we arefacing now today I think is rising inequality in the UnitedStates and elsewhere in the worldrdquo (The Huffington Post Oct15 2013)
A number of economic indexes are commonly usedto measure economic growth and income distribution Forexample real gross domestic product is used to measureeconomic growth Gini coefficient Lorenz curve and theratio of income share of highest 20 to that of lowest 20
measure income distribution However under certain cir-cumstances these two objectives (growth and distribution)are conflicting to each other For example if policy makersfocus on pursuing economic growth this may deteriorateuneven distribution (income gap) By contrast if they focuson decreasing uneven distribution this may lower the workincentives of high ability workers
For policy makers a single index that incorporatesgrowth as well as distribution may help to immediately crys-tallize the efficacy of certain policies Despite the prevalenceof many indexes for income inequality none of the indexesfor growth can to some extent reflect the degree of incomeinequalities The lack of such index necessitates the study ofbetter indexes that consider growth as well as distributionsimultaneously To this end this study intends to proposea new index Real National Income Average Growth Rate(hereafter RNIAGR) We justify the use of this index byshowing that this index can actually measure the ordering ofsocial welfare In addition we also show that when the realgrowth stagnates or even declines this index indicates thatincome distribution deteriorates
Hindawi Publishing CorporationEconomics Research InternationalVolume 2015 Article ID 678927 7 pageshttpdxdoiorg1011552015678927
2 Economics Research International
The reminder of this paper is organized as followsSection 2 reviews major economic growth indexes andincome distribution indexes in the existing literatureSection 3 defines the concept of real national income averagegrowth rate and Section 4 further discusses the advantages ofusing this new index In Section 5 using the data in Taiwanwe compare this new index with the usual real economicgrowth rate Finally Section 6 concludes this paperwith someremarks
2 Economic Index
21 Measuring Economic Growth Index The main economicindex for measuring economic growth is real economicgrowth rate The formula of the real economic growth rateis defined as follows
( Real GDP119905
Real GDP119905minus1
) minus 1 (1)
Real Economic Growth Rate119905represents real eco-
nomic growth rate of 119905th yearReal GDP
119905represents real gross domestic product of
119905th yearReal GDP
119905minus1represents real gross domestic product
of 119905 minus 1th year
Gross domestic product can be explained as the powerof the country Positive real economic growth rate means thepower of the country is increasing It seems every countryaims to promote their real economic growth rate
Real economic growth rate is calculated as the totalincome of all nationals in the last year divided by the totalnet increase income of all nationals in this year It can revealthe macroeconomic level of the entire nation but it does notdisplay the information of the income growth rate of eachindividual nationHowever promoting real economic growthrate usually leads to a side effect unequal income distribution[1 2]
22 Measuring Income Distribution Index The main eco-nomic index for measuring income distribution includesLorenz curve Gini coefficient and ratio of income share ofhighest 20 to that of lowest 20
Lorenz curve is an income aggregation curve whichaggregates income from the lowest income national to thehighest income national [3]
The Gini coefficient is a measuring index of statisticaldispersion formulated by Corrado Gini [4] Gini coefficientis usually defined mathematically based on the Lorenz curveGini coefficient ranges from 0 to 1 A low Gini coefficientindicates a more equal distribution Gini coefficient = 0 rep-resents complete equality Higher Gini coefficients indicatemore unequal distribution Gini coefficient = 1 representscomplete inequality Although Gini coefficient can explainthe unequal degree of income distribution it is useless to useGini coefficient to express the financial net increase incomedistribute of each national in each year
As implied by the name ratio of income share of highest20 to that of lowest 20means the total income of nationalswhose income rank is in lowest 20 divides the total incomeof nationals whose income rank is in highest 20 [5] Thedrawback of ratio of income share of highest 20 to that oflowest 20 is that it does not consider the incomedistributionof nationals whose income is in the middle
3 Real National Income Average Growth Rate
To consider economic growth and incomedistribution simul-taneous this research provides a new indexmdashreal nationalincome average growth rateThe concept of RNIAGR is aver-aged real income growth of each individual national Unlikereal economic growth rate that calculates the economicgrowth rate based on the total income of all nationals inprevious year RNIAGR is calculated from individual incomegrowth rate based on individual income in the previous yearand average of all of individual income growth rate RNIAGRcan reflect the average income growth status of individualnational This formula supposes that the volume of nationalsin 119905th year and in 119905minus1th year in the sameCountry is the same
RNIAGR119905= 1119901 lowast119901
sum119895=1
( 119868119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1 (2)
RNIAGR119905represents real national income average
growth rate in 119905th year119868119895119905represents the income of 119895th national in 119905th year
119868119895119905minus1
represents the income of 119895th national in 119905 minus 1thyear119865119905represents the inflation rate in 119905th year
119875 represents the volume of nationals in the country
Using Figure 1 as example 119909-axis represents the rank ofincome from low income national to high income nationalPoint 119860 represents the lowest income national and point 119861represents the highest incomenational Frompoint119860 to point119861 all of the points can reflect an income of one national
If Area119860119861119862 represents the total income of all nationals inlast year Area 119860119862119863 represents the net increase income of allnationals in this year So nominal economic growth rate canbe represented as Area 119860119861119862 divides Area 119860119862119863 From point119860 to point 119861 all of the points can reflect an income of onenational Every national uses the individual income as a baseto calculate the individual income growth rate And we canobtain nominal national income average growth by averagingthe individual income growth rate For example point 119894 thatis between point 119860 and point 119861 represents 119894th national Theincome of 119894th national in last year is line 119894119895 The net increaseincome of 119894th national in this year is line 119895119896 The individualincome growth rate of 119894th national is line 119894119895 divide line 119895119896In order to reflect the real income status of each nationalnominal national income average growth needs to be dividedby inflation rate of this year to acquire real national incomeaverage growth rate of this year
Economics Research International 3
A B
C
D
i
j
k
Citizen
Income
x-axis
Figure 1 National income distribution diagram Notice the orderof the citizens at axis ldquo119909rdquo can (and probably will) change from oneyear to another
Because it is not easy and is too complex to acquireincome information of each individual this study presentsother new indexesmdashfive-scale real national income averagegrowth rate (FSRNIAGR) which can roughly represent realnational income average growth rate FSRNIAGR can reducethe calculation complexity without losing the meaning ofRNIAGR First we divide the entire nationals into 5 scalesAnd then we aggregate the income of each national in eachscale in the last year and aggregate the net increase incomeof each national in each scale in this year In each scalethe aggregated income of each national in these scales inthe last year divides the aggregated net increase income ofeach national in these scales in this year as nominal nationalincome average growth rate in each scale Finally nominalfive-scale national income average growth rates are acquiredby averaging nominal national income average growth ratein each scale In order to reflect the real income status of eachnational nominal five-scale national income average growthneeds to be divided by inflation rate of this year to acquire realfive-scale national income average growth rate of this year(Figure 2)
FSRNIAGR119905
= (5
sum119894=1
( sum(1199011199055)lowast119894119895=(1199011199055)lowast(119894minus1)+1
119868119895119905
sum(119901119905minus15)lowast119894119895=(119901119905minus15)lowast(119894minus1)+1
119868119895119905minus1
)
lowast(119875119905minus1119875119905)(1 + 119865119905) ) times (5)minus1 minus 1
(3)
FSRNIAGR119905
represents five-scale real nationalincome average growth rate of 119905th year119868119895119905represents the ordered income of 119895th national in
119905th year119868119895119905minus1
represents the ordered income of 119895th national in119905 minus 1th year
A B
C
D
s1 s2 s3 s4
c1c2
c3
c4
d1
d2
d3
d4
Citizen
Income
x-axis
Figure 2 Five-scale national income distribution diagram
119865119905represents the inflation rate in 119905th year
119901119905represents the volume of nationals in the Country
in 119905th year119901119905minus1
represents the volumeof nationals in theCountryin 119905 minus 1th year(1199011199055)lowast (119894 minus 1) represents the lower bound of national
in 119894th scale in 119905th year(119901119905minus15)lowast(119894minus1) represents the lower bound of national
in 119894th scale in 119905 minus 1th year(1199011199055) lowast 119894 represents the upper bound of national in
119894th scale in 119905th year(119901119905minus15) lowast 119894 represents the upper bound of national in
119894th scale in 119905 minus 1th year
Because the volume of nationals in 119905th year and in 119905 minus 1thyear in the same Country is different FSRNIAGR
119905must be
adjusted by (119875119905minus1119875119905) for acquiring the rational growth rate
In reality the variance of income for each nationalbetween each year is not always positive and the nationals ofthe country are not usually adjusted their income accordingto their income in the previous year So 119868
119895119905minus1represents the
income of national whose financial rank is 119895th in 119905 minus 1th yearand 119868119895119905represents the income of national whose financial rank
is 119895th in 119905th yearUsing Figure 2 as an example 119909-axis represents the rank
of income from low income national to high income nationalPoint 119860 represents the lowest income national and point119861 represents the highest income national Line 119860119904
1 11990411199042
11990421199043 11990431199044 1199044119861 represents national sets The national whose
income is classified as the same income scale is in thesame national set Line 119860119904
1represents the nationals whose
income is ranking in lowest 20 Line 11990411199042represents the
nationals whose income is ranking between lowest 20and lowest 40 Line 119904
21199043represents the nationals whose
income is ranking between lowest 40 and lowest 60Line 119904
31199044represents the nationals whose income is ranking
between highest 20 and highest 40 Line 1199044119861 represents
the nationals whose income is ranking in highest 20
4 Economics Research International
Area 11986011990411198881represents the total income of the nationals
whose income is ranking in lowest 20 in the last year Area11986011990411198891represents the total income of the nationals whose
income is ranking in lowest 20 in this year Area 1199041119888111988821199042
represents the total income of the nationals whose income isranking between lowest 20 and lowest 40 in the last yearArea 119904
1119889111988921199042represents the total income of the nationals
whose income is ranking between lowest 20 and lowest 40in this year and suchlike
So nominal income growth rate of nationals whoseincome is ranking in lowest 20 can be represented as Area11986011990411198881divides Area119860119904
11198891minus1 Nominal income growth rate of
nationals whose income is ranking between lowest 20 andlowest 40 can be represented as Area 119904
1119888111988821199042divides Area
1199041119889111988921199042minus 1 and the like
Five-scale real national income average growth rate (FSR-NIAGR) of 119905th year can be presented as follows
FSRNIAGR119905
= ((119860 (11986011990411198891)119860 (11986011990411198881) +
119860 (1199041119889111988921199042)
119860 (1199041119888111988821199042) + 119860 (119904
2119889211988931199043)
119860 (1199042119888211988831199043)
+119860 (1199043119889311988941199044)119860 (1199043119888311988841199044) + 119860 (119904
41198894119863119861)
119860 (11990441198884119862119861) ) lowast (119875
119905minus1119875119905)
(1 + 119865119905) )
times (5)minus1 minus 1(4)
119860(11986011990411198891) represents the total income of nationals
whose income is ranking in lowest 20 in 119905th year119860(11986011990411198881) represents the total income of nationals
whose income is ranking in lowest 20 in 119905minus1th year119860(1199041119889111988921199042) represents the total income of nationals
whose income is ranking between lowest 20 andlowest 40 in 119905th year119860(1199041119888111988821199042) represents the total income of nationals
whose income is ranking between lowest 20 andlowest 40 in 119905 minus 1th year119860(1199042119889211988931199043) represents the total income of nationals
whose income is ranking between lowest 40 andlowest 60 in 119905th year119860(1199042119888211988831199043) represents the total income of nationals
whose income is ranking between lowest 40 andlowest 60 in 119905 minus 1th year119860(1199043119889311988941199044) represents the total income of nationals
whose income is ranking highest 20 and highest40 in 119905th year119860(1199043119888311988841199044) represents the total income of nationals
whose income is ranking between highest 20 andhighest 40 in 119905 minus 1th year119860(11990441198894119863119861) represents the total income of nationals
whose income is ranking in highest 20 in 119905th year119860(11990441198884119862119861) represents the total income of nationals
whose income is ranking in highest 20 in 119905 minus 1thyear
25000
20000
15000
10000
5000
0Low
nationalincome
High nationalincome
Low nationalincome
High nationalincome
Low nationalincome
High nationalincome
Figure 3 National income example
In order to reflect the real income status of each nationalfive-scale nominal national income average growth rate needsto be divided by inflation rate of this year to acquire five-scalereal national income average growth rate of this year
4 The Merits of the Real National IncomeAverage Growth Rate
The strong point of real national income average growth rateis that it can modify the drawback of real economic growthrate which did not consider income distribution
For example we suppose that there exists a country whopossesses two nationalsThe income of one national is 20000US dollars in last year (blue color area) and the income of theother national is 10000US dollars in last year (red color area)Suppose that gross domestic product increases 3000 US thisyear The inflation rate of this year is 2
So the real economic growth rate in this country is((20000 + 10000 + 3000)(20000 + 10000))(1 + 2) minus1 = 78
Case 1 (all additional income is acquired by the rich individ-ual) If all the economic profit is acquired by higher nationalthe real national income average growth rate is (05 lowast(1000010000) + 05 lowast (2300020000))(1 + 2) minus 1 = 54
Case 2 (all additional income is acquired by the poorindividual) If all the economic profit is acquired by lowernational the real national income average growth rate is 05 lowast(1300010000) + 05 lowast (2000020000) minus 1 = 127
Case 3 (all additional income is acquired by each individualand the additional income is distributed according to theprevious income of each individual) If economic profit isdistributed according to the income of each national lastyear the real national income average growth rate is (05 lowast(1100010000) + 05 lowast (2200020000))(1 + 2) minus 1 = 78(Refer to Figure 3)
When the level of unequal income distribution is lowerreal national income average growth rate (127) is largerthan real economic growth rate (78) Otherwise realnational income average growth rate (54) is larger thanreal economic growth rate (78) when the level of unequal
Economics Research International 5
Table 1 The relation of real economic growth rate real nationalincome average growth rate and income distribution
Real economic growth rateIncrease Decrease
The level ofunequalincomedistribution
Increase
RNIAGR isincreasing and
adjusted to lowerdown
RNIAGR isdecreasing andadjusted to lower
down more
Decrease
RNIAGR isincreasing andadjusted to bepromoted
RNIAGR isdecreasing andadjusted to
promote a few
income distribution is rising So government will get a betterperformance in real national income average growth rate(relative to real economic growth rate) when governmentpolicy can promote the income of lower income nationallargely
Real national income average growth rate not only can bepositive in relation to real economic growth rate but also canadjust real economic growth rate according to the conditionof the level of unequal income distribution For the relationof real economic growth rate real national income averagegrowth rate and income distribution refer to Table 1
5 Social Welfare Function
To give further rationale for this new index RNIAGR we setup a simplemodel to illustrate the relationship of real nationalincome average growth rate and some total social welfarefunction
We assume that each national has the same increasingutility function of income 119880(119868) = ln(119868) with a diminishingmarginal utility Further we assume that the total socialwelfare function is simply the summation of all nationalsrsquoutility function sum119901
119894=1119880(119868119894119905) where (119868
1119905 1198682119905 119868
119901119905) is the
income distribution of all nationals at time 119905We consider an income distribution 119868
119905minus1= (1198681119905minus1
1198682119905minus1
119868119901119905minus1
) at time 119905minus1 and two possible income distributions119868119905= (1198681119905 1198682119905 119868
119901119905) and 1198681015840
119905= (11986810158401119905 11986810158402119905 1198681015840
119901119905) at time 119905 We
also assume that the difference of income between time 119905 andtime 119905minus1 is relatively small that is 119868
119894119905minus119868119894119905minus1
≪ 119868119894119905minus1
and 1198681015840119894119905minus
119868119894119905minus1
≪ 119868119894119905minus1
for 119894 = 1 2 119901 Let Δ119880119895119905equiv 119880(119868
119895119905) minus 119880(119868
119895119905minus1)
andΔ1198801015840119895119905equiv 119880(1198681015840
119895119905)minus119880(119868
119895119905minus1)Therefore the difference of the
social welfare between two possible incomes is
sum119880(119868119895119905) minussum119880(1198681015840
119895119905)
= sum[119880 (119868119895119905minus1
) + Δ119880119894119905] minussum[119880 (119868
119895119905minus1) + Δ1015840
119895119905]
= sumΔ119880119895119905minussumΔ1198801015840
119895119905
(5)
For a small change in 119868 we might take (120597120597119868)119880(sdot)119889119868 as theapproximation to the resulting change in 119880 knowing thatthe smaller the 119889119868 the better the approximation There-fore sumΔ119880
119895119905asymp sum(120597120597119868)119880(119868
119895119905minus1) lowast 119889119868
119895and sumΔ1198801015840
119895119905asymp
sum(120597120597119868)119880(119868119895119905minus1
) lowast 1198891198681015840119895 where 119889119868
119895= 119868119895119905
minus 119868119895119905minus1
and
1198891198681015840119895
= 1198681015840119895119905
minus 119868119895119905minus1
We then define an approximation ofsum119880(119868
119895119905) minus sum119880(1198681015840
119895119905) to be
[sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886
equiv sum 120597120597119868119880 (119868
119895119905minus119894) lowast 119889119868 minussum 120597
120597119868119880 (119868119895119905minus1
) 1198891198681015840119895
= sum 119889119868119895minus 1198891198681015840119895
119868119895119905minus1
(6)
We are now ready to state the following proposition
Proposition 1 Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
ge 0 lt==gt [sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886 ge 0
(7)
Proof Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
= 1119875 sum( 119868119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
minus 1119875 sum( 1198681015840
119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
= 1119875 (1 + 119865
119905) (sum
119868119895119905
119868119895119905minus1
minussum 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119868119895119905minus 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
(119868119895119905minus 119868119895119905minus1
) minus (1198681015840119895119905minus 119868119895119905minus1
)119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119889119868119895minus 1198891198681015840119895
119868119895119905minus1
)
(8)
Since both 119875 and (1 + 119865119905) are bigger than zero it is obvious
that RNIAGR(119868119905) minus RNIAGR(1198681015840
119905) ge 0 lt==gt [sum119880(119868
119895119905) minus
sum119880(1198681015840119895119905)]119886 ge 0
With the above proposition we could use the RNIAGR asan approximation of social welfare
6 Examples
To explain the usefulness of real national income averagegrowth rate this study uses Taiwanrsquos data as an example tocompare the result of real economic growth rate and realnational income average growth rate The data about realGDP nominal GDP five-scale disposable incomes consumerprice index and Gini index are collected from Taiwanrsquosgovernment [6] Inflation rate is represented by consumer
6 Economics Research International
Table 2 The comparison result of real economic growth rate and real national income average growth rate in Taiwan
Year
National income growth rate based on different equal divisions of recipients
Real nationalincomeaveragegrowth rate
Real economicgrowth rate Gini IndexThe national
whose incomerank is inlowest 20
The nationalwhose income
rank isbetween
lowest 20and lowest
40
The nationalwhose income
rank isbetween
lowest 40and lowest
60
The nationalwhose income
rank isbetween
highest 20and highest
40
The nationalwhose incomerank is in
highest 20
1995 624 150 minus077 minus157 minus017 105 003 03171996 minus362 minus346 minus332 minus220 minus313 minus315 minus303 03171997 444 216 122 050 146 195 149 03201998 265 168 025 078 146 136 121 03241999 060 197 196 093 048 119 103 03252000 173 179 027 078 minus072 077 028 03262001 minus893 minus833 minus570 minus363 219 minus488 minus264 03502002 141 053 minus034 minus133 minus102 minus015 minus062 03452003 371 294 196 166 024 210 142 03432004 157 115 229 216 139 171 170 03382005 minus001 051 minus117 minus121 minus127 minus063 minus093 03402006 minus261 minus250 minus120 minus023 minus159 minus163 minus141 03392007 047 082 minus025 minus091 059 014 013 03402008 minus083 minus448 minus449 minus271 minus178 minus285 minus270 03412009 minus878 minus591 minus504 minus604 minus602 minus636 minus606 03452010 481 415 403 394 243 387 342 03422011 minus358 minus279 minus356 minus344 minus135 minus294 minus253 0342
price index The unit of data is 1 year The range of data isbetween 1995 and 2011 To compare the results of real eco-nomic growth rate and real national income average growthrate refer to Table 2 and Figure 4
As indicated by Taiwanrsquos economic data the real eco-nomic growth rate had been lower than 2 since 1995 exceptfor the 364 in 2010 Seven out of sixteen years had seennegative growthThe rates of growth in 2001 2008 2009 and2011 were all worse than minus2
Real national income average growth rate can adjust realeconomic growth rate based on the real growth situation ofcitizen group For example the real economic growth rate ofTaiwan in 1995 is only 003 Real income growth rate of thenational whose income is ranking in lowest 20 is 624 realincome growth rate of the national whose income is rankingbetween lowest 20 and lowest 40 is 150 Real nationalincome average growth rate is 105 Although the realeconomic growth rate does not increase real national incomeaverage growth rate also can acquire high performance if theunequal income distribution is improved
In 2001 the real economic growth rate was minus264 forTaiwan However the negative growth was more than 35for individuals at lower 80 income brackets and the indi-viduals at lower 40 income brackets saw a negative growthamounting to more than 8 But people in the top 20 sawtheir income growing by 219 Not only the real economicgrowth decrease but also the unequal income distribution got
worse so real national income average growth rate is minus488which is lower than real economic growth rate The Giniindex also got worse in this year (0350 gt 0326) (the higherGini index the more unequal in income distribution)
In 2010 after the poor performance in 2009 the realeconomic growth rate was 342 for Taiwan Because thepositive growth was higher than 342 for individuals atlower 80 income brackets and people in the top 20 onlysaw their income growing by 243 real national incomeaverage growth rate is 387 which is higher than realeconomic growth rate (342) In reality the Gini index alsogot better in this year (0342 lt 0345) The economic wasperforming well in this year because not only the economicgot better but also the unequal income distribution had beenimproved
The Gini index is defined based on the concept of stockbecause this index is determined according to the long termincome ability of each national The real national incomeaverage growth rate is developed by using the concept offlow because this index is generated by applying the data ofindividual national income in this year So the real nationalincome average growth rate reflects the practical phenomenaof economic more frequently than Gini index For examplethe unequal income distribution got worse quickly in Taiwanin 2001 so Gini index increased from 0326 to 0350 ButGini index decreased slowly in 2002sim2004 when the unequalincome distribution had been improved
Economics Research International 7
800
600
400
200
000
minus200
minus400
minus600
minus800
minus1000
1995
1996
1997
1998
1999
2000
2001
2002
2003
2005
2004
2006
2007
2008
2009
2010
2011
Real income growth rate of the national whose incomeis ranking in lowest 20Real income growth rate of the national whose incomeis ranking between lowest 20 and lowest 40Real income growth rate of the national whose incomeis ranking between lowest 40 and lowest 60
Real income growth rate of the national whose incomeis ranking between highest 20 and highest 40Real income growth rate of the national whose incomeis ranking in highest 20
Real national income average growth rate
Real economic growth rate
()
Figure 4 The comparison result of real economic growth rate andreal national income average growth rate in Taiwan
There is an interesting phenomenon that occurred inTaiwan real national income average growth rate usuallyperformed better than real economic growth rate when thereal economic growth rate was positive On the other handreal national income average growth rate usually performsworse than real economic growth rate when the real eco-nomic growth rate is negative
7 Conclusion and Future Research
In this study we develop a new economic indexmdashRNIAGRfor describing economic situation which considers economicgrowth and income distribution simultaneous Proposedindex not only can reflect real economic growth rate butalso can adjust real economic growth rate according to thecondition of the level of unequal income distribution Inorder to lower down calculation complexity this researchalso develops an economic indexmdashFSRNIAGR which cansimplify calculation process without losing the meaning ofRNIAGR
The reason of choosing FSRNIAGR is that the indexof FSRNIAGR can be generated by five-scale disposableincome which is easy to be acquired in the website in eachgovernment
In the future some economic numerical data will becollected and the economic performance comparison ofeach country based on proposed index will be discussedThe sensitivity analysis in relation to the arbitrary number
of classes which is used to classify the group of incomedistribution will be done by the simulation according to thepractical income distribution of each country
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R Kanbur ldquoChapter 13 Income distribution and developmentrdquoHandbook of Income Distribution vol 1 pp 791ndash841 2000
[2] R Kanbur ldquoEconomic policy distribution and poverty thenature of disagreementsrdquoWorld Development vol 29 no 6 pp1083ndash1094 2001
[3] V Fakoor M B Ghalibaf and H A Azarnoosh ldquoAsymptoticbehaviors of the Lorenz curve and Gini index in sampling froma length-biased distributionrdquo Statistics and Probability Lettersvol 81 no 9 pp 1425ndash1435 2011
[4] BMilanovic ldquoA simpleway to calculate theGini coefficient andsome implicationsrdquo Economics Letters vol 56 no 1 pp 45ndash491997
[5] R Anderton Macroeconomic Performance in a GlobalisingEconomy Cambridge University Press Cambridge UK 2010
[6] Dorectorate-General of Budget Accounting and Statistics ofExecutive Yuan Taiwan httpwwwdgbasgovtw
Submit your manuscripts athttpwwwhindawicom
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Psychiatry Journal
ArchaeologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AnthropologyJournal of
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Research and TreatmentSchizophrenia
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Urban Studies Research
Population ResearchInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CriminologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Aging ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NursingResearch and Practice
Current Gerontologyamp Geriatrics Research
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AddictionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geography Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentAutism
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Economics Research International
2 Economics Research International
The reminder of this paper is organized as followsSection 2 reviews major economic growth indexes andincome distribution indexes in the existing literatureSection 3 defines the concept of real national income averagegrowth rate and Section 4 further discusses the advantages ofusing this new index In Section 5 using the data in Taiwanwe compare this new index with the usual real economicgrowth rate Finally Section 6 concludes this paperwith someremarks
2 Economic Index
21 Measuring Economic Growth Index The main economicindex for measuring economic growth is real economicgrowth rate The formula of the real economic growth rateis defined as follows
( Real GDP119905
Real GDP119905minus1
) minus 1 (1)
Real Economic Growth Rate119905represents real eco-
nomic growth rate of 119905th yearReal GDP
119905represents real gross domestic product of
119905th yearReal GDP
119905minus1represents real gross domestic product
of 119905 minus 1th year
Gross domestic product can be explained as the powerof the country Positive real economic growth rate means thepower of the country is increasing It seems every countryaims to promote their real economic growth rate
Real economic growth rate is calculated as the totalincome of all nationals in the last year divided by the totalnet increase income of all nationals in this year It can revealthe macroeconomic level of the entire nation but it does notdisplay the information of the income growth rate of eachindividual nationHowever promoting real economic growthrate usually leads to a side effect unequal income distribution[1 2]
22 Measuring Income Distribution Index The main eco-nomic index for measuring income distribution includesLorenz curve Gini coefficient and ratio of income share ofhighest 20 to that of lowest 20
Lorenz curve is an income aggregation curve whichaggregates income from the lowest income national to thehighest income national [3]
The Gini coefficient is a measuring index of statisticaldispersion formulated by Corrado Gini [4] Gini coefficientis usually defined mathematically based on the Lorenz curveGini coefficient ranges from 0 to 1 A low Gini coefficientindicates a more equal distribution Gini coefficient = 0 rep-resents complete equality Higher Gini coefficients indicatemore unequal distribution Gini coefficient = 1 representscomplete inequality Although Gini coefficient can explainthe unequal degree of income distribution it is useless to useGini coefficient to express the financial net increase incomedistribute of each national in each year
As implied by the name ratio of income share of highest20 to that of lowest 20means the total income of nationalswhose income rank is in lowest 20 divides the total incomeof nationals whose income rank is in highest 20 [5] Thedrawback of ratio of income share of highest 20 to that oflowest 20 is that it does not consider the incomedistributionof nationals whose income is in the middle
3 Real National Income Average Growth Rate
To consider economic growth and incomedistribution simul-taneous this research provides a new indexmdashreal nationalincome average growth rateThe concept of RNIAGR is aver-aged real income growth of each individual national Unlikereal economic growth rate that calculates the economicgrowth rate based on the total income of all nationals inprevious year RNIAGR is calculated from individual incomegrowth rate based on individual income in the previous yearand average of all of individual income growth rate RNIAGRcan reflect the average income growth status of individualnational This formula supposes that the volume of nationalsin 119905th year and in 119905minus1th year in the sameCountry is the same
RNIAGR119905= 1119901 lowast119901
sum119895=1
( 119868119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1 (2)
RNIAGR119905represents real national income average
growth rate in 119905th year119868119895119905represents the income of 119895th national in 119905th year
119868119895119905minus1
represents the income of 119895th national in 119905 minus 1thyear119865119905represents the inflation rate in 119905th year
119875 represents the volume of nationals in the country
Using Figure 1 as example 119909-axis represents the rank ofincome from low income national to high income nationalPoint 119860 represents the lowest income national and point 119861represents the highest incomenational Frompoint119860 to point119861 all of the points can reflect an income of one national
If Area119860119861119862 represents the total income of all nationals inlast year Area 119860119862119863 represents the net increase income of allnationals in this year So nominal economic growth rate canbe represented as Area 119860119861119862 divides Area 119860119862119863 From point119860 to point 119861 all of the points can reflect an income of onenational Every national uses the individual income as a baseto calculate the individual income growth rate And we canobtain nominal national income average growth by averagingthe individual income growth rate For example point 119894 thatis between point 119860 and point 119861 represents 119894th national Theincome of 119894th national in last year is line 119894119895 The net increaseincome of 119894th national in this year is line 119895119896 The individualincome growth rate of 119894th national is line 119894119895 divide line 119895119896In order to reflect the real income status of each nationalnominal national income average growth needs to be dividedby inflation rate of this year to acquire real national incomeaverage growth rate of this year
Economics Research International 3
A B
C
D
i
j
k
Citizen
Income
x-axis
Figure 1 National income distribution diagram Notice the orderof the citizens at axis ldquo119909rdquo can (and probably will) change from oneyear to another
Because it is not easy and is too complex to acquireincome information of each individual this study presentsother new indexesmdashfive-scale real national income averagegrowth rate (FSRNIAGR) which can roughly represent realnational income average growth rate FSRNIAGR can reducethe calculation complexity without losing the meaning ofRNIAGR First we divide the entire nationals into 5 scalesAnd then we aggregate the income of each national in eachscale in the last year and aggregate the net increase incomeof each national in each scale in this year In each scalethe aggregated income of each national in these scales inthe last year divides the aggregated net increase income ofeach national in these scales in this year as nominal nationalincome average growth rate in each scale Finally nominalfive-scale national income average growth rates are acquiredby averaging nominal national income average growth ratein each scale In order to reflect the real income status of eachnational nominal five-scale national income average growthneeds to be divided by inflation rate of this year to acquire realfive-scale national income average growth rate of this year(Figure 2)
FSRNIAGR119905
= (5
sum119894=1
( sum(1199011199055)lowast119894119895=(1199011199055)lowast(119894minus1)+1
119868119895119905
sum(119901119905minus15)lowast119894119895=(119901119905minus15)lowast(119894minus1)+1
119868119895119905minus1
)
lowast(119875119905minus1119875119905)(1 + 119865119905) ) times (5)minus1 minus 1
(3)
FSRNIAGR119905
represents five-scale real nationalincome average growth rate of 119905th year119868119895119905represents the ordered income of 119895th national in
119905th year119868119895119905minus1
represents the ordered income of 119895th national in119905 minus 1th year
A B
C
D
s1 s2 s3 s4
c1c2
c3
c4
d1
d2
d3
d4
Citizen
Income
x-axis
Figure 2 Five-scale national income distribution diagram
119865119905represents the inflation rate in 119905th year
119901119905represents the volume of nationals in the Country
in 119905th year119901119905minus1
represents the volumeof nationals in theCountryin 119905 minus 1th year(1199011199055)lowast (119894 minus 1) represents the lower bound of national
in 119894th scale in 119905th year(119901119905minus15)lowast(119894minus1) represents the lower bound of national
in 119894th scale in 119905 minus 1th year(1199011199055) lowast 119894 represents the upper bound of national in
119894th scale in 119905th year(119901119905minus15) lowast 119894 represents the upper bound of national in
119894th scale in 119905 minus 1th year
Because the volume of nationals in 119905th year and in 119905 minus 1thyear in the same Country is different FSRNIAGR
119905must be
adjusted by (119875119905minus1119875119905) for acquiring the rational growth rate
In reality the variance of income for each nationalbetween each year is not always positive and the nationals ofthe country are not usually adjusted their income accordingto their income in the previous year So 119868
119895119905minus1represents the
income of national whose financial rank is 119895th in 119905 minus 1th yearand 119868119895119905represents the income of national whose financial rank
is 119895th in 119905th yearUsing Figure 2 as an example 119909-axis represents the rank
of income from low income national to high income nationalPoint 119860 represents the lowest income national and point119861 represents the highest income national Line 119860119904
1 11990411199042
11990421199043 11990431199044 1199044119861 represents national sets The national whose
income is classified as the same income scale is in thesame national set Line 119860119904
1represents the nationals whose
income is ranking in lowest 20 Line 11990411199042represents the
nationals whose income is ranking between lowest 20and lowest 40 Line 119904
21199043represents the nationals whose
income is ranking between lowest 40 and lowest 60Line 119904
31199044represents the nationals whose income is ranking
between highest 20 and highest 40 Line 1199044119861 represents
the nationals whose income is ranking in highest 20
4 Economics Research International
Area 11986011990411198881represents the total income of the nationals
whose income is ranking in lowest 20 in the last year Area11986011990411198891represents the total income of the nationals whose
income is ranking in lowest 20 in this year Area 1199041119888111988821199042
represents the total income of the nationals whose income isranking between lowest 20 and lowest 40 in the last yearArea 119904
1119889111988921199042represents the total income of the nationals
whose income is ranking between lowest 20 and lowest 40in this year and suchlike
So nominal income growth rate of nationals whoseincome is ranking in lowest 20 can be represented as Area11986011990411198881divides Area119860119904
11198891minus1 Nominal income growth rate of
nationals whose income is ranking between lowest 20 andlowest 40 can be represented as Area 119904
1119888111988821199042divides Area
1199041119889111988921199042minus 1 and the like
Five-scale real national income average growth rate (FSR-NIAGR) of 119905th year can be presented as follows
FSRNIAGR119905
= ((119860 (11986011990411198891)119860 (11986011990411198881) +
119860 (1199041119889111988921199042)
119860 (1199041119888111988821199042) + 119860 (119904
2119889211988931199043)
119860 (1199042119888211988831199043)
+119860 (1199043119889311988941199044)119860 (1199043119888311988841199044) + 119860 (119904
41198894119863119861)
119860 (11990441198884119862119861) ) lowast (119875
119905minus1119875119905)
(1 + 119865119905) )
times (5)minus1 minus 1(4)
119860(11986011990411198891) represents the total income of nationals
whose income is ranking in lowest 20 in 119905th year119860(11986011990411198881) represents the total income of nationals
whose income is ranking in lowest 20 in 119905minus1th year119860(1199041119889111988921199042) represents the total income of nationals
whose income is ranking between lowest 20 andlowest 40 in 119905th year119860(1199041119888111988821199042) represents the total income of nationals
whose income is ranking between lowest 20 andlowest 40 in 119905 minus 1th year119860(1199042119889211988931199043) represents the total income of nationals
whose income is ranking between lowest 40 andlowest 60 in 119905th year119860(1199042119888211988831199043) represents the total income of nationals
whose income is ranking between lowest 40 andlowest 60 in 119905 minus 1th year119860(1199043119889311988941199044) represents the total income of nationals
whose income is ranking highest 20 and highest40 in 119905th year119860(1199043119888311988841199044) represents the total income of nationals
whose income is ranking between highest 20 andhighest 40 in 119905 minus 1th year119860(11990441198894119863119861) represents the total income of nationals
whose income is ranking in highest 20 in 119905th year119860(11990441198884119862119861) represents the total income of nationals
whose income is ranking in highest 20 in 119905 minus 1thyear
25000
20000
15000
10000
5000
0Low
nationalincome
High nationalincome
Low nationalincome
High nationalincome
Low nationalincome
High nationalincome
Figure 3 National income example
In order to reflect the real income status of each nationalfive-scale nominal national income average growth rate needsto be divided by inflation rate of this year to acquire five-scalereal national income average growth rate of this year
4 The Merits of the Real National IncomeAverage Growth Rate
The strong point of real national income average growth rateis that it can modify the drawback of real economic growthrate which did not consider income distribution
For example we suppose that there exists a country whopossesses two nationalsThe income of one national is 20000US dollars in last year (blue color area) and the income of theother national is 10000US dollars in last year (red color area)Suppose that gross domestic product increases 3000 US thisyear The inflation rate of this year is 2
So the real economic growth rate in this country is((20000 + 10000 + 3000)(20000 + 10000))(1 + 2) minus1 = 78
Case 1 (all additional income is acquired by the rich individ-ual) If all the economic profit is acquired by higher nationalthe real national income average growth rate is (05 lowast(1000010000) + 05 lowast (2300020000))(1 + 2) minus 1 = 54
Case 2 (all additional income is acquired by the poorindividual) If all the economic profit is acquired by lowernational the real national income average growth rate is 05 lowast(1300010000) + 05 lowast (2000020000) minus 1 = 127
Case 3 (all additional income is acquired by each individualand the additional income is distributed according to theprevious income of each individual) If economic profit isdistributed according to the income of each national lastyear the real national income average growth rate is (05 lowast(1100010000) + 05 lowast (2200020000))(1 + 2) minus 1 = 78(Refer to Figure 3)
When the level of unequal income distribution is lowerreal national income average growth rate (127) is largerthan real economic growth rate (78) Otherwise realnational income average growth rate (54) is larger thanreal economic growth rate (78) when the level of unequal
Economics Research International 5
Table 1 The relation of real economic growth rate real nationalincome average growth rate and income distribution
Real economic growth rateIncrease Decrease
The level ofunequalincomedistribution
Increase
RNIAGR isincreasing and
adjusted to lowerdown
RNIAGR isdecreasing andadjusted to lower
down more
Decrease
RNIAGR isincreasing andadjusted to bepromoted
RNIAGR isdecreasing andadjusted to
promote a few
income distribution is rising So government will get a betterperformance in real national income average growth rate(relative to real economic growth rate) when governmentpolicy can promote the income of lower income nationallargely
Real national income average growth rate not only can bepositive in relation to real economic growth rate but also canadjust real economic growth rate according to the conditionof the level of unequal income distribution For the relationof real economic growth rate real national income averagegrowth rate and income distribution refer to Table 1
5 Social Welfare Function
To give further rationale for this new index RNIAGR we setup a simplemodel to illustrate the relationship of real nationalincome average growth rate and some total social welfarefunction
We assume that each national has the same increasingutility function of income 119880(119868) = ln(119868) with a diminishingmarginal utility Further we assume that the total socialwelfare function is simply the summation of all nationalsrsquoutility function sum119901
119894=1119880(119868119894119905) where (119868
1119905 1198682119905 119868
119901119905) is the
income distribution of all nationals at time 119905We consider an income distribution 119868
119905minus1= (1198681119905minus1
1198682119905minus1
119868119901119905minus1
) at time 119905minus1 and two possible income distributions119868119905= (1198681119905 1198682119905 119868
119901119905) and 1198681015840
119905= (11986810158401119905 11986810158402119905 1198681015840
119901119905) at time 119905 We
also assume that the difference of income between time 119905 andtime 119905minus1 is relatively small that is 119868
119894119905minus119868119894119905minus1
≪ 119868119894119905minus1
and 1198681015840119894119905minus
119868119894119905minus1
≪ 119868119894119905minus1
for 119894 = 1 2 119901 Let Δ119880119895119905equiv 119880(119868
119895119905) minus 119880(119868
119895119905minus1)
andΔ1198801015840119895119905equiv 119880(1198681015840
119895119905)minus119880(119868
119895119905minus1)Therefore the difference of the
social welfare between two possible incomes is
sum119880(119868119895119905) minussum119880(1198681015840
119895119905)
= sum[119880 (119868119895119905minus1
) + Δ119880119894119905] minussum[119880 (119868
119895119905minus1) + Δ1015840
119895119905]
= sumΔ119880119895119905minussumΔ1198801015840
119895119905
(5)
For a small change in 119868 we might take (120597120597119868)119880(sdot)119889119868 as theapproximation to the resulting change in 119880 knowing thatthe smaller the 119889119868 the better the approximation There-fore sumΔ119880
119895119905asymp sum(120597120597119868)119880(119868
119895119905minus1) lowast 119889119868
119895and sumΔ1198801015840
119895119905asymp
sum(120597120597119868)119880(119868119895119905minus1
) lowast 1198891198681015840119895 where 119889119868
119895= 119868119895119905
minus 119868119895119905minus1
and
1198891198681015840119895
= 1198681015840119895119905
minus 119868119895119905minus1
We then define an approximation ofsum119880(119868
119895119905) minus sum119880(1198681015840
119895119905) to be
[sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886
equiv sum 120597120597119868119880 (119868
119895119905minus119894) lowast 119889119868 minussum 120597
120597119868119880 (119868119895119905minus1
) 1198891198681015840119895
= sum 119889119868119895minus 1198891198681015840119895
119868119895119905minus1
(6)
We are now ready to state the following proposition
Proposition 1 Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
ge 0 lt==gt [sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886 ge 0
(7)
Proof Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
= 1119875 sum( 119868119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
minus 1119875 sum( 1198681015840
119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
= 1119875 (1 + 119865
119905) (sum
119868119895119905
119868119895119905minus1
minussum 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119868119895119905minus 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
(119868119895119905minus 119868119895119905minus1
) minus (1198681015840119895119905minus 119868119895119905minus1
)119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119889119868119895minus 1198891198681015840119895
119868119895119905minus1
)
(8)
Since both 119875 and (1 + 119865119905) are bigger than zero it is obvious
that RNIAGR(119868119905) minus RNIAGR(1198681015840
119905) ge 0 lt==gt [sum119880(119868
119895119905) minus
sum119880(1198681015840119895119905)]119886 ge 0
With the above proposition we could use the RNIAGR asan approximation of social welfare
6 Examples
To explain the usefulness of real national income averagegrowth rate this study uses Taiwanrsquos data as an example tocompare the result of real economic growth rate and realnational income average growth rate The data about realGDP nominal GDP five-scale disposable incomes consumerprice index and Gini index are collected from Taiwanrsquosgovernment [6] Inflation rate is represented by consumer
6 Economics Research International
Table 2 The comparison result of real economic growth rate and real national income average growth rate in Taiwan
Year
National income growth rate based on different equal divisions of recipients
Real nationalincomeaveragegrowth rate
Real economicgrowth rate Gini IndexThe national
whose incomerank is inlowest 20
The nationalwhose income
rank isbetween
lowest 20and lowest
40
The nationalwhose income
rank isbetween
lowest 40and lowest
60
The nationalwhose income
rank isbetween
highest 20and highest
40
The nationalwhose incomerank is in
highest 20
1995 624 150 minus077 minus157 minus017 105 003 03171996 minus362 minus346 minus332 minus220 minus313 minus315 minus303 03171997 444 216 122 050 146 195 149 03201998 265 168 025 078 146 136 121 03241999 060 197 196 093 048 119 103 03252000 173 179 027 078 minus072 077 028 03262001 minus893 minus833 minus570 minus363 219 minus488 minus264 03502002 141 053 minus034 minus133 minus102 minus015 minus062 03452003 371 294 196 166 024 210 142 03432004 157 115 229 216 139 171 170 03382005 minus001 051 minus117 minus121 minus127 minus063 minus093 03402006 minus261 minus250 minus120 minus023 minus159 minus163 minus141 03392007 047 082 minus025 minus091 059 014 013 03402008 minus083 minus448 minus449 minus271 minus178 minus285 minus270 03412009 minus878 minus591 minus504 minus604 minus602 minus636 minus606 03452010 481 415 403 394 243 387 342 03422011 minus358 minus279 minus356 minus344 minus135 minus294 minus253 0342
price index The unit of data is 1 year The range of data isbetween 1995 and 2011 To compare the results of real eco-nomic growth rate and real national income average growthrate refer to Table 2 and Figure 4
As indicated by Taiwanrsquos economic data the real eco-nomic growth rate had been lower than 2 since 1995 exceptfor the 364 in 2010 Seven out of sixteen years had seennegative growthThe rates of growth in 2001 2008 2009 and2011 were all worse than minus2
Real national income average growth rate can adjust realeconomic growth rate based on the real growth situation ofcitizen group For example the real economic growth rate ofTaiwan in 1995 is only 003 Real income growth rate of thenational whose income is ranking in lowest 20 is 624 realincome growth rate of the national whose income is rankingbetween lowest 20 and lowest 40 is 150 Real nationalincome average growth rate is 105 Although the realeconomic growth rate does not increase real national incomeaverage growth rate also can acquire high performance if theunequal income distribution is improved
In 2001 the real economic growth rate was minus264 forTaiwan However the negative growth was more than 35for individuals at lower 80 income brackets and the indi-viduals at lower 40 income brackets saw a negative growthamounting to more than 8 But people in the top 20 sawtheir income growing by 219 Not only the real economicgrowth decrease but also the unequal income distribution got
worse so real national income average growth rate is minus488which is lower than real economic growth rate The Giniindex also got worse in this year (0350 gt 0326) (the higherGini index the more unequal in income distribution)
In 2010 after the poor performance in 2009 the realeconomic growth rate was 342 for Taiwan Because thepositive growth was higher than 342 for individuals atlower 80 income brackets and people in the top 20 onlysaw their income growing by 243 real national incomeaverage growth rate is 387 which is higher than realeconomic growth rate (342) In reality the Gini index alsogot better in this year (0342 lt 0345) The economic wasperforming well in this year because not only the economicgot better but also the unequal income distribution had beenimproved
The Gini index is defined based on the concept of stockbecause this index is determined according to the long termincome ability of each national The real national incomeaverage growth rate is developed by using the concept offlow because this index is generated by applying the data ofindividual national income in this year So the real nationalincome average growth rate reflects the practical phenomenaof economic more frequently than Gini index For examplethe unequal income distribution got worse quickly in Taiwanin 2001 so Gini index increased from 0326 to 0350 ButGini index decreased slowly in 2002sim2004 when the unequalincome distribution had been improved
Economics Research International 7
800
600
400
200
000
minus200
minus400
minus600
minus800
minus1000
1995
1996
1997
1998
1999
2000
2001
2002
2003
2005
2004
2006
2007
2008
2009
2010
2011
Real income growth rate of the national whose incomeis ranking in lowest 20Real income growth rate of the national whose incomeis ranking between lowest 20 and lowest 40Real income growth rate of the national whose incomeis ranking between lowest 40 and lowest 60
Real income growth rate of the national whose incomeis ranking between highest 20 and highest 40Real income growth rate of the national whose incomeis ranking in highest 20
Real national income average growth rate
Real economic growth rate
()
Figure 4 The comparison result of real economic growth rate andreal national income average growth rate in Taiwan
There is an interesting phenomenon that occurred inTaiwan real national income average growth rate usuallyperformed better than real economic growth rate when thereal economic growth rate was positive On the other handreal national income average growth rate usually performsworse than real economic growth rate when the real eco-nomic growth rate is negative
7 Conclusion and Future Research
In this study we develop a new economic indexmdashRNIAGRfor describing economic situation which considers economicgrowth and income distribution simultaneous Proposedindex not only can reflect real economic growth rate butalso can adjust real economic growth rate according to thecondition of the level of unequal income distribution Inorder to lower down calculation complexity this researchalso develops an economic indexmdashFSRNIAGR which cansimplify calculation process without losing the meaning ofRNIAGR
The reason of choosing FSRNIAGR is that the indexof FSRNIAGR can be generated by five-scale disposableincome which is easy to be acquired in the website in eachgovernment
In the future some economic numerical data will becollected and the economic performance comparison ofeach country based on proposed index will be discussedThe sensitivity analysis in relation to the arbitrary number
of classes which is used to classify the group of incomedistribution will be done by the simulation according to thepractical income distribution of each country
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R Kanbur ldquoChapter 13 Income distribution and developmentrdquoHandbook of Income Distribution vol 1 pp 791ndash841 2000
[2] R Kanbur ldquoEconomic policy distribution and poverty thenature of disagreementsrdquoWorld Development vol 29 no 6 pp1083ndash1094 2001
[3] V Fakoor M B Ghalibaf and H A Azarnoosh ldquoAsymptoticbehaviors of the Lorenz curve and Gini index in sampling froma length-biased distributionrdquo Statistics and Probability Lettersvol 81 no 9 pp 1425ndash1435 2011
[4] BMilanovic ldquoA simpleway to calculate theGini coefficient andsome implicationsrdquo Economics Letters vol 56 no 1 pp 45ndash491997
[5] R Anderton Macroeconomic Performance in a GlobalisingEconomy Cambridge University Press Cambridge UK 2010
[6] Dorectorate-General of Budget Accounting and Statistics ofExecutive Yuan Taiwan httpwwwdgbasgovtw
Submit your manuscripts athttpwwwhindawicom
Child Development Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Education Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Biomedical EducationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Psychiatry Journal
ArchaeologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AnthropologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentSchizophrenia
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Urban Studies Research
Population ResearchInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CriminologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Aging ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NursingResearch and Practice
Current Gerontologyamp Geriatrics Research
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AddictionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geography Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentAutism
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Economics Research International
Economics Research International 3
A B
C
D
i
j
k
Citizen
Income
x-axis
Figure 1 National income distribution diagram Notice the orderof the citizens at axis ldquo119909rdquo can (and probably will) change from oneyear to another
Because it is not easy and is too complex to acquireincome information of each individual this study presentsother new indexesmdashfive-scale real national income averagegrowth rate (FSRNIAGR) which can roughly represent realnational income average growth rate FSRNIAGR can reducethe calculation complexity without losing the meaning ofRNIAGR First we divide the entire nationals into 5 scalesAnd then we aggregate the income of each national in eachscale in the last year and aggregate the net increase incomeof each national in each scale in this year In each scalethe aggregated income of each national in these scales inthe last year divides the aggregated net increase income ofeach national in these scales in this year as nominal nationalincome average growth rate in each scale Finally nominalfive-scale national income average growth rates are acquiredby averaging nominal national income average growth ratein each scale In order to reflect the real income status of eachnational nominal five-scale national income average growthneeds to be divided by inflation rate of this year to acquire realfive-scale national income average growth rate of this year(Figure 2)
FSRNIAGR119905
= (5
sum119894=1
( sum(1199011199055)lowast119894119895=(1199011199055)lowast(119894minus1)+1
119868119895119905
sum(119901119905minus15)lowast119894119895=(119901119905minus15)lowast(119894minus1)+1
119868119895119905minus1
)
lowast(119875119905minus1119875119905)(1 + 119865119905) ) times (5)minus1 minus 1
(3)
FSRNIAGR119905
represents five-scale real nationalincome average growth rate of 119905th year119868119895119905represents the ordered income of 119895th national in
119905th year119868119895119905minus1
represents the ordered income of 119895th national in119905 minus 1th year
A B
C
D
s1 s2 s3 s4
c1c2
c3
c4
d1
d2
d3
d4
Citizen
Income
x-axis
Figure 2 Five-scale national income distribution diagram
119865119905represents the inflation rate in 119905th year
119901119905represents the volume of nationals in the Country
in 119905th year119901119905minus1
represents the volumeof nationals in theCountryin 119905 minus 1th year(1199011199055)lowast (119894 minus 1) represents the lower bound of national
in 119894th scale in 119905th year(119901119905minus15)lowast(119894minus1) represents the lower bound of national
in 119894th scale in 119905 minus 1th year(1199011199055) lowast 119894 represents the upper bound of national in
119894th scale in 119905th year(119901119905minus15) lowast 119894 represents the upper bound of national in
119894th scale in 119905 minus 1th year
Because the volume of nationals in 119905th year and in 119905 minus 1thyear in the same Country is different FSRNIAGR
119905must be
adjusted by (119875119905minus1119875119905) for acquiring the rational growth rate
In reality the variance of income for each nationalbetween each year is not always positive and the nationals ofthe country are not usually adjusted their income accordingto their income in the previous year So 119868
119895119905minus1represents the
income of national whose financial rank is 119895th in 119905 minus 1th yearand 119868119895119905represents the income of national whose financial rank
is 119895th in 119905th yearUsing Figure 2 as an example 119909-axis represents the rank
of income from low income national to high income nationalPoint 119860 represents the lowest income national and point119861 represents the highest income national Line 119860119904
1 11990411199042
11990421199043 11990431199044 1199044119861 represents national sets The national whose
income is classified as the same income scale is in thesame national set Line 119860119904
1represents the nationals whose
income is ranking in lowest 20 Line 11990411199042represents the
nationals whose income is ranking between lowest 20and lowest 40 Line 119904
21199043represents the nationals whose
income is ranking between lowest 40 and lowest 60Line 119904
31199044represents the nationals whose income is ranking
between highest 20 and highest 40 Line 1199044119861 represents
the nationals whose income is ranking in highest 20
4 Economics Research International
Area 11986011990411198881represents the total income of the nationals
whose income is ranking in lowest 20 in the last year Area11986011990411198891represents the total income of the nationals whose
income is ranking in lowest 20 in this year Area 1199041119888111988821199042
represents the total income of the nationals whose income isranking between lowest 20 and lowest 40 in the last yearArea 119904
1119889111988921199042represents the total income of the nationals
whose income is ranking between lowest 20 and lowest 40in this year and suchlike
So nominal income growth rate of nationals whoseincome is ranking in lowest 20 can be represented as Area11986011990411198881divides Area119860119904
11198891minus1 Nominal income growth rate of
nationals whose income is ranking between lowest 20 andlowest 40 can be represented as Area 119904
1119888111988821199042divides Area
1199041119889111988921199042minus 1 and the like
Five-scale real national income average growth rate (FSR-NIAGR) of 119905th year can be presented as follows
FSRNIAGR119905
= ((119860 (11986011990411198891)119860 (11986011990411198881) +
119860 (1199041119889111988921199042)
119860 (1199041119888111988821199042) + 119860 (119904
2119889211988931199043)
119860 (1199042119888211988831199043)
+119860 (1199043119889311988941199044)119860 (1199043119888311988841199044) + 119860 (119904
41198894119863119861)
119860 (11990441198884119862119861) ) lowast (119875
119905minus1119875119905)
(1 + 119865119905) )
times (5)minus1 minus 1(4)
119860(11986011990411198891) represents the total income of nationals
whose income is ranking in lowest 20 in 119905th year119860(11986011990411198881) represents the total income of nationals
whose income is ranking in lowest 20 in 119905minus1th year119860(1199041119889111988921199042) represents the total income of nationals
whose income is ranking between lowest 20 andlowest 40 in 119905th year119860(1199041119888111988821199042) represents the total income of nationals
whose income is ranking between lowest 20 andlowest 40 in 119905 minus 1th year119860(1199042119889211988931199043) represents the total income of nationals
whose income is ranking between lowest 40 andlowest 60 in 119905th year119860(1199042119888211988831199043) represents the total income of nationals
whose income is ranking between lowest 40 andlowest 60 in 119905 minus 1th year119860(1199043119889311988941199044) represents the total income of nationals
whose income is ranking highest 20 and highest40 in 119905th year119860(1199043119888311988841199044) represents the total income of nationals
whose income is ranking between highest 20 andhighest 40 in 119905 minus 1th year119860(11990441198894119863119861) represents the total income of nationals
whose income is ranking in highest 20 in 119905th year119860(11990441198884119862119861) represents the total income of nationals
whose income is ranking in highest 20 in 119905 minus 1thyear
25000
20000
15000
10000
5000
0Low
nationalincome
High nationalincome
Low nationalincome
High nationalincome
Low nationalincome
High nationalincome
Figure 3 National income example
In order to reflect the real income status of each nationalfive-scale nominal national income average growth rate needsto be divided by inflation rate of this year to acquire five-scalereal national income average growth rate of this year
4 The Merits of the Real National IncomeAverage Growth Rate
The strong point of real national income average growth rateis that it can modify the drawback of real economic growthrate which did not consider income distribution
For example we suppose that there exists a country whopossesses two nationalsThe income of one national is 20000US dollars in last year (blue color area) and the income of theother national is 10000US dollars in last year (red color area)Suppose that gross domestic product increases 3000 US thisyear The inflation rate of this year is 2
So the real economic growth rate in this country is((20000 + 10000 + 3000)(20000 + 10000))(1 + 2) minus1 = 78
Case 1 (all additional income is acquired by the rich individ-ual) If all the economic profit is acquired by higher nationalthe real national income average growth rate is (05 lowast(1000010000) + 05 lowast (2300020000))(1 + 2) minus 1 = 54
Case 2 (all additional income is acquired by the poorindividual) If all the economic profit is acquired by lowernational the real national income average growth rate is 05 lowast(1300010000) + 05 lowast (2000020000) minus 1 = 127
Case 3 (all additional income is acquired by each individualand the additional income is distributed according to theprevious income of each individual) If economic profit isdistributed according to the income of each national lastyear the real national income average growth rate is (05 lowast(1100010000) + 05 lowast (2200020000))(1 + 2) minus 1 = 78(Refer to Figure 3)
When the level of unequal income distribution is lowerreal national income average growth rate (127) is largerthan real economic growth rate (78) Otherwise realnational income average growth rate (54) is larger thanreal economic growth rate (78) when the level of unequal
Economics Research International 5
Table 1 The relation of real economic growth rate real nationalincome average growth rate and income distribution
Real economic growth rateIncrease Decrease
The level ofunequalincomedistribution
Increase
RNIAGR isincreasing and
adjusted to lowerdown
RNIAGR isdecreasing andadjusted to lower
down more
Decrease
RNIAGR isincreasing andadjusted to bepromoted
RNIAGR isdecreasing andadjusted to
promote a few
income distribution is rising So government will get a betterperformance in real national income average growth rate(relative to real economic growth rate) when governmentpolicy can promote the income of lower income nationallargely
Real national income average growth rate not only can bepositive in relation to real economic growth rate but also canadjust real economic growth rate according to the conditionof the level of unequal income distribution For the relationof real economic growth rate real national income averagegrowth rate and income distribution refer to Table 1
5 Social Welfare Function
To give further rationale for this new index RNIAGR we setup a simplemodel to illustrate the relationship of real nationalincome average growth rate and some total social welfarefunction
We assume that each national has the same increasingutility function of income 119880(119868) = ln(119868) with a diminishingmarginal utility Further we assume that the total socialwelfare function is simply the summation of all nationalsrsquoutility function sum119901
119894=1119880(119868119894119905) where (119868
1119905 1198682119905 119868
119901119905) is the
income distribution of all nationals at time 119905We consider an income distribution 119868
119905minus1= (1198681119905minus1
1198682119905minus1
119868119901119905minus1
) at time 119905minus1 and two possible income distributions119868119905= (1198681119905 1198682119905 119868
119901119905) and 1198681015840
119905= (11986810158401119905 11986810158402119905 1198681015840
119901119905) at time 119905 We
also assume that the difference of income between time 119905 andtime 119905minus1 is relatively small that is 119868
119894119905minus119868119894119905minus1
≪ 119868119894119905minus1
and 1198681015840119894119905minus
119868119894119905minus1
≪ 119868119894119905minus1
for 119894 = 1 2 119901 Let Δ119880119895119905equiv 119880(119868
119895119905) minus 119880(119868
119895119905minus1)
andΔ1198801015840119895119905equiv 119880(1198681015840
119895119905)minus119880(119868
119895119905minus1)Therefore the difference of the
social welfare between two possible incomes is
sum119880(119868119895119905) minussum119880(1198681015840
119895119905)
= sum[119880 (119868119895119905minus1
) + Δ119880119894119905] minussum[119880 (119868
119895119905minus1) + Δ1015840
119895119905]
= sumΔ119880119895119905minussumΔ1198801015840
119895119905
(5)
For a small change in 119868 we might take (120597120597119868)119880(sdot)119889119868 as theapproximation to the resulting change in 119880 knowing thatthe smaller the 119889119868 the better the approximation There-fore sumΔ119880
119895119905asymp sum(120597120597119868)119880(119868
119895119905minus1) lowast 119889119868
119895and sumΔ1198801015840
119895119905asymp
sum(120597120597119868)119880(119868119895119905minus1
) lowast 1198891198681015840119895 where 119889119868
119895= 119868119895119905
minus 119868119895119905minus1
and
1198891198681015840119895
= 1198681015840119895119905
minus 119868119895119905minus1
We then define an approximation ofsum119880(119868
119895119905) minus sum119880(1198681015840
119895119905) to be
[sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886
equiv sum 120597120597119868119880 (119868
119895119905minus119894) lowast 119889119868 minussum 120597
120597119868119880 (119868119895119905minus1
) 1198891198681015840119895
= sum 119889119868119895minus 1198891198681015840119895
119868119895119905minus1
(6)
We are now ready to state the following proposition
Proposition 1 Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
ge 0 lt==gt [sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886 ge 0
(7)
Proof Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
= 1119875 sum( 119868119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
minus 1119875 sum( 1198681015840
119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
= 1119875 (1 + 119865
119905) (sum
119868119895119905
119868119895119905minus1
minussum 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119868119895119905minus 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
(119868119895119905minus 119868119895119905minus1
) minus (1198681015840119895119905minus 119868119895119905minus1
)119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119889119868119895minus 1198891198681015840119895
119868119895119905minus1
)
(8)
Since both 119875 and (1 + 119865119905) are bigger than zero it is obvious
that RNIAGR(119868119905) minus RNIAGR(1198681015840
119905) ge 0 lt==gt [sum119880(119868
119895119905) minus
sum119880(1198681015840119895119905)]119886 ge 0
With the above proposition we could use the RNIAGR asan approximation of social welfare
6 Examples
To explain the usefulness of real national income averagegrowth rate this study uses Taiwanrsquos data as an example tocompare the result of real economic growth rate and realnational income average growth rate The data about realGDP nominal GDP five-scale disposable incomes consumerprice index and Gini index are collected from Taiwanrsquosgovernment [6] Inflation rate is represented by consumer
6 Economics Research International
Table 2 The comparison result of real economic growth rate and real national income average growth rate in Taiwan
Year
National income growth rate based on different equal divisions of recipients
Real nationalincomeaveragegrowth rate
Real economicgrowth rate Gini IndexThe national
whose incomerank is inlowest 20
The nationalwhose income
rank isbetween
lowest 20and lowest
40
The nationalwhose income
rank isbetween
lowest 40and lowest
60
The nationalwhose income
rank isbetween
highest 20and highest
40
The nationalwhose incomerank is in
highest 20
1995 624 150 minus077 minus157 minus017 105 003 03171996 minus362 minus346 minus332 minus220 minus313 minus315 minus303 03171997 444 216 122 050 146 195 149 03201998 265 168 025 078 146 136 121 03241999 060 197 196 093 048 119 103 03252000 173 179 027 078 minus072 077 028 03262001 minus893 minus833 minus570 minus363 219 minus488 minus264 03502002 141 053 minus034 minus133 minus102 minus015 minus062 03452003 371 294 196 166 024 210 142 03432004 157 115 229 216 139 171 170 03382005 minus001 051 minus117 minus121 minus127 minus063 minus093 03402006 minus261 minus250 minus120 minus023 minus159 minus163 minus141 03392007 047 082 minus025 minus091 059 014 013 03402008 minus083 minus448 minus449 minus271 minus178 minus285 minus270 03412009 minus878 minus591 minus504 minus604 minus602 minus636 minus606 03452010 481 415 403 394 243 387 342 03422011 minus358 minus279 minus356 minus344 minus135 minus294 minus253 0342
price index The unit of data is 1 year The range of data isbetween 1995 and 2011 To compare the results of real eco-nomic growth rate and real national income average growthrate refer to Table 2 and Figure 4
As indicated by Taiwanrsquos economic data the real eco-nomic growth rate had been lower than 2 since 1995 exceptfor the 364 in 2010 Seven out of sixteen years had seennegative growthThe rates of growth in 2001 2008 2009 and2011 were all worse than minus2
Real national income average growth rate can adjust realeconomic growth rate based on the real growth situation ofcitizen group For example the real economic growth rate ofTaiwan in 1995 is only 003 Real income growth rate of thenational whose income is ranking in lowest 20 is 624 realincome growth rate of the national whose income is rankingbetween lowest 20 and lowest 40 is 150 Real nationalincome average growth rate is 105 Although the realeconomic growth rate does not increase real national incomeaverage growth rate also can acquire high performance if theunequal income distribution is improved
In 2001 the real economic growth rate was minus264 forTaiwan However the negative growth was more than 35for individuals at lower 80 income brackets and the indi-viduals at lower 40 income brackets saw a negative growthamounting to more than 8 But people in the top 20 sawtheir income growing by 219 Not only the real economicgrowth decrease but also the unequal income distribution got
worse so real national income average growth rate is minus488which is lower than real economic growth rate The Giniindex also got worse in this year (0350 gt 0326) (the higherGini index the more unequal in income distribution)
In 2010 after the poor performance in 2009 the realeconomic growth rate was 342 for Taiwan Because thepositive growth was higher than 342 for individuals atlower 80 income brackets and people in the top 20 onlysaw their income growing by 243 real national incomeaverage growth rate is 387 which is higher than realeconomic growth rate (342) In reality the Gini index alsogot better in this year (0342 lt 0345) The economic wasperforming well in this year because not only the economicgot better but also the unequal income distribution had beenimproved
The Gini index is defined based on the concept of stockbecause this index is determined according to the long termincome ability of each national The real national incomeaverage growth rate is developed by using the concept offlow because this index is generated by applying the data ofindividual national income in this year So the real nationalincome average growth rate reflects the practical phenomenaof economic more frequently than Gini index For examplethe unequal income distribution got worse quickly in Taiwanin 2001 so Gini index increased from 0326 to 0350 ButGini index decreased slowly in 2002sim2004 when the unequalincome distribution had been improved
Economics Research International 7
800
600
400
200
000
minus200
minus400
minus600
minus800
minus1000
1995
1996
1997
1998
1999
2000
2001
2002
2003
2005
2004
2006
2007
2008
2009
2010
2011
Real income growth rate of the national whose incomeis ranking in lowest 20Real income growth rate of the national whose incomeis ranking between lowest 20 and lowest 40Real income growth rate of the national whose incomeis ranking between lowest 40 and lowest 60
Real income growth rate of the national whose incomeis ranking between highest 20 and highest 40Real income growth rate of the national whose incomeis ranking in highest 20
Real national income average growth rate
Real economic growth rate
()
Figure 4 The comparison result of real economic growth rate andreal national income average growth rate in Taiwan
There is an interesting phenomenon that occurred inTaiwan real national income average growth rate usuallyperformed better than real economic growth rate when thereal economic growth rate was positive On the other handreal national income average growth rate usually performsworse than real economic growth rate when the real eco-nomic growth rate is negative
7 Conclusion and Future Research
In this study we develop a new economic indexmdashRNIAGRfor describing economic situation which considers economicgrowth and income distribution simultaneous Proposedindex not only can reflect real economic growth rate butalso can adjust real economic growth rate according to thecondition of the level of unequal income distribution Inorder to lower down calculation complexity this researchalso develops an economic indexmdashFSRNIAGR which cansimplify calculation process without losing the meaning ofRNIAGR
The reason of choosing FSRNIAGR is that the indexof FSRNIAGR can be generated by five-scale disposableincome which is easy to be acquired in the website in eachgovernment
In the future some economic numerical data will becollected and the economic performance comparison ofeach country based on proposed index will be discussedThe sensitivity analysis in relation to the arbitrary number
of classes which is used to classify the group of incomedistribution will be done by the simulation according to thepractical income distribution of each country
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R Kanbur ldquoChapter 13 Income distribution and developmentrdquoHandbook of Income Distribution vol 1 pp 791ndash841 2000
[2] R Kanbur ldquoEconomic policy distribution and poverty thenature of disagreementsrdquoWorld Development vol 29 no 6 pp1083ndash1094 2001
[3] V Fakoor M B Ghalibaf and H A Azarnoosh ldquoAsymptoticbehaviors of the Lorenz curve and Gini index in sampling froma length-biased distributionrdquo Statistics and Probability Lettersvol 81 no 9 pp 1425ndash1435 2011
[4] BMilanovic ldquoA simpleway to calculate theGini coefficient andsome implicationsrdquo Economics Letters vol 56 no 1 pp 45ndash491997
[5] R Anderton Macroeconomic Performance in a GlobalisingEconomy Cambridge University Press Cambridge UK 2010
[6] Dorectorate-General of Budget Accounting and Statistics ofExecutive Yuan Taiwan httpwwwdgbasgovtw
Submit your manuscripts athttpwwwhindawicom
Child Development Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Education Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Biomedical EducationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Psychiatry Journal
ArchaeologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AnthropologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentSchizophrenia
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Urban Studies Research
Population ResearchInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CriminologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Aging ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NursingResearch and Practice
Current Gerontologyamp Geriatrics Research
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AddictionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geography Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentAutism
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Economics Research International
4 Economics Research International
Area 11986011990411198881represents the total income of the nationals
whose income is ranking in lowest 20 in the last year Area11986011990411198891represents the total income of the nationals whose
income is ranking in lowest 20 in this year Area 1199041119888111988821199042
represents the total income of the nationals whose income isranking between lowest 20 and lowest 40 in the last yearArea 119904
1119889111988921199042represents the total income of the nationals
whose income is ranking between lowest 20 and lowest 40in this year and suchlike
So nominal income growth rate of nationals whoseincome is ranking in lowest 20 can be represented as Area11986011990411198881divides Area119860119904
11198891minus1 Nominal income growth rate of
nationals whose income is ranking between lowest 20 andlowest 40 can be represented as Area 119904
1119888111988821199042divides Area
1199041119889111988921199042minus 1 and the like
Five-scale real national income average growth rate (FSR-NIAGR) of 119905th year can be presented as follows
FSRNIAGR119905
= ((119860 (11986011990411198891)119860 (11986011990411198881) +
119860 (1199041119889111988921199042)
119860 (1199041119888111988821199042) + 119860 (119904
2119889211988931199043)
119860 (1199042119888211988831199043)
+119860 (1199043119889311988941199044)119860 (1199043119888311988841199044) + 119860 (119904
41198894119863119861)
119860 (11990441198884119862119861) ) lowast (119875
119905minus1119875119905)
(1 + 119865119905) )
times (5)minus1 minus 1(4)
119860(11986011990411198891) represents the total income of nationals
whose income is ranking in lowest 20 in 119905th year119860(11986011990411198881) represents the total income of nationals
whose income is ranking in lowest 20 in 119905minus1th year119860(1199041119889111988921199042) represents the total income of nationals
whose income is ranking between lowest 20 andlowest 40 in 119905th year119860(1199041119888111988821199042) represents the total income of nationals
whose income is ranking between lowest 20 andlowest 40 in 119905 minus 1th year119860(1199042119889211988931199043) represents the total income of nationals
whose income is ranking between lowest 40 andlowest 60 in 119905th year119860(1199042119888211988831199043) represents the total income of nationals
whose income is ranking between lowest 40 andlowest 60 in 119905 minus 1th year119860(1199043119889311988941199044) represents the total income of nationals
whose income is ranking highest 20 and highest40 in 119905th year119860(1199043119888311988841199044) represents the total income of nationals
whose income is ranking between highest 20 andhighest 40 in 119905 minus 1th year119860(11990441198894119863119861) represents the total income of nationals
whose income is ranking in highest 20 in 119905th year119860(11990441198884119862119861) represents the total income of nationals
whose income is ranking in highest 20 in 119905 minus 1thyear
25000
20000
15000
10000
5000
0Low
nationalincome
High nationalincome
Low nationalincome
High nationalincome
Low nationalincome
High nationalincome
Figure 3 National income example
In order to reflect the real income status of each nationalfive-scale nominal national income average growth rate needsto be divided by inflation rate of this year to acquire five-scalereal national income average growth rate of this year
4 The Merits of the Real National IncomeAverage Growth Rate
The strong point of real national income average growth rateis that it can modify the drawback of real economic growthrate which did not consider income distribution
For example we suppose that there exists a country whopossesses two nationalsThe income of one national is 20000US dollars in last year (blue color area) and the income of theother national is 10000US dollars in last year (red color area)Suppose that gross domestic product increases 3000 US thisyear The inflation rate of this year is 2
So the real economic growth rate in this country is((20000 + 10000 + 3000)(20000 + 10000))(1 + 2) minus1 = 78
Case 1 (all additional income is acquired by the rich individ-ual) If all the economic profit is acquired by higher nationalthe real national income average growth rate is (05 lowast(1000010000) + 05 lowast (2300020000))(1 + 2) minus 1 = 54
Case 2 (all additional income is acquired by the poorindividual) If all the economic profit is acquired by lowernational the real national income average growth rate is 05 lowast(1300010000) + 05 lowast (2000020000) minus 1 = 127
Case 3 (all additional income is acquired by each individualand the additional income is distributed according to theprevious income of each individual) If economic profit isdistributed according to the income of each national lastyear the real national income average growth rate is (05 lowast(1100010000) + 05 lowast (2200020000))(1 + 2) minus 1 = 78(Refer to Figure 3)
When the level of unequal income distribution is lowerreal national income average growth rate (127) is largerthan real economic growth rate (78) Otherwise realnational income average growth rate (54) is larger thanreal economic growth rate (78) when the level of unequal
Economics Research International 5
Table 1 The relation of real economic growth rate real nationalincome average growth rate and income distribution
Real economic growth rateIncrease Decrease
The level ofunequalincomedistribution
Increase
RNIAGR isincreasing and
adjusted to lowerdown
RNIAGR isdecreasing andadjusted to lower
down more
Decrease
RNIAGR isincreasing andadjusted to bepromoted
RNIAGR isdecreasing andadjusted to
promote a few
income distribution is rising So government will get a betterperformance in real national income average growth rate(relative to real economic growth rate) when governmentpolicy can promote the income of lower income nationallargely
Real national income average growth rate not only can bepositive in relation to real economic growth rate but also canadjust real economic growth rate according to the conditionof the level of unequal income distribution For the relationof real economic growth rate real national income averagegrowth rate and income distribution refer to Table 1
5 Social Welfare Function
To give further rationale for this new index RNIAGR we setup a simplemodel to illustrate the relationship of real nationalincome average growth rate and some total social welfarefunction
We assume that each national has the same increasingutility function of income 119880(119868) = ln(119868) with a diminishingmarginal utility Further we assume that the total socialwelfare function is simply the summation of all nationalsrsquoutility function sum119901
119894=1119880(119868119894119905) where (119868
1119905 1198682119905 119868
119901119905) is the
income distribution of all nationals at time 119905We consider an income distribution 119868
119905minus1= (1198681119905minus1
1198682119905minus1
119868119901119905minus1
) at time 119905minus1 and two possible income distributions119868119905= (1198681119905 1198682119905 119868
119901119905) and 1198681015840
119905= (11986810158401119905 11986810158402119905 1198681015840
119901119905) at time 119905 We
also assume that the difference of income between time 119905 andtime 119905minus1 is relatively small that is 119868
119894119905minus119868119894119905minus1
≪ 119868119894119905minus1
and 1198681015840119894119905minus
119868119894119905minus1
≪ 119868119894119905minus1
for 119894 = 1 2 119901 Let Δ119880119895119905equiv 119880(119868
119895119905) minus 119880(119868
119895119905minus1)
andΔ1198801015840119895119905equiv 119880(1198681015840
119895119905)minus119880(119868
119895119905minus1)Therefore the difference of the
social welfare between two possible incomes is
sum119880(119868119895119905) minussum119880(1198681015840
119895119905)
= sum[119880 (119868119895119905minus1
) + Δ119880119894119905] minussum[119880 (119868
119895119905minus1) + Δ1015840
119895119905]
= sumΔ119880119895119905minussumΔ1198801015840
119895119905
(5)
For a small change in 119868 we might take (120597120597119868)119880(sdot)119889119868 as theapproximation to the resulting change in 119880 knowing thatthe smaller the 119889119868 the better the approximation There-fore sumΔ119880
119895119905asymp sum(120597120597119868)119880(119868
119895119905minus1) lowast 119889119868
119895and sumΔ1198801015840
119895119905asymp
sum(120597120597119868)119880(119868119895119905minus1
) lowast 1198891198681015840119895 where 119889119868
119895= 119868119895119905
minus 119868119895119905minus1
and
1198891198681015840119895
= 1198681015840119895119905
minus 119868119895119905minus1
We then define an approximation ofsum119880(119868
119895119905) minus sum119880(1198681015840
119895119905) to be
[sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886
equiv sum 120597120597119868119880 (119868
119895119905minus119894) lowast 119889119868 minussum 120597
120597119868119880 (119868119895119905minus1
) 1198891198681015840119895
= sum 119889119868119895minus 1198891198681015840119895
119868119895119905minus1
(6)
We are now ready to state the following proposition
Proposition 1 Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
ge 0 lt==gt [sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886 ge 0
(7)
Proof Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
= 1119875 sum( 119868119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
minus 1119875 sum( 1198681015840
119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
= 1119875 (1 + 119865
119905) (sum
119868119895119905
119868119895119905minus1
minussum 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119868119895119905minus 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
(119868119895119905minus 119868119895119905minus1
) minus (1198681015840119895119905minus 119868119895119905minus1
)119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119889119868119895minus 1198891198681015840119895
119868119895119905minus1
)
(8)
Since both 119875 and (1 + 119865119905) are bigger than zero it is obvious
that RNIAGR(119868119905) minus RNIAGR(1198681015840
119905) ge 0 lt==gt [sum119880(119868
119895119905) minus
sum119880(1198681015840119895119905)]119886 ge 0
With the above proposition we could use the RNIAGR asan approximation of social welfare
6 Examples
To explain the usefulness of real national income averagegrowth rate this study uses Taiwanrsquos data as an example tocompare the result of real economic growth rate and realnational income average growth rate The data about realGDP nominal GDP five-scale disposable incomes consumerprice index and Gini index are collected from Taiwanrsquosgovernment [6] Inflation rate is represented by consumer
6 Economics Research International
Table 2 The comparison result of real economic growth rate and real national income average growth rate in Taiwan
Year
National income growth rate based on different equal divisions of recipients
Real nationalincomeaveragegrowth rate
Real economicgrowth rate Gini IndexThe national
whose incomerank is inlowest 20
The nationalwhose income
rank isbetween
lowest 20and lowest
40
The nationalwhose income
rank isbetween
lowest 40and lowest
60
The nationalwhose income
rank isbetween
highest 20and highest
40
The nationalwhose incomerank is in
highest 20
1995 624 150 minus077 minus157 minus017 105 003 03171996 minus362 minus346 minus332 minus220 minus313 minus315 minus303 03171997 444 216 122 050 146 195 149 03201998 265 168 025 078 146 136 121 03241999 060 197 196 093 048 119 103 03252000 173 179 027 078 minus072 077 028 03262001 minus893 minus833 minus570 minus363 219 minus488 minus264 03502002 141 053 minus034 minus133 minus102 minus015 minus062 03452003 371 294 196 166 024 210 142 03432004 157 115 229 216 139 171 170 03382005 minus001 051 minus117 minus121 minus127 minus063 minus093 03402006 minus261 minus250 minus120 minus023 minus159 minus163 minus141 03392007 047 082 minus025 minus091 059 014 013 03402008 minus083 minus448 minus449 minus271 minus178 minus285 minus270 03412009 minus878 minus591 minus504 minus604 minus602 minus636 minus606 03452010 481 415 403 394 243 387 342 03422011 minus358 minus279 minus356 minus344 minus135 minus294 minus253 0342
price index The unit of data is 1 year The range of data isbetween 1995 and 2011 To compare the results of real eco-nomic growth rate and real national income average growthrate refer to Table 2 and Figure 4
As indicated by Taiwanrsquos economic data the real eco-nomic growth rate had been lower than 2 since 1995 exceptfor the 364 in 2010 Seven out of sixteen years had seennegative growthThe rates of growth in 2001 2008 2009 and2011 were all worse than minus2
Real national income average growth rate can adjust realeconomic growth rate based on the real growth situation ofcitizen group For example the real economic growth rate ofTaiwan in 1995 is only 003 Real income growth rate of thenational whose income is ranking in lowest 20 is 624 realincome growth rate of the national whose income is rankingbetween lowest 20 and lowest 40 is 150 Real nationalincome average growth rate is 105 Although the realeconomic growth rate does not increase real national incomeaverage growth rate also can acquire high performance if theunequal income distribution is improved
In 2001 the real economic growth rate was minus264 forTaiwan However the negative growth was more than 35for individuals at lower 80 income brackets and the indi-viduals at lower 40 income brackets saw a negative growthamounting to more than 8 But people in the top 20 sawtheir income growing by 219 Not only the real economicgrowth decrease but also the unequal income distribution got
worse so real national income average growth rate is minus488which is lower than real economic growth rate The Giniindex also got worse in this year (0350 gt 0326) (the higherGini index the more unequal in income distribution)
In 2010 after the poor performance in 2009 the realeconomic growth rate was 342 for Taiwan Because thepositive growth was higher than 342 for individuals atlower 80 income brackets and people in the top 20 onlysaw their income growing by 243 real national incomeaverage growth rate is 387 which is higher than realeconomic growth rate (342) In reality the Gini index alsogot better in this year (0342 lt 0345) The economic wasperforming well in this year because not only the economicgot better but also the unequal income distribution had beenimproved
The Gini index is defined based on the concept of stockbecause this index is determined according to the long termincome ability of each national The real national incomeaverage growth rate is developed by using the concept offlow because this index is generated by applying the data ofindividual national income in this year So the real nationalincome average growth rate reflects the practical phenomenaof economic more frequently than Gini index For examplethe unequal income distribution got worse quickly in Taiwanin 2001 so Gini index increased from 0326 to 0350 ButGini index decreased slowly in 2002sim2004 when the unequalincome distribution had been improved
Economics Research International 7
800
600
400
200
000
minus200
minus400
minus600
minus800
minus1000
1995
1996
1997
1998
1999
2000
2001
2002
2003
2005
2004
2006
2007
2008
2009
2010
2011
Real income growth rate of the national whose incomeis ranking in lowest 20Real income growth rate of the national whose incomeis ranking between lowest 20 and lowest 40Real income growth rate of the national whose incomeis ranking between lowest 40 and lowest 60
Real income growth rate of the national whose incomeis ranking between highest 20 and highest 40Real income growth rate of the national whose incomeis ranking in highest 20
Real national income average growth rate
Real economic growth rate
()
Figure 4 The comparison result of real economic growth rate andreal national income average growth rate in Taiwan
There is an interesting phenomenon that occurred inTaiwan real national income average growth rate usuallyperformed better than real economic growth rate when thereal economic growth rate was positive On the other handreal national income average growth rate usually performsworse than real economic growth rate when the real eco-nomic growth rate is negative
7 Conclusion and Future Research
In this study we develop a new economic indexmdashRNIAGRfor describing economic situation which considers economicgrowth and income distribution simultaneous Proposedindex not only can reflect real economic growth rate butalso can adjust real economic growth rate according to thecondition of the level of unequal income distribution Inorder to lower down calculation complexity this researchalso develops an economic indexmdashFSRNIAGR which cansimplify calculation process without losing the meaning ofRNIAGR
The reason of choosing FSRNIAGR is that the indexof FSRNIAGR can be generated by five-scale disposableincome which is easy to be acquired in the website in eachgovernment
In the future some economic numerical data will becollected and the economic performance comparison ofeach country based on proposed index will be discussedThe sensitivity analysis in relation to the arbitrary number
of classes which is used to classify the group of incomedistribution will be done by the simulation according to thepractical income distribution of each country
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R Kanbur ldquoChapter 13 Income distribution and developmentrdquoHandbook of Income Distribution vol 1 pp 791ndash841 2000
[2] R Kanbur ldquoEconomic policy distribution and poverty thenature of disagreementsrdquoWorld Development vol 29 no 6 pp1083ndash1094 2001
[3] V Fakoor M B Ghalibaf and H A Azarnoosh ldquoAsymptoticbehaviors of the Lorenz curve and Gini index in sampling froma length-biased distributionrdquo Statistics and Probability Lettersvol 81 no 9 pp 1425ndash1435 2011
[4] BMilanovic ldquoA simpleway to calculate theGini coefficient andsome implicationsrdquo Economics Letters vol 56 no 1 pp 45ndash491997
[5] R Anderton Macroeconomic Performance in a GlobalisingEconomy Cambridge University Press Cambridge UK 2010
[6] Dorectorate-General of Budget Accounting and Statistics ofExecutive Yuan Taiwan httpwwwdgbasgovtw
Submit your manuscripts athttpwwwhindawicom
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Economics Research International
Economics Research International 5
Table 1 The relation of real economic growth rate real nationalincome average growth rate and income distribution
Real economic growth rateIncrease Decrease
The level ofunequalincomedistribution
Increase
RNIAGR isincreasing and
adjusted to lowerdown
RNIAGR isdecreasing andadjusted to lower
down more
Decrease
RNIAGR isincreasing andadjusted to bepromoted
RNIAGR isdecreasing andadjusted to
promote a few
income distribution is rising So government will get a betterperformance in real national income average growth rate(relative to real economic growth rate) when governmentpolicy can promote the income of lower income nationallargely
Real national income average growth rate not only can bepositive in relation to real economic growth rate but also canadjust real economic growth rate according to the conditionof the level of unequal income distribution For the relationof real economic growth rate real national income averagegrowth rate and income distribution refer to Table 1
5 Social Welfare Function
To give further rationale for this new index RNIAGR we setup a simplemodel to illustrate the relationship of real nationalincome average growth rate and some total social welfarefunction
We assume that each national has the same increasingutility function of income 119880(119868) = ln(119868) with a diminishingmarginal utility Further we assume that the total socialwelfare function is simply the summation of all nationalsrsquoutility function sum119901
119894=1119880(119868119894119905) where (119868
1119905 1198682119905 119868
119901119905) is the
income distribution of all nationals at time 119905We consider an income distribution 119868
119905minus1= (1198681119905minus1
1198682119905minus1
119868119901119905minus1
) at time 119905minus1 and two possible income distributions119868119905= (1198681119905 1198682119905 119868
119901119905) and 1198681015840
119905= (11986810158401119905 11986810158402119905 1198681015840
119901119905) at time 119905 We
also assume that the difference of income between time 119905 andtime 119905minus1 is relatively small that is 119868
119894119905minus119868119894119905minus1
≪ 119868119894119905minus1
and 1198681015840119894119905minus
119868119894119905minus1
≪ 119868119894119905minus1
for 119894 = 1 2 119901 Let Δ119880119895119905equiv 119880(119868
119895119905) minus 119880(119868
119895119905minus1)
andΔ1198801015840119895119905equiv 119880(1198681015840
119895119905)minus119880(119868
119895119905minus1)Therefore the difference of the
social welfare between two possible incomes is
sum119880(119868119895119905) minussum119880(1198681015840
119895119905)
= sum[119880 (119868119895119905minus1
) + Δ119880119894119905] minussum[119880 (119868
119895119905minus1) + Δ1015840
119895119905]
= sumΔ119880119895119905minussumΔ1198801015840
119895119905
(5)
For a small change in 119868 we might take (120597120597119868)119880(sdot)119889119868 as theapproximation to the resulting change in 119880 knowing thatthe smaller the 119889119868 the better the approximation There-fore sumΔ119880
119895119905asymp sum(120597120597119868)119880(119868
119895119905minus1) lowast 119889119868
119895and sumΔ1198801015840
119895119905asymp
sum(120597120597119868)119880(119868119895119905minus1
) lowast 1198891198681015840119895 where 119889119868
119895= 119868119895119905
minus 119868119895119905minus1
and
1198891198681015840119895
= 1198681015840119895119905
minus 119868119895119905minus1
We then define an approximation ofsum119880(119868
119895119905) minus sum119880(1198681015840
119895119905) to be
[sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886
equiv sum 120597120597119868119880 (119868
119895119905minus119894) lowast 119889119868 minussum 120597
120597119868119880 (119868119895119905minus1
) 1198891198681015840119895
= sum 119889119868119895minus 1198891198681015840119895
119868119895119905minus1
(6)
We are now ready to state the following proposition
Proposition 1 Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
ge 0 lt==gt [sum119880(119868119895119905) minussum119880(1198681015840
119895119905)]119886 ge 0
(7)
Proof Consider the following
RNIAGR (119868119905) minus RNIAGR (1198681015840
119905)
= 1119875 sum( 119868119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
minus 1119875 sum( 1198681015840
119895119905
119868119895119905minus1
lowast (1 + 119865119905)) minus 1
= 1119875 (1 + 119865
119905) (sum
119868119895119905
119868119895119905minus1
minussum 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119868119895119905minus 1198681015840119895119905
119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
(119868119895119905minus 119868119895119905minus1
) minus (1198681015840119895119905minus 119868119895119905minus1
)119868119895119905minus1
)
= 1119875 (1 + 119865
119905) (sum
119889119868119895minus 1198891198681015840119895
119868119895119905minus1
)
(8)
Since both 119875 and (1 + 119865119905) are bigger than zero it is obvious
that RNIAGR(119868119905) minus RNIAGR(1198681015840
119905) ge 0 lt==gt [sum119880(119868
119895119905) minus
sum119880(1198681015840119895119905)]119886 ge 0
With the above proposition we could use the RNIAGR asan approximation of social welfare
6 Examples
To explain the usefulness of real national income averagegrowth rate this study uses Taiwanrsquos data as an example tocompare the result of real economic growth rate and realnational income average growth rate The data about realGDP nominal GDP five-scale disposable incomes consumerprice index and Gini index are collected from Taiwanrsquosgovernment [6] Inflation rate is represented by consumer
6 Economics Research International
Table 2 The comparison result of real economic growth rate and real national income average growth rate in Taiwan
Year
National income growth rate based on different equal divisions of recipients
Real nationalincomeaveragegrowth rate
Real economicgrowth rate Gini IndexThe national
whose incomerank is inlowest 20
The nationalwhose income
rank isbetween
lowest 20and lowest
40
The nationalwhose income
rank isbetween
lowest 40and lowest
60
The nationalwhose income
rank isbetween
highest 20and highest
40
The nationalwhose incomerank is in
highest 20
1995 624 150 minus077 minus157 minus017 105 003 03171996 minus362 minus346 minus332 minus220 minus313 minus315 minus303 03171997 444 216 122 050 146 195 149 03201998 265 168 025 078 146 136 121 03241999 060 197 196 093 048 119 103 03252000 173 179 027 078 minus072 077 028 03262001 minus893 minus833 minus570 minus363 219 minus488 minus264 03502002 141 053 minus034 minus133 minus102 minus015 minus062 03452003 371 294 196 166 024 210 142 03432004 157 115 229 216 139 171 170 03382005 minus001 051 minus117 minus121 minus127 minus063 minus093 03402006 minus261 minus250 minus120 minus023 minus159 minus163 minus141 03392007 047 082 minus025 minus091 059 014 013 03402008 minus083 minus448 minus449 minus271 minus178 minus285 minus270 03412009 minus878 minus591 minus504 minus604 minus602 minus636 minus606 03452010 481 415 403 394 243 387 342 03422011 minus358 minus279 minus356 minus344 minus135 minus294 minus253 0342
price index The unit of data is 1 year The range of data isbetween 1995 and 2011 To compare the results of real eco-nomic growth rate and real national income average growthrate refer to Table 2 and Figure 4
As indicated by Taiwanrsquos economic data the real eco-nomic growth rate had been lower than 2 since 1995 exceptfor the 364 in 2010 Seven out of sixteen years had seennegative growthThe rates of growth in 2001 2008 2009 and2011 were all worse than minus2
Real national income average growth rate can adjust realeconomic growth rate based on the real growth situation ofcitizen group For example the real economic growth rate ofTaiwan in 1995 is only 003 Real income growth rate of thenational whose income is ranking in lowest 20 is 624 realincome growth rate of the national whose income is rankingbetween lowest 20 and lowest 40 is 150 Real nationalincome average growth rate is 105 Although the realeconomic growth rate does not increase real national incomeaverage growth rate also can acquire high performance if theunequal income distribution is improved
In 2001 the real economic growth rate was minus264 forTaiwan However the negative growth was more than 35for individuals at lower 80 income brackets and the indi-viduals at lower 40 income brackets saw a negative growthamounting to more than 8 But people in the top 20 sawtheir income growing by 219 Not only the real economicgrowth decrease but also the unequal income distribution got
worse so real national income average growth rate is minus488which is lower than real economic growth rate The Giniindex also got worse in this year (0350 gt 0326) (the higherGini index the more unequal in income distribution)
In 2010 after the poor performance in 2009 the realeconomic growth rate was 342 for Taiwan Because thepositive growth was higher than 342 for individuals atlower 80 income brackets and people in the top 20 onlysaw their income growing by 243 real national incomeaverage growth rate is 387 which is higher than realeconomic growth rate (342) In reality the Gini index alsogot better in this year (0342 lt 0345) The economic wasperforming well in this year because not only the economicgot better but also the unequal income distribution had beenimproved
The Gini index is defined based on the concept of stockbecause this index is determined according to the long termincome ability of each national The real national incomeaverage growth rate is developed by using the concept offlow because this index is generated by applying the data ofindividual national income in this year So the real nationalincome average growth rate reflects the practical phenomenaof economic more frequently than Gini index For examplethe unequal income distribution got worse quickly in Taiwanin 2001 so Gini index increased from 0326 to 0350 ButGini index decreased slowly in 2002sim2004 when the unequalincome distribution had been improved
Economics Research International 7
800
600
400
200
000
minus200
minus400
minus600
minus800
minus1000
1995
1996
1997
1998
1999
2000
2001
2002
2003
2005
2004
2006
2007
2008
2009
2010
2011
Real income growth rate of the national whose incomeis ranking in lowest 20Real income growth rate of the national whose incomeis ranking between lowest 20 and lowest 40Real income growth rate of the national whose incomeis ranking between lowest 40 and lowest 60
Real income growth rate of the national whose incomeis ranking between highest 20 and highest 40Real income growth rate of the national whose incomeis ranking in highest 20
Real national income average growth rate
Real economic growth rate
()
Figure 4 The comparison result of real economic growth rate andreal national income average growth rate in Taiwan
There is an interesting phenomenon that occurred inTaiwan real national income average growth rate usuallyperformed better than real economic growth rate when thereal economic growth rate was positive On the other handreal national income average growth rate usually performsworse than real economic growth rate when the real eco-nomic growth rate is negative
7 Conclusion and Future Research
In this study we develop a new economic indexmdashRNIAGRfor describing economic situation which considers economicgrowth and income distribution simultaneous Proposedindex not only can reflect real economic growth rate butalso can adjust real economic growth rate according to thecondition of the level of unequal income distribution Inorder to lower down calculation complexity this researchalso develops an economic indexmdashFSRNIAGR which cansimplify calculation process without losing the meaning ofRNIAGR
The reason of choosing FSRNIAGR is that the indexof FSRNIAGR can be generated by five-scale disposableincome which is easy to be acquired in the website in eachgovernment
In the future some economic numerical data will becollected and the economic performance comparison ofeach country based on proposed index will be discussedThe sensitivity analysis in relation to the arbitrary number
of classes which is used to classify the group of incomedistribution will be done by the simulation according to thepractical income distribution of each country
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R Kanbur ldquoChapter 13 Income distribution and developmentrdquoHandbook of Income Distribution vol 1 pp 791ndash841 2000
[2] R Kanbur ldquoEconomic policy distribution and poverty thenature of disagreementsrdquoWorld Development vol 29 no 6 pp1083ndash1094 2001
[3] V Fakoor M B Ghalibaf and H A Azarnoosh ldquoAsymptoticbehaviors of the Lorenz curve and Gini index in sampling froma length-biased distributionrdquo Statistics and Probability Lettersvol 81 no 9 pp 1425ndash1435 2011
[4] BMilanovic ldquoA simpleway to calculate theGini coefficient andsome implicationsrdquo Economics Letters vol 56 no 1 pp 45ndash491997
[5] R Anderton Macroeconomic Performance in a GlobalisingEconomy Cambridge University Press Cambridge UK 2010
[6] Dorectorate-General of Budget Accounting and Statistics ofExecutive Yuan Taiwan httpwwwdgbasgovtw
Submit your manuscripts athttpwwwhindawicom
Child Development Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Education Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Biomedical EducationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Psychiatry Journal
ArchaeologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AnthropologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentSchizophrenia
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Urban Studies Research
Population ResearchInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CriminologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Aging ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NursingResearch and Practice
Current Gerontologyamp Geriatrics Research
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AddictionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geography Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentAutism
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Economics Research International
6 Economics Research International
Table 2 The comparison result of real economic growth rate and real national income average growth rate in Taiwan
Year
National income growth rate based on different equal divisions of recipients
Real nationalincomeaveragegrowth rate
Real economicgrowth rate Gini IndexThe national
whose incomerank is inlowest 20
The nationalwhose income
rank isbetween
lowest 20and lowest
40
The nationalwhose income
rank isbetween
lowest 40and lowest
60
The nationalwhose income
rank isbetween
highest 20and highest
40
The nationalwhose incomerank is in
highest 20
1995 624 150 minus077 minus157 minus017 105 003 03171996 minus362 minus346 minus332 minus220 minus313 minus315 minus303 03171997 444 216 122 050 146 195 149 03201998 265 168 025 078 146 136 121 03241999 060 197 196 093 048 119 103 03252000 173 179 027 078 minus072 077 028 03262001 minus893 minus833 minus570 minus363 219 minus488 minus264 03502002 141 053 minus034 minus133 minus102 minus015 minus062 03452003 371 294 196 166 024 210 142 03432004 157 115 229 216 139 171 170 03382005 minus001 051 minus117 minus121 minus127 minus063 minus093 03402006 minus261 minus250 minus120 minus023 minus159 minus163 minus141 03392007 047 082 minus025 minus091 059 014 013 03402008 minus083 minus448 minus449 minus271 minus178 minus285 minus270 03412009 minus878 minus591 minus504 minus604 minus602 minus636 minus606 03452010 481 415 403 394 243 387 342 03422011 minus358 minus279 minus356 minus344 minus135 minus294 minus253 0342
price index The unit of data is 1 year The range of data isbetween 1995 and 2011 To compare the results of real eco-nomic growth rate and real national income average growthrate refer to Table 2 and Figure 4
As indicated by Taiwanrsquos economic data the real eco-nomic growth rate had been lower than 2 since 1995 exceptfor the 364 in 2010 Seven out of sixteen years had seennegative growthThe rates of growth in 2001 2008 2009 and2011 were all worse than minus2
Real national income average growth rate can adjust realeconomic growth rate based on the real growth situation ofcitizen group For example the real economic growth rate ofTaiwan in 1995 is only 003 Real income growth rate of thenational whose income is ranking in lowest 20 is 624 realincome growth rate of the national whose income is rankingbetween lowest 20 and lowest 40 is 150 Real nationalincome average growth rate is 105 Although the realeconomic growth rate does not increase real national incomeaverage growth rate also can acquire high performance if theunequal income distribution is improved
In 2001 the real economic growth rate was minus264 forTaiwan However the negative growth was more than 35for individuals at lower 80 income brackets and the indi-viduals at lower 40 income brackets saw a negative growthamounting to more than 8 But people in the top 20 sawtheir income growing by 219 Not only the real economicgrowth decrease but also the unequal income distribution got
worse so real national income average growth rate is minus488which is lower than real economic growth rate The Giniindex also got worse in this year (0350 gt 0326) (the higherGini index the more unequal in income distribution)
In 2010 after the poor performance in 2009 the realeconomic growth rate was 342 for Taiwan Because thepositive growth was higher than 342 for individuals atlower 80 income brackets and people in the top 20 onlysaw their income growing by 243 real national incomeaverage growth rate is 387 which is higher than realeconomic growth rate (342) In reality the Gini index alsogot better in this year (0342 lt 0345) The economic wasperforming well in this year because not only the economicgot better but also the unequal income distribution had beenimproved
The Gini index is defined based on the concept of stockbecause this index is determined according to the long termincome ability of each national The real national incomeaverage growth rate is developed by using the concept offlow because this index is generated by applying the data ofindividual national income in this year So the real nationalincome average growth rate reflects the practical phenomenaof economic more frequently than Gini index For examplethe unequal income distribution got worse quickly in Taiwanin 2001 so Gini index increased from 0326 to 0350 ButGini index decreased slowly in 2002sim2004 when the unequalincome distribution had been improved
Economics Research International 7
800
600
400
200
000
minus200
minus400
minus600
minus800
minus1000
1995
1996
1997
1998
1999
2000
2001
2002
2003
2005
2004
2006
2007
2008
2009
2010
2011
Real income growth rate of the national whose incomeis ranking in lowest 20Real income growth rate of the national whose incomeis ranking between lowest 20 and lowest 40Real income growth rate of the national whose incomeis ranking between lowest 40 and lowest 60
Real income growth rate of the national whose incomeis ranking between highest 20 and highest 40Real income growth rate of the national whose incomeis ranking in highest 20
Real national income average growth rate
Real economic growth rate
()
Figure 4 The comparison result of real economic growth rate andreal national income average growth rate in Taiwan
There is an interesting phenomenon that occurred inTaiwan real national income average growth rate usuallyperformed better than real economic growth rate when thereal economic growth rate was positive On the other handreal national income average growth rate usually performsworse than real economic growth rate when the real eco-nomic growth rate is negative
7 Conclusion and Future Research
In this study we develop a new economic indexmdashRNIAGRfor describing economic situation which considers economicgrowth and income distribution simultaneous Proposedindex not only can reflect real economic growth rate butalso can adjust real economic growth rate according to thecondition of the level of unequal income distribution Inorder to lower down calculation complexity this researchalso develops an economic indexmdashFSRNIAGR which cansimplify calculation process without losing the meaning ofRNIAGR
The reason of choosing FSRNIAGR is that the indexof FSRNIAGR can be generated by five-scale disposableincome which is easy to be acquired in the website in eachgovernment
In the future some economic numerical data will becollected and the economic performance comparison ofeach country based on proposed index will be discussedThe sensitivity analysis in relation to the arbitrary number
of classes which is used to classify the group of incomedistribution will be done by the simulation according to thepractical income distribution of each country
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R Kanbur ldquoChapter 13 Income distribution and developmentrdquoHandbook of Income Distribution vol 1 pp 791ndash841 2000
[2] R Kanbur ldquoEconomic policy distribution and poverty thenature of disagreementsrdquoWorld Development vol 29 no 6 pp1083ndash1094 2001
[3] V Fakoor M B Ghalibaf and H A Azarnoosh ldquoAsymptoticbehaviors of the Lorenz curve and Gini index in sampling froma length-biased distributionrdquo Statistics and Probability Lettersvol 81 no 9 pp 1425ndash1435 2011
[4] BMilanovic ldquoA simpleway to calculate theGini coefficient andsome implicationsrdquo Economics Letters vol 56 no 1 pp 45ndash491997
[5] R Anderton Macroeconomic Performance in a GlobalisingEconomy Cambridge University Press Cambridge UK 2010
[6] Dorectorate-General of Budget Accounting and Statistics ofExecutive Yuan Taiwan httpwwwdgbasgovtw
Submit your manuscripts athttpwwwhindawicom
Child Development Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Education Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Biomedical EducationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Psychiatry Journal
ArchaeologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AnthropologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentSchizophrenia
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Urban Studies Research
Population ResearchInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CriminologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Aging ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NursingResearch and Practice
Current Gerontologyamp Geriatrics Research
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AddictionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geography Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentAutism
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Economics Research International
Economics Research International 7
800
600
400
200
000
minus200
minus400
minus600
minus800
minus1000
1995
1996
1997
1998
1999
2000
2001
2002
2003
2005
2004
2006
2007
2008
2009
2010
2011
Real income growth rate of the national whose incomeis ranking in lowest 20Real income growth rate of the national whose incomeis ranking between lowest 20 and lowest 40Real income growth rate of the national whose incomeis ranking between lowest 40 and lowest 60
Real income growth rate of the national whose incomeis ranking between highest 20 and highest 40Real income growth rate of the national whose incomeis ranking in highest 20
Real national income average growth rate
Real economic growth rate
()
Figure 4 The comparison result of real economic growth rate andreal national income average growth rate in Taiwan
There is an interesting phenomenon that occurred inTaiwan real national income average growth rate usuallyperformed better than real economic growth rate when thereal economic growth rate was positive On the other handreal national income average growth rate usually performsworse than real economic growth rate when the real eco-nomic growth rate is negative
7 Conclusion and Future Research
In this study we develop a new economic indexmdashRNIAGRfor describing economic situation which considers economicgrowth and income distribution simultaneous Proposedindex not only can reflect real economic growth rate butalso can adjust real economic growth rate according to thecondition of the level of unequal income distribution Inorder to lower down calculation complexity this researchalso develops an economic indexmdashFSRNIAGR which cansimplify calculation process without losing the meaning ofRNIAGR
The reason of choosing FSRNIAGR is that the indexof FSRNIAGR can be generated by five-scale disposableincome which is easy to be acquired in the website in eachgovernment
In the future some economic numerical data will becollected and the economic performance comparison ofeach country based on proposed index will be discussedThe sensitivity analysis in relation to the arbitrary number
of classes which is used to classify the group of incomedistribution will be done by the simulation according to thepractical income distribution of each country
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R Kanbur ldquoChapter 13 Income distribution and developmentrdquoHandbook of Income Distribution vol 1 pp 791ndash841 2000
[2] R Kanbur ldquoEconomic policy distribution and poverty thenature of disagreementsrdquoWorld Development vol 29 no 6 pp1083ndash1094 2001
[3] V Fakoor M B Ghalibaf and H A Azarnoosh ldquoAsymptoticbehaviors of the Lorenz curve and Gini index in sampling froma length-biased distributionrdquo Statistics and Probability Lettersvol 81 no 9 pp 1425ndash1435 2011
[4] BMilanovic ldquoA simpleway to calculate theGini coefficient andsome implicationsrdquo Economics Letters vol 56 no 1 pp 45ndash491997
[5] R Anderton Macroeconomic Performance in a GlobalisingEconomy Cambridge University Press Cambridge UK 2010
[6] Dorectorate-General of Budget Accounting and Statistics ofExecutive Yuan Taiwan httpwwwdgbasgovtw
Submit your manuscripts athttpwwwhindawicom
Child Development Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Education Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Biomedical EducationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Psychiatry Journal
ArchaeologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AnthropologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentSchizophrenia
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Urban Studies Research
Population ResearchInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CriminologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Aging ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NursingResearch and Practice
Current Gerontologyamp Geriatrics Research
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AddictionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geography Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentAutism
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Economics Research International
Submit your manuscripts athttpwwwhindawicom
Child Development Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Education Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Biomedical EducationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Psychiatry Journal
ArchaeologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AnthropologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentSchizophrenia
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Urban Studies Research
Population ResearchInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CriminologyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Aging ResearchJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NursingResearch and Practice
Current Gerontologyamp Geriatrics Research
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AddictionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Geography Journal
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Research and TreatmentAutism
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Economics Research International