For the comparisons of incomes per capita of the countries, the income unequality is examined with some methods mainly by Gini Index. Nevertheless, most of these methods do not give any idea that how the national income is reflected to the country` population. Namely, the effectiveness of income on population is not able to be measured. The people in a society as much as possible have income close to average income per capita, shows the good quality of society income distribution. In a country, the rate of sum of population of the every individual ,who possesses an income equal to and above the average disposable income of the country, to total country`s population is called "Bozdağ Population Efficiency Coefficient" (briefly Bozdağ Coefficient). There is no data related to the size of the population whose incomes are compare to average income per capita, therefore, Bozdağ Coefficient is estimated by using income and consumption tables - the Lorez curves- in five equal groups which are in 20 percentiles of the population. Then `Bozdağ Population Efficiency Index (briefly Bozdağ Index) is driven from utilitizing Bozdağ Coefficient and income per capita. The structure of income distributions of the selected EU countries is represented with using Gini Index and Bozdağ Coefficient and Index.
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