Economics Research International

Volume 2015, Article ID 678927, 7 pages

http://dx.doi.org/10.1155/2015/678927

## Real National Income Average Growth Rate: A Novel Economic Growth and Social Fair Evaluation Index

^{1}Department of Economics, National Chi Nan University, No. 1, University Road, Puli, Nantou County 54561, Taiwan^{2}Department of International Tourism and Recreation, Hsing-Kuo University, No. 600, Section 3, Taijiang Boulevard, Annan District, Tainan, Taiwan

Received 4 September 2014; Accepted 12 December 2014

Academic Editor: João Ricardo Faria

Copyright © 2015 Chien Wei Wu and Wei Zhan Hung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The purpose of this study is to propose a new economic index, namely, real national income average growth rate (RNIAGR), which measures the performance of economic growth with consideration for income distribution. This study also develops another new economic index, called five-scale real national income average growth rate (FSRNIAGR), which simplifies the calculation of RNIAGR. The merits of these new indexes are discussed to justify their efficacy. This paper also justifies the use of proposed index by showing that this index can actually measure the ordering of social welfare. To highlight the difference between this new index and the traditional ones, this paper compares the index with real economic growth rate using the data of Taiwan. In addition, this paper 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 a common phenomenon across borders. For example, according to a report published by the Organization for Economic Cooperation and Development (OECD) in 2011, the average income of the richest 10% of the population is about nine times that of the poorest 10% across the OECD, up from seven times in 1985. Hence, income distribution has been a central concern for both academics and policy makers in developed countries as well as developing countries. As pointed out by Robert Shiller, one of the winners of the Nobel Prize for Economics in 2013, “The most important problem that we are facing now today, I think, is rising inequality in the United States and elsewhere in the world” (The Huffington Post, Oct 15, 2013).

A number of economic indexes are commonly used to measure economic growth and income distribution. For example, real gross domestic product is used to measure economic growth: Gini coefficient, Lorenz curve, and the ratio of income share of highest 20% to that of lowest 20% measure income distribution. However, under certain circumstances, these two objectives (growth and distribution) are conflicting to each other. For example, if policy makers focus on pursuing economic growth, this may deteriorate uneven distribution (income gap). By contrast, if they focus on decreasing uneven distribution, this may lower the work incentives of high ability workers.

For policy makers, a single index that incorporates growth as well as distribution may help to immediately crystallize the efficacy of certain policies. Despite the prevalence of many indexes for income inequality, none of the indexes for growth can to some extent reflect the degree of income inequalities. The lack of such index necessitates the study of better indexes that consider growth as well as distribution simultaneously. To this end, this study intends to propose a new index: Real National Income Average Growth Rate (hereafter, RNIAGR). We justify the use of this index by showing that this index can actually measure the ordering of social welfare. In addition, we also show that when the real growth stagnates or even declines, this index indicates that income distribution deteriorates.

The reminder of this paper is organized as follows. Section 2 reviews major economic growth indexes and income distribution indexes in the existing literature. Section 3 defines the concept of real national income average growth rate, and Section 4 further discusses the advantages of using this new index. In Section 5, using the data in Taiwan, we compare this new index with the usual real economic growth rate. Finally, Section 6 concludes this paper with some remarks.

#### 2. Economic Index

##### 2.1. Measuring Economic Growth Index

The main economic index for measuring economic growth is real economic growth rate. The formula of the real economic growth rate is defined as follows: Real Economic Growth represents real economic growth rate of th year. Real represents real gross domestic product of th year. Real represents real gross domestic product of th year.

Gross domestic product can be explained as the power of the country. Positive real economic growth rate means the power of the country is increasing. It seems every country aims to promote their real economic growth rate.

Real economic growth rate is calculated as the total income of all nationals in the last year divided by the total net increase income of all nationals in this year. It can reveal the macroeconomic level of the entire nation, but it does not display the information of the income growth rate of each individual nation. However, promoting real economic growth rate usually leads to a side effect: unequal income distribution [1, 2].

##### 2.2. Measuring Income Distribution Index

The main economic index for measuring income distribution includes Lorenz curve, Gini coefficient, and ratio of income share of highest 20% to that of lowest 20%.

Lorenz curve is an income aggregation curve which aggregates income from the lowest income national to the highest income national [3].

The Gini coefficient is a measuring index of statistical dispersion formulated by Corrado Gini [4]. Gini coefficient is usually defined mathematically based on the Lorenz curve. Gini coefficient ranges from 0 to 1. A low Gini coefficient indicates a more equal distribution. Gini coefficient = 0 represents complete equality. Higher Gini coefficients indicate more unequal distribution. Gini coefficient = 1 represents complete inequality. Although Gini coefficient can explain the unequal degree of income distribution, it is useless to use Gini coefficient to express the financial net increase income distribute of each national in each year.

As implied by the name, ratio of income share of highest 20% to that of lowest 20% means the total income of nationals whose income rank is in lowest 20% divides the total income of nationals whose income rank is in highest 20% [5]. The drawback of ratio of income share of highest 20% to that of lowest 20% is that it does not consider the income distribution of nationals whose income is in the middle.

#### 3. Real National Income Average Growth Rate

To consider economic growth and income distribution simultaneous, this research provides a new index—real national income average growth rate. The concept of RNIAGR is averaged real income growth of each individual national. Unlike real economic growth rate that calculates the economic growth rate based on the total income of all nationals in previous year, RNIAGR is calculated from individual income growth rate based on individual income in the previous year and average of all of individual income growth rate. RNIAGR can reflect the average income growth status of individual national. This formula supposes that the volume of nationals in th year and in th year in the same Country is the same: represents real national income average growth rate in th year. represents the income of th national in th year. represents the income of th national in th year. represents the inflation rate in th year. represents the volume of nationals in the country.

Using Figure 1 as example, -axis represents the rank of income from low income national to high income national. Point represents the lowest income national and point represents the highest income national. From point to point , all of the points can reflect an income of one national.