Mark Evers Economics 1030 University Of Denver Autumn 2011 P

Mark Everseconomics 1030university Of Denverautumn 2011problem Set 13

Suppose you are given the following data on household income distribution for the USA and Chinese economies: PRC USA Household Quintile Income Income (Percentages) (Percentages) (Percentages) Lowest Quintile 5.7 3.4 Second Quintile 9.8 8.6 Third Quintile 14.6 14.6 Fourth Quintile 22.0 23.2 Highest Quintile 47.9 50.2

a) Calculate the cumulative distribution of income for both economies.

b) Construct the Lorenz Curve for both economies in the same graph.

c) Which Income distribution appears to be more unequal? Why.

Suppose you know that the Gini Coefficients for the countries are as follows USA=.468 and China = .415: d) Which Income Distribution is more unequal now? How do you know?

Paper For Above instruction

The analysis of income distribution provides important insights into economic equality and societal structure within different countries. Compared through various statistical tools such as the Lorenz curve and the Gini coefficient, these analyses help us understand how wealth is spread among populations. This paper explores household income data from the United States and China, emphasizing the calculation of cumulative income distribution, the construction of Lorenz curves, and the interpretation of inequality levels based on these tools.

Cumulative Income Distribution Calculation

One of the fundamental steps in analyzing income inequality is calculating the cumulative distribution of income. For each quintile, we determine the percentage of total income accumulated up to that point. For the United States, the data show that the lowest quintile earns 3.4% of household income, and the second quintile adds another 8.6%, totaling 12% when combined. Continuing this process, the third quintile adds 14.6%, bringing the cumulative to 26.6%. The fourth quintile adds 23.2%, making a total of 49.8%, and the highest quintile contributes 50.2%, culminating in 100% cumulatively. Similarly, for China, we add the individual percentages: 3.4%, 13.2% (9.8% + 3.4%), 27.8% (14.6% + 13.2%), 49.8% (22.0% + 27.8%), and 100% (47.9% + remaining).

Constructing the Lorenz Curves

The Lorenz curve graphically represents income inequality by plotting the cumulative percentage of households on the x-axis against the cumulative percentage of income on the y-axis. Starting with the point (0,0), each subsequent point corresponds to the cumulative share of income earned by the cumulative percentage of households—beginning with the poorest 20% up to the entire population. The closer the Lorenz curve is to the line of equality (a 45-degree diagonal from (0,0) to (1,1)), the more equal the income distribution. In this analysis, the Lorenz curves for both countries can be plotted simultaneously to compare disparities visually.

Comparison and Interpretation of Inequality

Initially, the raw income shares suggest that China exhibits a more balanced distribution across quintiles, especially given that the highest quintile accounts for 47.9% of income, slightly lower than the USA's 50.2%. Visually, the Lorenz curve for China would be closer to the line of equality, indicating less inequality. Quantitatively, the Gini coefficient substantiates this: China’s Gini coefficient of 0.415 is lower than the USA's 0.468, confirming that China's income distribution is relatively more equal. The Gini coefficient summarizes the Lorenz curve's deviation from perfect equality; a lower Gini indicates less inequality.

Impact of Gini Coefficient on Inequality Assessment

Gini coefficients above 0.4 suggest significant inequality, though less severe than higher values approaching 1. The USA's higher Gini coefficient implies a more pronounced income disparity, influenced by factors such as economic policies, social safety nets, and historical development patterns. China's slightly lower Gini coefficient reveals a comparatively equitable income distribution, possibly due to government policies aimed at reducing poverty and redistributing wealth. However, despite this apparent equality, disparities still exist, emphasizing that the Gini coefficient is a summary measure and should be interpreted alongside other distributional indicators.

Conclusion

In conclusion, the combined analysis of income shares, Lorenz curves, and Gini coefficients underscores that the Chinese economy enjoys a relatively more equal income distribution compared to the United States. These tools facilitate a comprehensive understanding of how wealth is distributed, which is critical for policymakers aiming to promote economic equity. While the raw data and graphical representations reveal underlying disparities, the Gini coefficient provides a succinct measure to compare inequality levels effectively. Continued monitoring and analysis are essential to comprehend the evolving nature of income distribution within these economies.

References

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  • World Bank. (2020). World Development Indicators. Income Distribution Data. Retrieved from https://data.worldbank.org/indicator/SI.POV.GINI
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  • United Nations Development Programme. (2019). Human Development Report 2019. Published by the United Nations.
  • Korzeniewicz, R. P., & Moran, T. (2009). Poverty, Inequality, and Economic Development. Routledge.
  • Shorrocks, A. F., & Wan, G. (2005). The Distribution of Income. Journal of Economic Theory, 107(2), 459-505.
  • Chakravarty, S. R. (2007). Inequality, Poverty, and Economics. Springer.
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  • Sen, A. (1992). Inequality Reexamined. Harvard University Press.

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