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Show graphically or mathematically how an increase of the wage rate for educated workers affects the Lorenz curve and Gin coefficient for the society.

Microeconomics

13th Edition

ISBN:9781337617406

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter15: The Distribution Of Income And Poverty

Section: Chapter Questions

Problem 10QP

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Show graphically or mathematically how an increase of the wage rate for educated workers affects the Lorenz curve and Gin coefficient for the society.

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Scientists studying the economics of a country, community, or group of people are often interested in the distribution of wealth, where wealth is understood to mean the income or the personal assets of individual households. A powerful tool for illustrating how wealth is distributed across a society is the Lorenz curve (invented by the American economist Max Otto Lorenz in 1905). A typical Lorenz curve is given by y = L(x), where 0 < x < 1 and 0 < y < 1. The variable I represents the fraction of all households in the society and y = L(x) represents the fraction of the total wealth that is owned by the fraction x of the society. For example, for the Lorenz curve shown in Figure 1, we see that L(0.5) = 0.2, which means that 0.5 (50%) of the society owns 0.2 (20%) of the wealth. bottom botom y A 1- Line of perfect equality 0.8 of households control 0.6 of the wealth. Lorenz curve 0.5 of households control 0.2 of the wealth. 0.2 B 0.5 0.8 a1 1 Fraction of Households Figure I Fraction of…
Explain how the Gini coefficient is derived from the Lorenz curve by making use of the graph provided;
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Imagine an economy with only two types of workers, unskilled (u) and skilled (s). The supply curves of these workers are, respectively, LSU=20wu-10 and LSS=20ws-60. Initially, labour demand curves are LDU=170-10wu and LDS=164-8ws. At equilibrium, what are the inequality measures for this economy? Mean = 80:20 Ratio 80:50 Ratio 50:20 Ratio