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Consider the data from Table 1. As shown below, the variance was originally computed as 2,400, the coefficient of variation as 0.61, and the 80-20 ratio as 5. TABLET Worker Earnings (5) 1 2 3 4 5 Total 20 40 SO 100 160 400 10 20 25 40 100 400 where mean carings are given by IE *= 80 and the variance of earnings is given by 5 Σ (E-E) N (20-80) +(40-80) + (80-80) + (100-80) +(160-80) = 2,400 The coefficient of variation is given by V 2400 CV = = 0.61 80 The 80-20 earnings ratio is given by Earnings at 80th perele 100 -5 Earnings at 20th percentile 20 Suppose $20 is redistributed from worker 5 to worker 1. Compute the new variance and coefficient of variation. a.) b.) c.) Suppose $20 is redistributed from worker 5 to worker 4. Compute the new variance and the coefficient of variation. Intuitively, which redistribution brings about more income equality? Which measure of dispersion changes in a way that corresponds to your intuition? For the two redistributions described above, what happens to the 80-20 ratio? For each case, does the change in the ratio correspond with your intuition about what constitutes more income equality? d.)
9. b.) c.) Consider the data from Table 1. Draw the Lorenz curve consistent with the data. Be sure to indicate the line of perfect equality. Compute the Gini coefficient associated with this earnings distribution. Now suppose the distribution of earnings changes so that the earnings levels are now TABLE 2 Worker Earnings ($) 32 2 48 3 60 4 5 Total 1 80 180 400 d.) e.) .) 10. . Total camnings are still $400. Draw the new Lorenz curve. Is it clear from the Lorenz curves which distribution is more equal? Compute the Gini coefficient associated with the new earnings distribution. Consider the data from Table 1. The Lorenz curve and Gini coefficient for this data were computed in problem 2. How would the Lorenz curve change if all camings levels were multiplied by 1,000? Suppose cach worker in the economy received an additional $20 in camings. Draw the new Lorenz curve and compute the new Gini coefficient. Lorenz curves can be drawn to represent the distribution of earnings or income. In this example, since there is no nonlabor income or taxes, the two curves would be the same. In general, this would not be true. Would you expect the distribution of eamings to be more or less equal than the distribution of income? a.) b.) c.)