Welfare Economics Final Assignment

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Welfare Economics

Final Assignment

Problem 1. (3 marks) Let IG denote the Gini coe cient. Choose below all correct explanations of inequality measurement for income distributions x = (x1 , . . . , x5), y = (y1 , . . . , y5) for 5 persons.

(a) If x = (10, 30, 30, 30, 100), then IG(x) = 0.36.

(b) If x = (2, 2, 2, 2, 2) and y = (3, 3, 3, 3, 3), then IG(x) < IG(y). (c) If x = (1, 3, 3, 3, 10), then IG(x) = 0.3. (d) If x = (20, 30, 30, 30, 90), then IG(x) = 0.36. (e) If x = (10, 30, 30, 30, 100) and y = (10, 20, 30, 30, 30), then y Lorenz-dominates x. (f) If x = (2, 2, 2, 2, 2) and y = (3, 3, 3, 3, 3), then y Lorenz-dominates x. Problem 2. (3 marks) Let IT , IMLD, and ICV denote the Theil index, the mean logarithmic deviation, and the coe cient of variation, respectively. Choose below all correct explanations of inequality measure- ment for income distributions x = (x1 , . . . , x3), y = (y1 , . . . , y3) for 3 persons. (a) If x = (8, 12, 16) and y = (1, 2, 6), then IT(x) < IT(y). (b) If x = (8, 12, 16) and y = (1, 2, 6), then ICV(x) > ICV(y).

(c) If x = (8, 12, 16) and y = (1, 2, 6), then IMLD(x) < IMLD(y). (d) If x = (2, 8, 14) and y = (1, 2, 6), then IMLD(x) > IMLD(y).

(e) If x = (2, 8, 14) and y = (1, 2, 6), then y Lorenz-dominates x.

Problem 3. (3 marks) Let IG , IA , WG, and WA denote the Gini coe cient, the Atkinson measure asso- ciated with β, the Gini SWF, and the Atkinson SWF associated with β, respectively. Choose below all correct explanations of inequality measurement and social welfare measurement of income distributions x = (x1 , . . . , xn) and y = (y1 , . . . , yn).

(a) If x = (x1 , x2 , x3) = (6, 8, 18), then the EDEI of x according to WG is 10.

(b) If x = (1, 3, 3, 3, 10), then the EDEI of x according to WG is 7.2.

(c) If x = (2, 2, 2, 2, 2), then the EDEI of x according to WA is 1.

(d) Suppose that IA is associated with β = 0. If IMLD(x) < IMLD(y), then IA(x) < IA(y). (e) If the EDEI of x = (x1 , . . . , xn) according to WA(x) is 100 and the mean income is μ(x) = 300, then IA(x) = . Problem 4. (5 marks) Suppose that you made a cross-national comparison of income inequality between countries A and B, and then, you obtained the result that IG(x) < IG(y) and IMLD(x) > IMLD(y), where (i) IG and IMLD denote the Gini coe cient and the mean logarithmic deviation, and (ii) x is the income distribution of country A and y is that of country B. In this case, you can immediately conclude that the Lorenz curve of the distribution x of country A and that of the distribution y of country B intersect. Explain why.

Problem 5. (7 marks) Using PovcalNet, make the gure of the Lorenz curves for Namibia and Mada- gascar in 2010. Then,

(1) Report the gure you made; strongly recommend ”saving the gure as picture” (e.g., as pdf) rst, then, inserting it to your answer sheet.

(2) Report (i) the Gini coe cient, (ii) the mean logarithmic deviation, and (iii) the Atkinson measure associated with β = 0 for each country. You can summarize the results using a table if you prefer; when reporting the table, again, strongly recommend ”saving the table as picture” (e.g., as pdf) rst, then, inserting it to your answer sheet.

Problem 6. (7 marks) Using PovcalNet, get the poverty data of Bangladesh in 2000, 2010, and 2016. Then,

(1) Report (i) the headcount ratio, (ii) the poverty gap measure, (iii) the squared poverty gap measure, (iv) the Watts measure, and (v) the income gap ratio for each year. You can summarize the results using a table if you prefer; when reporting the table, again, strongly recommend ”saving the table as picture” (e.g., as pdf) rst, then, inserting it to your answer sheet.

(2) Report inequality among the poor using (i) the coe cient of variation, (ii) the mean logarithmic deviation, and (iii) the Atkinson measure associated with β = 0 for each year. You can summarize the results using a table if you prefer.

(3) Discuss how poverty and inequality among the poor in Bangladesh changed over the three reference years.

Problem 7. (12 marks) Using PovcalNet, work on any “one” (not all) of the following three tasks:

(i) Make cross-national comparisons of inequality of “consumption expenditure” between at least three countries in 2016; you can freely choose the comparison countries

(ii) Make cross-national comparisons of poverty and inequality among the poor of “consumption ex- penditure” between at least three countries in 2016; you can freely choose the comparison countries

(iii) Choose a single country other than Bangladesh, make an inter-temporal comparison of poverty and

inequality among the poor in “consumption expenditure” over at least three reference years. Discussion about cross-national/inter-temporal di erences in inequality/poverty must be provided.