Suppose that in country A the “bottom” 40% of the population receives 10% of the country’s income. The “top” 60% receives the remaining 90% of the country’s income. What is the Gini index in country A? Now suppose that in country B the bottom 20% of people receives 5% of the country’s income, and the top 20% of people receives 55% of the country’s income. What is the Gini index in country B? (a) Which country has greater inequality? Graph the Lorenz curves (connecting points using straight lines) and show your algebra. (b) Would your answer change if country A was ten times richer than country B (i.e., total income in country B equaled ten times the total income in country A)? Explain. (c) Some people argue that the difference between the maximum and minimum income (i.e., the range: ymax – ymin) in a given country would be a good measure of relative inequality. However, this principle violates one of the four principles of inequality we discussed in class. Which one? Why? Hint: consider four distinct incomes (y1 < y2 < y3 < y4) and a redistribution of income among the two middle incomes. 4 Principles discussed in class: 1. anonymity: names do not matter; y1 a > y2 b > y3 c same inequality as y1 c > y2 b > y3 a where incomes y1; y2; y3 unchanged but owner changed 2. population: cloning entire population =) same inequality, i.e., (ya; yb; yc ) same inequality as (ya; ya; yb; yb; yc ; yc ) 3. relative income: (ya; yb; yc ) same inequality as (lambda ya; lambda yb; lambda yc ) for all 4. Dalton(-Pigou) transfer rule: inequality must increase if ya greater than or equal to yb and b gives money to a