Answer the following questions briefly and clearly.
1) (20 marks) Calculate the Gini coefficient and the coefficient of variation for the following income distributions. For each distribution, the first set of numbers represents the various incomes and the second set of numbers the number of people earning each of these incomes.
(200, 400, 600, 800); (125, 25, 125, 50) (100, 200, 300, 400); (50, 15, 95, 15) (100, 200, 300, 400); (50, 35, 55, 35)
Compare briefly the different distributions.
2) The economy of Pordosol has people in three income categories: poor, middle class, and rich. The poor earn £400 per year and have to spend it all to meet their consumption needs. The middle class earn £2,000 per year, of which £1,500 is spent and the rest saved. The rich earn £10,000 per year, and consume 80% of it, saving the rest.
(a) (20 marks) Calculate the overall savings rate in Pordosol if 20% of the people are poor and 50% are in the middle class.
(b) (20 marks) Suppose that all growth occurs by moving people from the poor category to the middle-class category. Will the savings rate rise over time or fall? Using the Harrod-Domar
model and assuming that population growth is zero and all other variables are exogenous, predict whether the resulting growth rate will rise or fall over time.
(c) (20 marks) In the same setting of b), explain what happens to the growth rate if some people move from the middle class into the rich category, everything else equal.
(d) (20 marks) Using the Solow model, explain how the changes in b) and c) affect growth and per capita income in the short and long-run