HomeAs8 - Fall 2010 - Answer Key

# HomeAs8 - Fall 2010 - Answer Key - Home Assignment#8 Answer...

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Home Assignment #8: Answer Key The economy of Avataria has people in three income categories: poor, middle class, and rich. The poor ear \$500 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) Calculate the overall saving rate in Avataria if 20% of the people are poor and 50% are in the middle class. Answer: Let’s denote the number of people by N. Then Group # people Group Income Group Savings Poor 0.2N 100N 0 Middle 0.5N 1000N 250N Rich 0.3N 3000N 600N Total N 4100N 850N The saving rate here is s = (Total Savings)/(Total Income) = 850N/4100N = 850/4100 = .207 or 20.7% (b) Suppose that all growth occurs by moving people from the poor category to the middle-class category. Will the saving rate rise over time or fall? Answer: Let’s denote the number of people by N. Group # people Group Income Group Savings Poor 0 0 0 Middle 0.7N 1400N 350N Rich 0.3N 3000N 600N Total N 4400N 950N The saving rate here is s = (Total Savings)/(Total Income) = 950N/4400N = 950/4400 = .216 or 21.6%. It rises over time.

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