# MSU EC 410 Problem Set 2 Latest Oct’2015

1. Consider a country in which Y = 200 K2/5N3/5. Assume in this country they save20% of their income, population grows at 3% per year, and depreciation of capitaloccurs at 10% per year. Use the Solow model.a. Compare the effectiveness of i) a 50% increase in the savings rate (to 30%), ii) a67% decline in the population growth rate (to 1%), and iii) a 10% increase in productivity(to 220). That is, for each, give the percent by which it increases long-run averageincome (y*) and long-run average consumption (c*).b. Give one policy each that could be undertaken to accomplish i)-iii). Which policy hasthe greatest impact on long-run well-being (assuming each policy has zero costs)?2. Imagine the following goal of Lenin/Stalin at the beginning of the Soviet regimein Russia: to overtake (i.e. equal) and surpass the world’s industrialized economiesin terms of GDP per capita. To achieve this goal, the main instrument of control isthe fraction of national production that is devoted to building the nation’s productivecapacity: new machines, factories, transportation equipment, and roads (i.e. investmentas a share of GDP). The rest of national production is used for consumer items likeclothing and food. The country begins with relatively little capital, being mostly rural andnon-industrialized. Assume each of the following: – GDP per capita starts in Russia at $300/year.- The world’s industrialized economies start with GDP per capita of $5000/year. – Population growth rates are 2% everywhere in the world. – All capital depreciates at 8% per year.Assume the basic growth framework of Solow. Further assume y = 400k1/3 in Russia.a. Solve for Soviet long-run GDP per capita (y*) as a function of its savings rate.For parts b.-d., assume long-run GDP per capita equals $10,000 in the industrializedcountries, and that they are saving 10% of income.b. What fraction of national output should be devoted by the Soviet Union to buildingnew capital goods in order to overtake, i.e. equal, the industrialized nations’ GDP percapita in the long-run? What fraction is left for consumer items?c. What fraction of national output should be devoted by the Soviet Union to buildingnew capital goods in order to surpass, i.e. double, the industrialized nations’ GDP percapita in the long-run? What fraction is left for consumer items?d. In the long run, what is the ratio of Soviet GDP per capita to GDP per capita inthe industrialized countries, and what is the ratio of Soviet consumption per capita toconsumption per capita in industrialized countries if the Soviet Union achieves the goalof part b? of part c? (That is, find four ratios.)e. Comparing the outcomes of part d. of this question to the same question answeredusing the Harrod-Domar model (5e. from problem set 1), which model produces a moreoptimistic outlook for achieving, by saving and investing at high rates, the Soviet goalsof overtaking andsurpassing industrialized countries’ living standards? Remember that living standardsare best measured by consumption here.3. a. Use the Solow model to determine the a) instantaneous impact on GDP percapita, b) instantaneous impact on consumption per capita, c) impact on long-run GDPper capita, d) impact on long-run consumption per capita, e) impact on long-run GDPper capita growth rate, and f) impact on long-run GDP growth rate of a one-time andinstantaneous increase in the population Nt, through wartime refugee immigration,say. Assume the country begins at its steady state value of k* before this eventoccurs. Justify your answer by use of graph and/or equation. [Hint: this should not beconsidered a change in n, since the population continues to grow at rate n after the onetimejump; it should be modeled as a one-time jump in Nt.]b. Graph the path of yt and ct against time for the event analyzed in part a.c. Use the Harrod-Domar model to determine the a) instantaneous impact on GDP percapita, b)instantaneous impact on consumption per capita, c) impact on long-run GDP percapita growth rate, and d) impact on long-run GDP growth rate of a one-time andinstantaneous increase in the population N, through wartime refugee immigration, say.Justify your answer by use of graph and/or equation.d. Graph the path of yt and ct (or ln yt and ln ct, which are typically linear) against timefor the event analyzed in part c.4. Discuss whether, to what extent, and why the following are true or false. (Adaptedfrom Ray ch. 3, exercise 8.)a. The Harrod-Domar model predicts that a country’s long-run per capita growth ratedepends on its rate of savings, whereas the Solow model predicts that it does not.b. According to both the Harrod-Domar and Solow models, if total factor productivity (i.e.A) is higher in one country than in another, the country with the higher productivity willsee faster long-run growth in GDP per capita.c. The Solow model predicts that a change in the population growth rate affects neitherthe long-run growth rate of GDP nor the long-run growth rate of GDP per capita.d. In the Solow model, output per capita (y) goes down as capital per capita (k)increases, because of diminishing returns.e. Both the Solow and the Harrod-Domar model point to the inadequacy of GDP percapita (i.e. y) as a measure of well-being.