Suppose that there are two countries, X and Y, which differ in both their rates of investment and their population growth rates. In Country X, investment is 25% of GDP and the population grows at 0% per year. In Country Y, investment is 5% of GDP, and the population grows at 5% per year. The two countries have the same levels of productivity, A. In both countries, the rate of depreciation, 8, is 10%.
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- Suppose, a country X has a GDP level of 4, 50,000 and a growth rate of 10% in 2007(calculated at the end of the fiscal year 2007). The experts predict that the growth ofthe economy of Country X will gradually slowdown in the coming years. Moreprecisely, they foresee the following growth rates for the future:2007 – 2010 = 10%2010 – 2013 = 9%2013 – 2016 = 7.5%2016 – 2019 = 5%2019 – on = 1% Hint: The list above should be read as saying that, for instance, the growth rate fromthe end of the fiscal year 2007 until the end of 2010 will be 10 %, then from the end of2010 until the end of 2013 it will be 9% and so on. Assuming that the predictions of the experts listed above are accurate, when in thefuture will Country X’s GDP double compared to the GDP level of 2007? Consider now the more optimistic scenario in which the economy does not slow downand the current growth rate of 10% remains constant in the coming years. How longwill it take for the GDP level to double in this scenario? Express…Would you expect capital deepening to result in diminished1etmns? Why or why not? Would you expect improvements in technology to result in diminished returns? Why or why not?Why dues productivity growth in high-income economies not slow down as it runs into diminishing returns from additional investments in physical capital and human capital? Does this show one area where the theory of diminishing returns fails to apply? Why or why not?
- Exercise 2: Growth and developmentCountries 1 and 2 have the production function: Yt = AiKαt L1−αt , where country 1 hasTotal Factor Productivity (TFP) of A1 = 25, country 2 has TFP A2 = 100, and α = 0.35for both. In the two countries population is constant and there is no technological progress.Every year capital depreciates by 6% in both countries. Country 1 saves 40% of output, andcountry 2 saves 20%.a) Write down the function of production per unit of labor. Suppose the two countriesstart with an initial capital stock (per unit of labor) of 500, what are the initial income andconsumption per unit of labor in both countries?b) Determine their steady state levels of capital, income and consumption per unit oflabor.c) Determine the difference in their steady state level of income per unit of labor, andhow much of that difference is due to differences in TFP and how much is due to differencesin capital per unit of labor.d) Suppose now that country 2 suddenly has access to the country 1…e ncia.wwnorton.com b. Per capita real GDP doubled in South Korea again in only seven years, reaching $1600.00 by 1988.00. What was the average annual economic growth rate between 1981 and 1988.00? (NOTE: Round this to two places past the decimal point.) % 4th attempt 3rd attempt Okay Elizabeth 4 8 Q W E Y U P @ 23 & return A F G H J K % ! V N M .?123 .?123estion 30 A country with neither population growth nor technological progress is nitaly in the golden-rule steady state. Carefuly ilustrate this situation using a graph with output per worker, investment per worker, and depreciation per worker on the vertical axis and capital per worker on the horizontal axis. Now suppose climate change increases the depreciation rate. If the country adjusts its saving rate to reach the new golden- rule steady state, is it possible to determine how output per worker and consumption per worker in the new steady state compare to their levels in the initial steady state? Explain.
- If X grows at a rate of 9% a year, and Y grows at a rate of 14 percent per year, what is the growth rate of X/Y? a. 23% b. -5% c. 5% d. (9/14) % A nation’s population is growing 5% per year, and its total GDP is growing 1% per year. What is the annual rate of growth of GDP per capita? Feel free to round to the nearest percentage point:.5. Suppose that the Country of Eldesarrollo has a gross savings rate of 25%, a depreciation rate of 3%, an incremental capital-output ratio of 2.75, a population growth rate of 1.5% per year, and a per capita income of $1500. a. Using the Harrod-Domar (or AK) growth model, calculate the implied rate of growth of total GNI in Eldesarrollo. b. What is the implied rate of growth of GNI per capita? c. How much would the rate of gross savings have to increase to raise the growth rate of total GNI to 9%? d. Suppose that one-quarter of all investment is completely wasted in Eldesarrollo. Returning to the original numbers, what is the resulting effective ICOR, and what is the corresponding new implied growth rate of total GNI?QUESTION 2 If Z = (XY)2, and we know that the annual growth rate of Z is 3%, and the annual growth rate of X is 2%, the annual growth rate of Y is а. - 1% b. - 0.5% C. 0.5% d. 1.0%
- Consider a country with production function unction ? = 5? 1/2, where y is the output per worker and kis capital per worker. Suppose the investment in capital occurs at a rate of 35% of income perworker every period, the depreciation rate is 1.5% and the population growth rate is 2%. Use excel toplot the production function, investment line and capital depletion line with k on the x-axis (usethe attached spreadsheet to draw your graphs).a. What is the steady state level of y and k.b. Suppose TFP increases by 20%. What happens to the steady state y and k?c. Suppose the investment rate increases to 40%. What happens to the steady state y and k?3 pts in the Solow model, the economy reaches a steady-state because as capital per worker increases O savings per worker is constant, while the population growth rate is contare and the depreciation rate of capital decen, ing that the economy w gro endogenously while the population growth rate and the depreciation rate of capital are comitant implying that the economy will converge to a sady O marginal savings per worker diminishes, while the population growth rate and the depreciation rate of capital are constant implying that the economy will gro endogenously Osaving perv state. O marginal savings per worker diminishes, while the population growth rate and the depreciation rate of capital are constant, implying that the economy will converge to a steady-stateA5. Why does productivity growth in high-income economies not slow down as it runs into diminishing returns from additional investments in physical capital and human capital? Does this show one area where the theory of diminishing returns fails to apply? Why or why not? Write 30 lines for this.