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##### Econ 490 ? Midterm (Topics in Economic Growth)

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Question;Econ 490 ? Topics in Economic GrowthSpring 2014Practice Questions ? MIDTERM I1) A country is described by the Solow Model, with a production function of y=k 1/2. Suppose that k is equal to 400. The fraction of output invested is 50%. The depreciation rate is 5%. Is the country at its steady-state level of output per worker, above the steady state, or below the steady state? Show how you reached your conclusion.;2) The following tables show data on investment rates and output per worker in for three pairs of countries. For each country pair, calculate the ratio of GDP per worker in steady state that is predicted by the Solow model, assuming that all countries have the same values of A and? and that the value of? is 1/3. Then calculate the actual ratio of GDP per worker for each pair of countries. For which pairs of countries does the Solow model do a good job of predicting relative income? For which pair does the Solow model do a poor job? Why do you think it?s happening?a) Country Thailand Boliviab) Country Nigeria Turkeyc) Country Japan New Zealand;Investment Rate (Average 1975-2009)35.2%12.6%;Output per Worker in 2009;Investment Rate(Average 1975-2009)6.4%16.3%;Output per Worker in 2009;Investment Rate(Average 1975-2009)29.9%19.6%;Output per Worker in 2009;$13,279$8,202;$6,064$29,699;$57,929$49,837;3) Country X and Country Y have the same level of output per worker. They also have the same values for the rate of depreciation,?, and the measure of productivity, A. In country X output per worker is growing, whereas in Country Y it is falling. What can you say about the two countries? rates of investment?;4) In a country the production function is y=k 1/2. The fraction of output invested,?, is 0.25. The depreciation rate,?, is 0.05. a) What are the steady-state levels of capital per worker, k, and output per worker, y?b) In year 1, the level of capital per worker is 16. In a table such as the following on, show capital and output change over time (The beginning is filled in as a demonstration).;Continue this table up to year 8.YearCapitalOutput (y=k1/2) Investment(?y) Depreciation(?k)Change inCapital Stock116410.80.2216.2;c) Calculate the growth rate of output between 1 and 2d) Calculate the growth rate of output between 7 and 8e) Comparing your answers from parts c and d, what can you conclude about the speed of output growth as a country approaches its steady state?5) In a country, output is produced with labor and physical capital. The production function in per-worker terms is y = k1/2. The depreciation rate is 2%. The investment rate (?) is determined as follows:? = 0.20 if y? 10? = 0.40 if y >10Draw a diagram showing the steady state(s) of this model. Calculate the values of any steady state levels of k and y. Also, indicate on the diagram and describe briefly in words how the levels of y and k behave outside the steady state. Comment briefly on the stability of the steady state(s);6) Suppose that there are two countries, X and Y, that differ in both their rates of investment and their population growth rates. In Country X, investment is 20% of GDP and the population grows at 0% per year. In country Y, investment is 5% of GDP, and the population grows at 4% per year. The two countries have the same levels of productivity, A. In both countries, the rate of depreciation,?, is 5%. Use the Solow model to calculate the ratio of their steady-statelevels of income per capita, assuming that? = 1/3.;7) Consider the Solow model with population growth, as presented in the text. Assume that population can grow at two different rates n1 and n2, where n1 > n2. The population growth rate depends on the level of output per capita (and therefore the level of capital per capita). Specifically, population grows to rate n1 when k?f(k) and that (n2 +?) k

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