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Problem_Set_2_Solutions - Economics W3213 Spring 2010 Bruce...

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Economics W3213 Spring 2010 Bruce Preston Problem Set 2 Solutions Textbook Questions 1. Chapter 6: Exercise 4, 5, 8 and 9 (for practice only): Solutions at the end of this document. Short Answer Questions Indicate whether you think the following statements are true, false or uncertain. Support your answer by giving all necessary reasoning and calculations. 1. A Solow model without increasing returns to scale in production can explain the average growth rates observed in Sub-Saharan Africa over recent decades. Solution: False The answer to this question is based on our discussion of the article by Sachs et. al. The central hypothesis of the paper was that countries could become stuck in a poverty trap. If capital-labor ratios are below some threshold level they may experience negative growth. Three mechanisms that might generate negative growth in the Solow model are: i) increasing returns to scale in production over some range of capital-labor ratio; ii) savings rates that varied with the level of capital so that savings are not a constant proportion of income. In particular, savings are negligible for the poor, but increase at higher income levels; and ii) extremely high fertility rates for poor countries. Each of these mechanisms had the property that they generated three steady states in the Solow model. Two are familiar to the standard model: capital holdings of zero and the high steady state to which capital holdings are ultimately predicted to converge. With any of the above mechanisms a third steady state exists between zero and the high steady-state levels of capital. This was called the threshold level of capital or the poverty trap level of capital. Countries that have capital holdings below this level experience negative growth because saving and investment are too low relative to the required investment to maintain a given capital stock. Hence the answer is false because increasing returns are not essential to this outcome. For a diagrammatic treatment please see class notes or the Sachs article. 2. In the Romer model, changes in educational policies, which lead to a greater fraction of the labor force working in the sector producing °nal goods, will lead to higher economic growth. 1
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Solution: False This is directly from Chapter 6. page 141. The growth rate in the Romer model is determined by the equation ° A t A t = ± z ± l ± N = ± g: Educational policies that tend to increase the fraction of the labor force working in the sector producing °nal good implies an increase in 1 ° ± l and therefore a fall in ± l . The growth rate must fall in the Romer economy as labor resources are moved out of the ideas producing sector into the °nal goods sector. 3. Consider a Solow model with Cobb-Douglas production function Y t = AK ° t L 1 ° ° t where 0 < ° < 1 . Cross-country di/erences in per capita incomes between rich and poor countries can be shown to depend only upon the di/erence in total factor productivities and the di/erence in saving/investment rates (assuming identical production functions, population growth rates, and depreciation rates.) A model in which the elasticity of out-
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