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# 4805 - 14.452 Economic Growth Problem Set 1 Due date...

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14.452: Economic Growth Problem Set 1 Due date: November 6, 2009 in Recitation. Exercise 1: growth model where the aggregate production function is F ( K;L;Z ) = L K ± Z 1 ± ; where Z + ± < 1 , capital depreciates at the rate ² , and there is an exogenous saving rate of s . 1. First suppose that there is no population growth. Find the steady-state capital-labor ratio and the steady-state output level. Prove that the steady state is unique and globally stable. 2. Now suppose that there is population growth at the rate n , that is, _ L=L = n . What happens to the capital-labor ratio and output level as t ! 1 ? What happens to returns to land and the wage rate as t ! 1 ? 3. Would you expect the population growth rate n or the saving rate s to change over time in this economy? If so, how? Exercise 2: Consider the discrete-time Solow growth model with constant population growth at the rate n , no technological change and depreciation rate of capital equal to ² . Assume that the saving rate is a function of the capital- labor ratio, thus given by s ( k ) . 1. Suppose that f ( k ) = Ak and s ( k ) = s 0 k 1 1 . Show that if A + ² n = 2 , then for any k (0) 2 (0 ;As 0 = (1 + n )) , the economy immediately settles into an asymptotic cycle and continuously ±uctuates between

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4805 - 14.452 Economic Growth Problem Set 1 Due date...

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