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Ans10154a - Economics 154a Spring 2005 Intermediate Macroeconomics Problem Set 10 Answer Key 1 This problem studies a version of the Solow growth

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Economics 154a, Spring 2005 Intermediate Macroeconomics Problem Set 10: Answer Key April 25, 2005 1. This problem studies a version of the Solow growth model developed in Chapter 6 of the textbook. Suppose that aggregate output in period t is given by: Y t = K 0 . 3 t N 0 . 7 ... (a) Calculate the steady-state capital stock implied by the law of motion for ag- gregate capital. Calculate the level of steady-state consumption implied by the steady-state capital stock. .. ANSWER : The steady state capital stock is the value for capital K * such that K * = (1 - d ) K * + sY ( K * ). Note that we have assumed N t = N = 1, so we simply plug it in: K * = (1 - d ) K * + sY ( K * ) = (1 - 0 . 1) K * + 0 . 2( K * ) 0 . 3 (1) 0 . 7 K * (0 . 1) = 0 . 2( K * ) 0 . 3 ( K * ) 0 . 7 = 0 . 2 / 0 . 1 K * = (0 . 2 / 0 . 1) 1 / 0 . 7 = 2 . 69 To obtain consumption, simply find which part of output (the steady state output given by steady state capital K * ) is not saved but consumed: C * = Y * - I * = (1 - s ) Y * = 0 . 8 × 2 . 69 0 . 3 = 0 . 8 × 1 . 34 = 1 . 07 (b) Suppose that s increases to 0.25. What is the new steady-state capital stock? What is the new level of steady-state consumption? ANSWER : Clearly, substituting 0.25 instead of 0.2 in the equation above gives: K * = 2 . 5 1 / 0 . 7 = 3 . 70 C * = 0 . 75 × 3 . 70 0 . 3 = 0 . 75 × 1 . 48 = 1 . 11 1
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(c) Describe in qualitative terms the dynamic behavior of the capital stock after the increase in the savings rate (assume that the economy is in a steady state before the increase). Support your answer using an appropriate diagram. ANSWER : Qualitatively, when the rate of saving increases, there is less output available for consumption and more for investment out of the original output, Y ( K * ), so that consumption falls first, while capital starts growing until it reaches its new steady state ˆ K * . Consumption in this new steady state might be above or
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This homework help was uploaded on 04/06/2008 for the course ECON 154 taught by Professor Bjoernbruegemann during the Spring '07 term at Yale.

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Ans10154a - Economics 154a Spring 2005 Intermediate Macroeconomics Problem Set 10 Answer Key 1 This problem studies a version of the Solow growth

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