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Unformatted text preview: ECON 202, SPRING 2009 Malhar Nabar Answer Key # 6 Posted: May 12 Note: This assignment also doubles up as a review for the &nal exam. It has six questions in total, covering material from the start of the semester to the most recent topics covered in class. 1. Solow Model: Theory An economy is described by the following aggregate production function Y = K : 5 ( el ) : 5 The depreciation rate & on capital is 0.03. The growth rate of the labor force n is 0.01. The growth rate of technology g is 0.01. The saving rate is 10 per cent of GDP. a. Please write down the "intensive form" of the production (i.e. the production function in per e/ective worker terms). e y = Y el = K : 5 ( el ) : 5 el = K : 5 el : 5 = e k : 5 ) e y = e k : 5 b. Provide the equation that describes the accumulation of capital per e/ective worker in this economy. The capital accumulation equation in per e/ective worker terms is & e k = s e k : 5 & ( n + g + & ) e k & e k = 0 : 1 e k : 5 & (0 : 05) e k c. Calculate the steady state levels of capital per e/ective worker and output per e/ective worker. In steady state the accumulation equation above becomes: & e k = ) : 1 e k : 5 ss & (0 : 05) e k ss = 0 ) e k : 5 ss = : 1 : 05 = 2 = ) e k ss = 2 2 = 4 Substituting this value into the production function: e y ss = e k : 5 ss = 2 1 d. Calculate the steady state aggregate capital to aggregate output ( K=Y ) ratio. The steady state aggregate capital output ratio is given by K Y = e k ( el ) e y ( el ) = e k ss e y ss = 4 2 = 2 e. Suppose that the saving rate is raised to 15% of GDP. Calculate the new ( K=Y ) ratio. If the saving rate is raised to 15% of GDP, the steady state e k will be e k ss = & s ( n + g + & ) ¡ 2 = & : 15 : 05 ¡ 2 = 9 e y ss = e k : 5 ss = 9 : 5 = 3 The (K/Y) ratio is: K Y = e k ss e y ss = 9 3 = 3 2. Policy analysis using the Solow Model You are the newly appointed Chief Economic Adviser to the President. The President is con cerned that living standards have begun to stagnate and wishes to raise both the level and the growth rate of output per worker in the economy. Your brief is to suggest policy measures to accomplish the two objectives. You ask your sta/ for input and they come back to you with the following recommendation: "An increase in the saving rate will increase the equilibrium capitaloutput ratio and so increase both output per worker and the rate of economic growth in both the short run and the long run"....
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This note was uploaded on 06/15/2010 for the course ECON 202 taught by Professor Nabar during the Spring '08 term at Wellesley College.
 Spring '08
 Nabar

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