# answerkey2 - ECON 202 SPRING 2008 Malhar Nabar Answer Key 2...

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ECON 202, SPRING 2008 Malhar Nabar Answer Key # 2 Posted: February 29 Note : There are six questions in total. You may consult with other students, but please turn in your own individual answer sheet with the names of all group members listed on the front page. 1. Solow Model: Theory Country C and Country D have the following production function Y = K 1 3 L 2 3 The two countries have identical growth rates for the labor force and share an identical depre- ciation rate of capital, but country C invests 20% of output per year while Country D invests 5% of output per year. Suppose the countries have reached their steady states. Calculate the following steady state ratios: k C k D and y C y D The production function in per worker terms y = k 1 = 3 The capital accumulation equation is k = sk 1 = 3 ( n + ) k In steady state, k = 0 and the steady state level of the per worker capital stock k s ( k ) 1 = 3 ( n + ) k = 0 ) k = s n + ± 1 1 ± 1 = 3 = s n + ± 3 2 This general formula applies to both countries (since they share the same aggregate production function). Their steady state ratio k C k D therefore is k C k D = s c s D ± 3 2 = & 0 : 2 0 : 05 ± 3 2 = 4 3 2 = 8 And their steady state ratio y C y D follows as y C y D = k C k D ± 1 = 3 = 8 1 = 3 = 2 1

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Solow Model with technological progress Chapter 8, problems and applications, #2. We are given the following data Capital Share of GDP ( ) = 0.3 Growth rate of Output (n+g) = 0.03 Depreciation rate ( ± ) = 0.04 a. In the steady state, the investment per worker is exactly equal to the break-even investment per worker (using the hint provided): s e y = ( n + g + ± ) e k Also note that e k e y = K el Y el = K Y = 2 : 5 Substituting in the relevant values from the above table, we see that s = ( n + g + ± ) e k e y = 0 : 175 Note that although the book refers to this as the saving rate what the author really has in mind is the investment rate. In a closed economy it doesn±t matter since saving and investment are equal. But it is more correct to talk about the investment rate in the Solow Model rather than the saving rate. This is the constant fraction of output that±s invested in each time period. b. Recall that the capital share of income is given by = MPK K Y So from this MPK = ( K=Y ) = 0 : 12 c. In the golden rule steady state, MPK GR = ( n + g + ± ) = 0 : 07 Comparing with (b) we see that current MPK > MPK GR . Due to diminishing marginal returns to capital, we can conclude that the current steady state capital per e²ective worker is lower than the golden rule steady capital per e²ective worker (i.e. we are to the left of the steady state). 2
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