# PS3 - Problem Set 3 Solutions Chapter 7#2 a The production...

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Problem Set # 3 Solutions Chapter 7 #2 a) The production function in the Solow growth model is Y = f(K,L), or expressed in terms of output per worker, y = f(k). If a war reduces the labor force through casualties, the L falls but Capital-labor ratio k = K/L rises. The production function tells us that total output falls because there are fewer workers. Output per worker increases, however, since each worker has more capital. b) The reduction in the labor force means that the capital stock per worker is higher after the war. Therefore, if the economy were in a steady state prior to the war, then after the war the economy has a capital stock that is higher than the steady-state level. This is shown in the figure below as an increase in capital per worker from k 1 to k 2 . As the economy returns to the steady state, the capital stock per worker falls from k 2 back to k 1 , so output per worker also falls. Chapter 7 #4 Suppose the economy begins with an initial steady-state capital stock below the Golden Rule level. The immediate effect of devoting a larger share of national output to investment is that the economy devotes a smaller share to consumption; that is, “living standards” as measured by consumption fall. The higher investment rate means that the capital stock increases more quickly, so the growth rates of output and output per worker rise. The productivity of workers is the average amount produced by each worker – that is, output per worker. So productivity growth rises. Hence, the immediate effect is that living standards fall but productivity growth rises. k = K/L y = Y/L y = f(k) sy (n+d)k k 1 k 2 y 2 y 1

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In the new steady state, output grows at rate n+g, while output per worker grows at rate g. This means that in the steady state, productivity growth is independent of the rate of investment. Since we begin with an initial steady-state capital stock below the Golden rule level, the higher investment rate means that the new steady state has a higher level of consumption, so living standards are higher Thus, an increase in the investment rate increases the productivity growth rate in the short run but
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## This note was uploaded on 10/25/2010 for the course MBA GloEco taught by Professor N.m. during the Spring '10 term at Institute of Business Administration.

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PS3 - Problem Set 3 Solutions Chapter 7#2 a The production...

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