10. Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for conve- nience, and that there is labor-augmenting tech- nological progress, with a production function Y = F(K, bN), where b denotes the number of units of "human capital" per worker, and bN is “efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1+f)b, where f is the growth rate in human capital. (a) Show that the long-run equilibrium has the K property that k** what rate does aggregate output, aggregate consumption, aggregate investment, and per capita income grow in this steady state? Explain. is a constant. At bN

10. Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for conve- nience, and that there is labor-augmenting tech- nological progress, with a production function Y = F(K, bN), where b denotes the number of units of "human capital" per worker, and bN is “efficiency units" of labor. Letting b' denote future human capital per worker, assume that b' = (1+f)b, where f is the growth rate in human capital. (a) Show that the long-run equilibrium has the K property that k** what rate does aggregate output, aggregate consumption, aggregate investment, and per capita income grow in this steady state? Explain. is a constant. At bN

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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9. Consider our graph of the basic Solow growth model. steady state dk y=F(() F() (-7' in LF equilibrium) On the graph above: y represents real output (or income) per worker; y-F(k) is the production function; is the capital stock per worker; s is the savings rate; 8 is the rate of depreciation of capital; 'i' represents business investment (purchases of capital) per worker); 'LF' stands for Loanable Funds. (For purposed of intuition, think of capital as 'machines.) If we started out with a capital (per worker) stock higher than the steady-state stock (above), we would expect to see which of the following happen over time? Positive growth rates while the capital stock increases. Positive growth rates while the capital stock stays less than the steady-state level. Negative growth rates while the capital stock increases. Positive growth rates while the capital stock decreases. Negative growth rates while the capital stock decreases.
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In the Solow growth model without population growth and technological progress, consumption per worker will be maximized in the steady state when: (1) Output per worker is maximized. (ii) Investment per worker is maximized. (iii) The marginal product of capital equals the depreciation rate. O a. (i), (ii), and (ii) O b. Only (iii) O c. Only (ii) Od. Only (1)
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Consider the Solow growth model with no population growth and no tech- nology growth, i.e., n = x = 0. Output is created by a Cobb-Douglas pro- duction function combining Labor, Lt, and capital, Kt, such that output Yt is given by Y₁ = A+ KL-a = = 2. Recall that, without population growth, Lt = Lo and assume that Lo Furthermore, recall that, without technology growth, At Ao and assume that A0 = 1. Assume that the savings rate is s = 0.4, the depreciation rate is = 0.15, and that the capital share is a = 0.3. A lower case letter denotes a variable in per capita. For example, kt = K₁/Lt. In the following questions, choose the closest number. What is the value of kss? (a) 40.6 (b) 4.1 c) 2.8 (d) 28
Consider the Solow growth model with no population growth and no tech- nology growth, i.e., n = x = 0. Output is created by a Cobb-Douglas pro- duction function combining Labor, Lt, and capital, Kt, such that output Yt is given by Y₁ = A+ KL₁-a = = Ao and Recall that, without population growth, Lt Lo and assume that Lo = 10. Furthermore, recall that, without technology growth, At assume that A0 = 2. Assume that the savings rate is s = 0.2, the depre- ciation rate is 8 = 0.1, and that the capital share is a = 0.3. A lower case letter denotes a variable in per capita. For example, kt= Kt/Lt. In the following questions, choose the closest number. What is the value of kss? (a) 72 (b) 27 (c) 7.2 (d) 2.7 What is the value of Yss for the Economy described in Question 7 (a) 36 (b) 3.6 (c) 2.7 (d) 27 Suppose that the economy described in Question 7 economy starts with Ко = 10. Choose the correct one for the change in capital over time. (a) fall (b) grow (c) Once dropped, it grows (d) unchange…