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• (ii) What is the relation between Kt and He? Use this relation to write down total output as a function of Ktonly. Imagine that the number of people in this economy, Nt, is different from the number of workers because some people do not work. Let l; Lt - be the number of workers per capita (the fraction of the population that works). Let y, = be output per capita and Yt %3D Nt Nt Kt k, = - be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. Nt (iii) Using the "effective production function" you derived in (b), write down output per capita, yt, as a function of capital per capita, kt, labor per capita, lt, the level of population N+, and the level of technology, A. Following Solow and Swan, assume there is no government and no net exports, that the depreciation rate of capital is the constant 8 > 0 and the savings rate is constant 0 < s<1. • (iv) DERIVE the fundamental equation of Solow-Swan. How does the growth rate of capital depend on employment per person, le? Explain intuitively.

• (ii) What is the relation between Kt and He? Use this relation to write down total output as a function of Ktonly. Imagine that the number of people in this economy, Nt, is different from the number of workers because some people do not work. Let l; Lt - be the number of workers per capita (the fraction of the population that works). Let y, = be output per capita and Yt %3D Nt Nt Kt k, = - be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. Nt (iii) Using the "effective production function" you derived in (b), write down output per capita, yt, as a function of capital per capita, kt, labor per capita, lt, the level of population N+, and the level of technology, A. Following Solow and Swan, assume there is no government and no net exports, that the depreciation rate of capital is the constant 8 > 0 and the savings rate is constant 0 < s<1. • (iv) DERIVE the fundamental equation of Solow-Swan. How does the growth rate of capital depend on employment per person, le? Explain intuitively.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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- **(ii)** What is the relation between \( K_t \) and \( H_t \)? Use this relation to write down total output as a function of \( K_t \) only. Imagine that the number of people in this economy, \( N_t \), is different from the number of workers because some people do not work. Let \( l_t = \frac{L_t}{N_t} \) be the number of workers per capita (the fraction of the population that works). Let \( y_t = \frac{Y_t}{N_t} \) be output per capita and \( k_t = \frac{K_t}{N_t} \) be capital per capita. Finally, let \( n \) be the rate of population growth and \( \gamma_L \) be the growth rate of labor. - **(iii)** Using the “effective production function” you derived in (b), write down output per capita, \( y_t \), as a function of capital per capita, \( k_t \), labor per capita, \( l_t \), the level of population \( N_t \), and the level of technology, \( A \). Following Solow and Swan, assume there is no government and no net exports, that the depreciation rate of capital is the constant \( \delta > 0 \) and the savings rate is constant \( 0 < s < 1 \). - **(iv)** DERIVE the fundamental equation of Solow-Swan. How does the growth rate of capital depend on employment per person, \( l_t \)? Explain intuitively. - **(v)** Does the equation of the growth rate of capital depend on the growth rate of population, \( n \), or the growth rate of employment? Explain intuitively.
Transcribed Image Text:- **(ii)** What is the relation between \( K_t \) and \( H_t \)? Use this relation to write down total output as a function of \( K_t \) only. Imagine that the number of people in this economy, \( N_t \), is different from the number of workers because some people do not work. Let \( l_t = \frac{L_t}{N_t} \) be the number of workers per capita (the fraction of the population that works). Let \( y_t = \frac{Y_t}{N_t} \) be output per capita and \( k_t = \frac{K_t}{N_t} \) be capital per capita. Finally, let \( n \) be the rate of population growth and \( \gamma_L \) be the growth rate of labor. - **(iii)** Using the “effective production function” you derived in (b), write down output per capita, \( y_t \), as a function of capital per capita, \( k_t \), labor per capita, \( l_t \), the level of population \( N_t \), and the level of technology, \( A \). Following Solow and Swan, assume there is no government and no net exports, that the depreciation rate of capital is the constant \( \delta > 0 \) and the savings rate is constant \( 0 < s < 1 \). - **(iv)** DERIVE the fundamental equation of Solow-Swan. How does the growth rate of capital depend on employment per person, \( l_t \)? Explain intuitively. - **(v)** Does the equation of the growth rate of capital depend on the growth rate of population, \( n \), or the growth rate of employment? Explain intuitively.
**Production Function and Investment in Human Capital** **Production Function:** Consider the following production function: \[ Y_t = AK_t^\alpha H_t^{1-\alpha} L_t^\beta \] where \( K_t \) is capital, \( H_t \) is human capital, \( L_t \) is the amount of workers, and \( A \) is the (constant) level of technology. - **(i) Analysis:** Does this production function satisfy all the neoclassical properties? Discuss the meaning of each property intuitively. **Investment in Human Capital:** Imagine that parents invest in the human capital of their children up to the point where the marginal product of physical capital, \( K_t \), is equal to the marginal product of human capital, \( H_t \).
Transcribed Image Text:**Production Function and Investment in Human Capital** **Production Function:** Consider the following production function: \[ Y_t = AK_t^\alpha H_t^{1-\alpha} L_t^\beta \] where \( K_t \) is capital, \( H_t \) is human capital, \( L_t \) is the amount of workers, and \( A \) is the (constant) level of technology. - **(i) Analysis:** Does this production function satisfy all the neoclassical properties? Discuss the meaning of each property intuitively. **Investment in Human Capital:** Imagine that parents invest in the human capital of their children up to the point where the marginal product of physical capital, \( K_t \), is equal to the marginal product of human capital, \( H_t \).
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