ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKa L¹-a 1. Use the production function to compute output per capita, y = Y/L, as a function of capital per person, k = K/L, A and a. 2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps. Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 8 = 0.15 and n = 0.04 respectively. You do not know the value of A or a. 3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k, A and a. 4. In the steady state, the growth rate of capital is zero. Using the parameters assumed above, find the steady-state level of capital per person, k* as a function of A and a. 5. Calculate GDP per capita at the steady state, as a function of A and a. 6. Imagine that this country is in its steady state, so its capital stock is k*. Imagine that the country gives away one unit of capital to the world bank (i.e., the capital stock is now suddenly k*-1). What is happening immediately to the growth rate after the donation? Why? What will the capital stock be in the long run? Explain. 5.2 clarification: Derive the fundamental equation of the Solow-Swan model. Please show all the steps. 5.3 clarification: imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 6 = 0.15 and n = 0.04 respectively. You do not know the value of A or a. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k, A and a. In other words, The answer to Problem 5.2 should be in terms of s, d, n, k, A, and a.
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Transcribed Image Text:Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKa L¹-a 1. Use the production function to compute output per capita, y = Y/L, as a function of capital per person, k = K/L, A and a. 2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps. Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 8 = 0.15 and n = 0.04 respectively. You do not know the value of A or a. 3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k, A and a. 4. In the steady state, the growth rate of capital is zero. Using the parameters assumed above, find the steady-state level of capital per person, k* as a function of A and a. 5. Calculate GDP per capita at the steady state, as a function of A and a. 6. Imagine that this country is in its steady state, so its capital stock is k*. Imagine that the country gives away one unit of capital to the world bank (i.e., the capital stock is now suddenly k*-1). What is happening immediately to the growth rate after the donation? Why? What will the capital stock be in the long run? Explain. 5.2 clarification: Derive the fundamental equation of the Solow-Swan model. Please show all the steps. 5.3 clarification: imagine that the savings, depreciation, and population growth rates take the values s = 0.3, 6 = 0.15 and n = 0.04 respectively. You do not know the value of A or a. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k, A and a. In other words, The answer to Problem 5.2 should be in terms of s, d, n, k, A, and a.
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Step 1: Define solow swan model
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Step 2: Solve for per capita output and fundamental equation
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