Please refer to the clarification of specific questions Consider the Solow-Swan model of growth. Imagine that the production function isY= AKa L¹-a1. Use the production function to compute output per capita, y = Y/L, as a function of capitalper 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 thevalues 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 ofcapital 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 thecountry gives away one unit of capital to the world bank (i.e., the capital stock is nowsuddenly 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 thesteps.5.3 clarification: imagine that the savings, depreciation, and population growth rates take thevalues 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 tocompute the growth rate of capital per person as afunction 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.

The Solow-Swan model, also known as the Solow growth model or the neoclassical growth model, is a…

Consider the Solow-Swan model of growth. Imagine that the production function is Y = AK¤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.

Consider the Solow-Swan model of growth. Imagine that the production function is Y = AK¤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.

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter20: Economic Growth In The Global Economy

Section: Chapter Questions

Problem 5P

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Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKªL²-a 1. Use the production function to compute output per capita, y= Y /L, as a function of capital per person, k = K/L. 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= 0.1 and n =0.01. You do not know the value of 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.
Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKªL²-a 1. Use the production function to compute output per capita, y = Y /L, as a function of capital per person, k = K/L. 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= 0.1 and n =0.01. You do not know the value of 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. 4. In the steady-state, the growth rate of capital is zero. Using the parameters assumed above, find the steady-state level of the capital stock, k_. 5. Calculate GDP per capita at the steady state. 6. Imagine that this country is in its steady state so its capital stock is k_. Imagine that the country receives a gift of one unit of capital from the world bank (so, suddenly, the capital stock is k_+1). Can you say…
Production function is given by Y= (1/2)K^a(AN)^(1-a), where a=2/3. The rate of depreciation of capital is equal to 15 percent, the rate of technological progress is equal to 3 percent, and the rate of population growth is equal to 2 percent. The economy was in the steady state at time tand the level of technology was equal to A=80. Use the Solow growth model to answer the following questions. 1. If the saving rate s=80 percent, the steady state level of output per unit of effective labor at time tis equal to ... 2. If the saving rate s=80 percent, the steady state level of consumption per unit of effective labor at time tis equal to ... 3. If the saving rate s=80 percent, the steady state level of consumption per worker at time tis equal to ..
Production function is given by Y = 3K"(AN)!-a, where a=2/3. The rate of depreciation of capital is equal to 12 percent, the rate of technological progress is equal to 5 percent, and the rate of population growth is equal to 3 percent. The economy was in the steady state at time t and the level of technology was equal to A:=30. Use the Solow growth model to answer the following questions. (Please fill in numbers; use a comma as a decimal separator: 10,5) 1. If the saving rate s=40 percent, the steady state level of output per unit of effective labor at time t is equal to 2. If the saving rate s=40 percent, the steady state level of consumption per unit of effective labor at time t is equal to 3. If the saving rate s=40 percent, the steady state level of consumption per worker at time t is equal to
Alter the Solow growth model so that the production technology is given by Y= zK, where Y is outputi, Kis capital, and z is total factor productivity. Thus, output is produced only with capital. Click the icon the view information about the initial model used here. a. Show that it is possible for income per person to grow indefinitely. Also show that an increase in the savings rate increases the growth rate in per capita income. In terms of s, z, d, and n, the growth rate of income per person is If the value of this expression is M then income per person will grow; this can continue indefinitely because b. An increase in the savings rate the growth rate in per capita income (assuming z>0). c. What are some differences between this model and the basic Solow growth model? (Select all that apply.) DA In this model, the marginal product of capital is increasing in capital. B. in this model, the marginal product of capital is constant in capital. O C. In this model, it is possible for total…
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In Solow model, we assumed that population growth rate is irrelevant to saving rate and technological progress. In this question, we will relax this assumption. Assume that population growth would reduce technological progress, what would happen to the steady state level of capital per capita? What if otherwise population growth increases technological progress? Explain mathematically and graphically.
9. Consider a numerical example using the Solow growth model. Suppose that F(K, N) KO.5N0.5, with d = z = 1, and take a period to be a year. (a) Determine capital per worker, income per capita, and consumption per capita in the steady state. 0.1, s = 0.2, n = 0.01, and
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Consider the following numerical examples for the Solow Growth Model: Economy A z=1 s=0.5 F(K,N)=K0.3N0.7 n=0.01 d=0.1 Economy B z=1 s=0.2 F(K,N)=K0.3N0.7 n=0.01 d=0.1 In which economy is GDP per capita higher in steady state? O Economy A O Economy B O Not enough Information
This question is about the Solow model. For 2 countries, 1 and 2 which has the same rate of population growth and depreciation and the same saving rate, and are in initial steady state, their capital have equal importance for production for both countries with the same value of α = 1/2 a. In the initial steady state, country 1 has 2 times the output per capita to country 2 because of its greater productivity A. Please use the steady-state equation to find the ratio of the 2 countries’ ratio of productivity and explain it. b. Find the 2 countries’ ratio of capital per capita and explain it. c. Please explain in detail if the capital owners in country 1 are motivated to move their capital from country 1 which is capital abundant, to country 2 which is more capital scarce? Hint: the 2 countries’ payment per unit of capital d. Does workers in country 2 motivated to immigrate to country 1? Please explain from the perspective of the 2 countries’ wages.
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