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1.(20 pts) Consider the following production function: Y 4K NI-a and assume that a= ½ a....
3. Suppose that the production function is given by Y=0.5VKVN (a) Transform the production function into...
3. Suppose that the production function is given by Y=0.5VKVN (a) Transform the production function into a relationship between output per worker and capital per worker (b) Derive the steady-state levels of capital per worker and output per worker in terms of the saving rate (s) and the depreciation rate (8) (c) Derive the equation for steady-state consumption per worker in terms of s and 8
Suppose that an economy has the per-worker production function given as: y = 4k., where y...
Suppose that an economy has the per-worker production function given as: y = 4k., where y is output per worker and k is capital per worker. In addition, national savings is given as: S, = 0.10Y, where S is national savings and Y is total output. The depreciation rate is d = 0.10 and the population growth rate is n = 0.10. The steady-state value of the capital-labor ratio, kis 4.00. The steady-state value of output per worker, y is...
Suppose the production function is given by ? = ?^a?'^1-a, where Y is output; K is...
Suppose the production function is given by ? = ?^a?'^1-a, where Y is output; K is capital stock and N is Labor (look Appendix in Chapter 16). a. Is this production function characterized by constant return to scale? How? Show the work. b. Write this production function as a relationship between output per worker and capital per worker. c. If saving (S) equals investment (I), and S = sY, where s is saving rate, what is the corresponding investment per...
1. Country A and country B both have the production function Y = F(K,L)= VKL. (5...
1. Country A and country B both have the production function Y = F(K,L)= VKL. (5 Points) Does this production function have constant returns to scale? Explain. (5 Points) What is the per-worker production function, y=f(k)? (10 Points) Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using...
1. (10 pts). Assume that the per-worker production function is y, = 10.k'. Further, assume that...
1. (10 pts). Assume that the per-worker production function is y, = 10.k'. Further, assume that the saving rate, s = 0.2, the depreciation rate, 8 = 0.4, and the population growth rate, n= 0. Calculate the following: (a) The steady-state values of the capital-labor ratio, k*, output per worker, y, and consumption, c. (b) The new steady-state values of the capital-labor ratio, output, and consumption (ki, yi, and Ci), if there is an increase in the saving rate, so...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that the size of the population, the labour participation rate and the unemployment rate are all constant. a) Does this production function exhibit constant returns to scale? Explain (5 marks) b) Explain the difference between returns to factors of production and returns to scale (4 marks) cTransform the production function into a relationship between output per worker and capital per worker. (5 marks) d) Assume...
An economy has the per-worker production Y = 3k^.5 Where y is output per worker and...
An economy has the per-worker production Y = 3k^.5 Where y is output per worker and k is the capital to labor ratio. The depreciation rate is 0.1, and the population growth rate is 0.05 Total saving is S=0.3Y S is total saving and Y is total output a. What are the steady state values of the capital to labor ratio, output per worker, and consumption? b. Repeat part (a) for saving rate of 0.4. c. Repeat part (a) for...
2. (15 pts). Assume that the per-worker production function is y, 5.k Further, assume that the...
2. (15 pts). Assume that the per-worker production function is y, 5.k Further, assume that the saving rate, s = 0.2, the depreciation rate, 8 0.04, and the population growth rate, n- 0. Calculate the following: (a) The steady-state values of the capital-labor ratio, k", output per worker, y, and consumption, c'. (b) The new steady-state values of the capital-labor ratio, output, and consumption (k, yi, and ci), if there is population growth so that n: 0.06. (c) Show your...
3)- Consider an economy with the production function: Y=4K0.6 No.4, in the framework of the Solow...
3)- Consider an economy with the production function: Y=4K0.6 No.4, in the framework of the Solow Model, with usual definitions. Suppose, the labor force is growing at 1% a year, depreciation rate is 4%, and saving rate is 20%. (Total 17 points) a)- Find the steady state equilibrium of per worker levels of capital, output, and consumption. (4) b)- Find the golden rule saving rate, and golden rule per worker levels of output, capital, and consumption. (4) c)- How much...
3. (15 pts). Assume that the per-worker production function is yr = 20 k'. Further, assume...
3. (15 pts). Assume that the per-worker production function is yr = 20 k'. Further, assume that the saving rate, s = 0.1, the depreciation rate, = 0.125, and the population growth rate, n= 0. Calculate the following: (a) The steady-state values of the capital-labor ratio, k", output per worker, y, and consumption, c. (b) The new steady-state values of the capital-labor ratio, output, and consumption (ki. Yi, and ci) if there is a technological progress and A increases from...
3. Suppose that the production function is given by Y=0.5VKVN (a) Transform the production function into a relationship between output per worker and capital per worker (b) Derive the steady-state levels of capital per worker and output per worker in terms of the saving rate (s) and the depreciation rate (8) (c) Derive the equation for steady-state consumption per worker in terms of s and 8
Suppose that an economy has the per-worker production function given as: y = 4k., where y is output per worker and k is capital per worker. In addition, national savings is given as: S, = 0.10Y, where S is national savings and Y is total output. The depreciation rate is d = 0.10 and the population growth rate is n = 0.10. The steady-state value of the capital-labor ratio, kis 4.00. The steady-state value of output per worker, y is...
1. Country A and country B both have the production function Y = F(K,L)= VKL. (5 Points) Does this production function have constant returns to scale? Explain. (5 Points) What is the per-worker production function, y=f(k)? (10 Points) Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using...
1. (10 pts). Assume that the per-worker production function is y, = 10.k'. Further, assume that the saving rate, s = 0.2, the depreciation rate, 8 = 0.4, and the population growth rate, n= 0. Calculate the following: (a) The steady-state values of the capital-labor ratio, k*, output per worker, y, and consumption, c. (b) The new steady-state values of the capital-labor ratio, output, and consumption (ki, yi, and Ci), if there is an increase in the saving rate, so...
Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that the size of the population, the labour participation rate and the unemployment rate are all constant. a) Does this production function exhibit constant returns to scale? Explain (5 marks) b) Explain the difference between returns to factors of production and returns to scale (4 marks) cTransform the production function into a relationship between output per worker and capital per worker. (5 marks) d) Assume...
2. (15 pts). Assume that the per-worker production function is y, 5.k Further, assume that the saving rate, s = 0.2, the depreciation rate, 8 0.04, and the population growth rate, n- 0. Calculate the following: (a) The steady-state values of the capital-labor ratio, k", output per worker, y, and consumption, c'. (b) The new steady-state values of the capital-labor ratio, output, and consumption (k, yi, and ci), if there is population growth so that n: 0.06. (c) Show your...
3)- Consider an economy with the production function: Y=4K0.6 No.4, in the framework of the Solow Model, with usual definitions. Suppose, the labor force is growing at 1% a year, depreciation rate is 4%, and saving rate is 20%. (Total 17 points) a)- Find the steady state equilibrium of per worker levels of capital, output, and consumption. (4) b)- Find the golden rule saving rate, and golden rule per worker levels of output, capital, and consumption. (4) c)- How much...
3. (15 pts). Assume that the per-worker production function is yr = 20 k'. Further, assume that the saving rate, s = 0.1, the depreciation rate, = 0.125, and the population growth rate, n= 0. Calculate the following: (a) The steady-state values of the capital-labor ratio, k", output per worker, y, and consumption, c. (b) The new steady-state values of the capital-labor ratio, output, and consumption (ki. Yi, and ci) if there is a technological progress and A increases from...
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