![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 that the saving rate is 16% and that capital depreciates at a rate of 8%. Calculate the steady-state output per worker and capital per worker. (6 marks) What is the effect of an increase in capital per worker on output per worker and what is the effect of technological progress on output per worker? What is the main difference between the two effects? Explain with the aid of a diagram. (10 marks)](http://img.homeworklib.com/questions/28b01380-794d-11eb-89e9-d188bc5a49a3.png?x-oss-process=image/resize,w_560)
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Question 2 130 marks] Suppose that the production function is given by Y 0.5VKv/N. Assume that...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of δ, the rate of technological progress is g, the population is growing at a rate of n and the saving rate is s. I5 marks] i. Determine the scale of production? Suppose capital is increased by a...
1.(20 pts) Consider the following production function: Y 4K NI-a and assume that a= ½ a....
1.(20 pts) Consider the following production function: Y 4K NI-a and assume that a= ½ a. Is this production function characterized by diminishing returns, constant returns, or increasing returns to scale? Justify your answer. Is the function characterized by diminishing or increasing returns to capital? Justify your answer. b. Transform the production function into a relation between output per worker (Y/N) and capital per worker (K/N), and then calculate the steady state levels of capital stock per worker, output per...
Assume a production function, Y = KαL1 – α.. Assume constant population growth (n). In the...
Assume a production function, Y = KαL1 – α.. Assume constant population growth (n). In the Solow model, the steady-state level of output per worker is a function of: productivity. population, the depreciation rate, and the saving rate. poverty, productivity, and the saving rate. poverty, productivity, and the depreciation rate. poverty and the steady-state level of capital stock. 35. In the Solow model, it is assumed that a(n) __________ fraction of capital depreciates regardless of the capital stock. a. increasing...
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...
Suppose the production function is given by yt=kt1/2 where y is the output per worker and k...
Suppose the production function is given by yt=kt1/2 where y is the output per worker and k is the capital per worker. Assume that the saving rate (S) is exogenous and the capital depreciates at δ rate. If the sum of both the depreciation rate and saving rate equals 1. Furthermore, assume that S=3δ. The steady state output is
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...
supposed the production function is given by yt=kt1/2 where y is the output per worker and...
supposed the production function is given by yt=kt1/2 where y is the output per worker and k is the capital per worker. assume that the saving rate (s) is exogenous and the capital depreciates at S rate. If the sum of both is depreciation rate and the saving rate equals 1. Furthermore, assume that s=3S The steady state output a)9 b)2.25 c)3 d)0.75
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
pls solve parts g,h,i, j Suppose Country X's production function is given by F(K, A,N) =...
pls solve parts g,h,i, j
Suppose Country X's production function is given by F(K, A,N) = 206,05(A, N,905 where K, is the capital and A, N, is the effective worker. The evolution of the capital stock is given by K +1 = 0.74K, +1 where the depreciation rate is 26%. Additionally, the saving rate is 36%, the population growth rate is 4% and the technological growth rate is 10% (a) Derive and show that in the Solow growth model, the...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by: Y = 6K1/3L2/3 In this economy, workers consume 80% of income and save the rest. The labour force is growing at 2% per year while the annual rate of capital depreciation is 5.5%. a) Solve for the steady state capital-labour ratio and consumption per worker. The economy is in its steady state as described in part (a). Suppose both the stock of capital...
d. Assume that the aggregate production function is given by: where Y is aggregate output, K is capital, L is the number of workers in the economy and E is the state of technology. Further assume that capital depreciates at a rate of δ, the rate of technological progress is g, the population is growing at a rate of n and the saving rate is s. I5 marks] i. Determine the scale of production? Suppose capital is increased by a...
1.(20 pts) Consider the following production function: Y 4K NI-a and assume that a= ½ a. Is this production function characterized by diminishing returns, constant returns, or increasing returns to scale? Justify your answer. Is the function characterized by diminishing or increasing returns to capital? Justify your answer. b. Transform the production function into a relation between output per worker (Y/N) and capital per worker (K/N), and then calculate the steady state levels of capital stock per worker, output per...
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...
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
pls solve parts g,h,i, j
Suppose Country X's production function is given by F(K, A,N) = 206,05(A, N,905 where K, is the capital and A, N, is the effective worker. The evolution of the capital stock is given by K +1 = 0.74K, +1 where the depreciation rate is 26%. Additionally, the saving rate is 36%, the population growth rate is 4% and the technological growth rate is 10% (a) Derive and show that in the Solow growth model, the...
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