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3. Suppose that the production function is given by Y=0.5VKVN (a) Transform the production function into...
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...
2. that the production function is given by: Suppose where Yis output, K is capital and...
2. that the production function is given by: Suppose where Yis output, K is capital and N is the number of workers. The steady-state level of capital per worker, in terms of the saving rate, s., and the depreciation rate, ,s KIN(Enter your response as an expression.) YIN=□ (Enter your response as an expression.) CIN=□ (Enter your response as an expression ) The steady-state level of output per worker, in terms of the saving rate, s, and the depreciation rate,...
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...
3. If the production function is given by y=k:13 where yt where yt is the output...
3. If the production function is given by y=k:13 where yt where yt is the output per worker and kt is the capital per worker. Suppose that the saving rate (s) equals the depreciation rate (8) plus 0.4. Find the steady state capital, output, investment, and consumption? Hint: all steady state values are functions of either (s) or (8)
d) (7pts) Suppose that the production function is Y = 12K1/3 (EL)23 and capital lasts for...
d) (7pts) Suppose that the production function is Y = 12K1/3 (EL)23 and capital lasts for an average of 10 years so that 10% of capital wears out every year (depreciate rate = 1/10 = 0.1 or 10%). Assume that the rate of growth of population is 4 percent, and the rate of technological growth is 2 percent. 1. (1pt) Derive the equation for output per effective worker y = Y/(EL) = f(k). 2. (3pts) Calculate the Golden Rule level...
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...
3. The land of Grim can be described by the following production func- tion Y =...
3. The land of Grim can be described by the following production func- tion Y = KÈL Moreover, there is no population growth nor is there technological progress. (a) Find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate. (b) Research shows that the depreciation rate in the Land of Grim is 10% per year. Make a table showing steady-state capital per worker, output per...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K >0 The...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K >0 The population grows at the exogenously given rate n, so that N n)N (a) Derive the per worker production function, where y-Y/N is output per worker and k = K/N is capital per worker (b) Derive the aggregate accumulation equation for capital per worker expressed solely as a function of k. k', A, and parameters (s. θ, d, n). Recall the law of motion for...
Suppose that the production function Y = 0.5K0.5N0.5 1. Derive the steady state equations for output...
Suppose that the production function Y = 0.5K0.5N0.5 1. Derive the steady state equations for output per worker, capital per worker and consump- tion per worker. 2. Assume that the depreciation rate is d=0.05. Compute steady state output per worker and consumption per worker for the following 11 values of savings rate: s = {0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1}. Plot the values of output per worker and consumption per worker on the same graph....
(2) Solow Model Arithmetic: Suppose that the economy has the following production function K >O The...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function K >O The population grows at the exogenously given rate n, so that N-(1+n)N (a) Derive the per worker production function, where y- Y/N is output per worker and k = K/N is capital per worker. (b) Derive the aggregate accumulation equation for capital per worker expressed solely as a function of k, ,A, and parameters (s,8, d,n). Recall the law of motion for capital: (e) Show...
2. that the production function is given by: Suppose where Yis output, K is capital and N is the number of workers. The steady-state level of capital per worker, in terms of the saving rate, s., and the depreciation rate, ,s KIN(Enter your response as an expression.) YIN=□ (Enter your response as an expression.) CIN=□ (Enter your response as an expression ) The steady-state level of output per worker, in terms of the saving rate, s, and the depreciation rate,...
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...
3. If the production function is given by y=k:13 where yt where yt is the output per worker and kt is the capital per worker. Suppose that the saving rate (s) equals the depreciation rate (8) plus 0.4. Find the steady state capital, output, investment, and consumption? Hint: all steady state values are functions of either (s) or (8)
d) (7pts) Suppose that the production function is Y = 12K1/3 (EL)23 and capital lasts for an average of 10 years so that 10% of capital wears out every year (depreciate rate = 1/10 = 0.1 or 10%). Assume that the rate of growth of population is 4 percent, and the rate of technological growth is 2 percent. 1. (1pt) Derive the equation for output per effective worker y = Y/(EL) = f(k). 2. (3pts) Calculate the Golden Rule level...
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...
3. The land of Grim can be described by the following production func- tion Y = KÈL Moreover, there is no population growth nor is there technological progress. (a) Find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate. (b) Research shows that the depreciation rate in the Land of Grim is 10% per year. Make a table showing steady-state capital per worker, output per...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function: K >0 The population grows at the exogenously given rate n, so that N n)N (a) Derive the per worker production function, where y-Y/N is output per worker and k = K/N is capital per worker (b) Derive the aggregate accumulation equation for capital per worker expressed solely as a function of k. k', A, and parameters (s. θ, d, n). Recall the law of motion for...
(2) Solow Model Arithmetic: Suppose that the economy has the following production function K >O The population grows at the exogenously given rate n, so that N-(1+n)N (a) Derive the per worker production function, where y- Y/N is output per worker and k = K/N is capital per worker. (b) Derive the aggregate accumulation equation for capital per worker expressed solely as a function of k, ,A, and parameters (s,8, d,n). Recall the law of motion for capital: (e) Show...
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