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Consider an economy described by the production function: Y = F(K, L) = (0.25 0.75 a....
An economy has a Cobb-Douglas production function: Y = K"(LE)!-a The economy has a capital share...
An economy has a Cobb-Douglas production function: Y = K"(LE)!-a The economy has a capital share of 0.25, a saving rate of 40 percent, a depreciation rate of 3.00 percent, a rate of population growth of 0.75 percent, and a rate of labor- augmenting technological change of 2.0 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital.
1) Consider an economy with the following the production function: Y = F(K,L) = K^0.4L^0.6 a)...
1) Consider an economy with the following the production function: Y = F(K,L) = K^0.4L^0.6 a) Find output per worker b) Find the marginal product of capital c) Find the steady state level of capital per worker given a savings rate of 0.1, the depreciation rate of 0.2, and population growth of 0.05 d) Show graphically or analytically what will happen if there is a decrease in the rate of depreciation. What effect does this have on steady-state levels of...
1. Assume that an economy described by a Solow model has a per-worker production function given...
1. Assume that an economy described by a Solow model has a per-worker production function given by y- k05, where y is output per worker and k is capital stock per worker (capital-labor ratio). Assume also that the depreciation rate δ is 5%. This economy has no technological progress and no population growth (n 0). Both capital and labor are paid for their marginal products and the economy has been in a steady state with capital stock per worker at...
An economy has a Cobb-Douglas production function: Y = K°(LE)1-a The economy has a capital share...
An economy has a Cobb-Douglas production function: Y = K°(LE)1-a The economy has a capital share of 0.25, a saving rate of 43 percent, a depreciation rate of 3.00 percent, a rate of population growth of 4.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = 2.83 y* * = 1.30 =...
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...
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...
3. A closed economy has a production function: Y-K1 3L2/3, where K denotes machines and L...
3. A closed economy has a production function: Y-K1 3L2/3, where K denotes machines and L denotes workers. The population grows at a rate 2% per year and there is no technological progress. The depreciation rate is 3%. The saving rate, s, depends on the level of capital per worker, k, as follows: 5% if k < 5 (7k-30)% if 5 < k < 10 40% if k > 10 8 There are three steady states with k > 0:...
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...
Economic Growth II — Work It Out Question 1 An economy has a Cobb-Douglas production function:...
Economic Growth II — Work It Out Question 1 An economy has a Cobb-Douglas production function: Y = K (LE)-a The economy has a capital share of 0.25, a saving rate of 47 percent, a depreciation rate of 4.00 percent, a rate of population growth of 2.25 percent, and a rate of labor-augmenting technological change of 2.5 percent. It is in steady state. a. At what rates do total output and output per worker grow? Total output growth rate: %...
2. Suppose an economy described by the Solow model has the following production function and capital...
2. Suppose an economy described by the Solow model has the following production function and capital law of motion, with the variables as defined in class: Y =K^(1/2)(LE)^(1/2) ∆k = sy − (δ + n + g)k The economy has a saving rate of 24 percent, a depreciation rate of 3 percent, a population growth rate of 2 percent, and a growth rate of labor productivity of 1 percent. (a) At what rate do total output (Y ), output per...
An economy has a Cobb-Douglas production function: Y = K"(LE)!-a The economy has a capital share of 0.25, a saving rate of 40 percent, a depreciation rate of 3.00 percent, a rate of population growth of 0.75 percent, and a rate of labor- augmenting technological change of 2.0 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital.
1. Assume that an economy described by a Solow model has a per-worker production function given by y- k05, where y is output per worker and k is capital stock per worker (capital-labor ratio). Assume also that the depreciation rate δ is 5%. This economy has no technological progress and no population growth (n 0). Both capital and labor are paid for their marginal products and the economy has been in a steady state with capital stock per worker at...
An economy has a Cobb-Douglas production function: Y = K°(LE)1-a The economy has a capital share of 0.25, a saving rate of 43 percent, a depreciation rate of 3.00 percent, a rate of population growth of 4.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = 2.83 y* * = 1.30 =...
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...
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. A closed economy has a production function: Y-K1 3L2/3, where K denotes machines and L denotes workers. The population grows at a rate 2% per year and there is no technological progress. The depreciation rate is 3%. The saving rate, s, depends on the level of capital per worker, k, as follows: 5% if k < 5 (7k-30)% if 5 < k < 10 40% if k > 10 8 There are three steady states with k > 0:...
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...
Economic Growth II — Work It Out Question 1 An economy has a Cobb-Douglas production function: Y = K (LE)-a The economy has a capital share of 0.25, a saving rate of 47 percent, a depreciation rate of 4.00 percent, a rate of population growth of 2.25 percent, and a rate of labor-augmenting technological change of 2.5 percent. It is in steady state. a. At what rates do total output and output per worker grow? Total output growth rate: %...
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