Let Y=10 * sqrt(K) * sqrt(L) Suppose households save 10% of all output. This savings is...
Let Y=10 * sqrt(K) * sqrt(L)
Suppose households save 10% of all output. This savings is added to the capital stock for the next period. On the other hand, depreciation destroys 3% of capital in each period.
- Draw a graph depicting the steady state equilibrium. (You should have per capita capital on the x axis and per capita investment on the y axis.)
- Solve for the equilibrium, giving values for y*, k*, i*, and c*.
- Suppose the savings rate were to increase to 15%.
- Show the effect of this change on a graph like that you drew for part a.
ii. Draw a graph showing income across time. Start the graph a little before the change in savings, assuming the economy was in the steady state in part a. Then show how incomes change over time after the one-time change in the savings rate.
- Go back to the original problem. Now suppose the shift to computer technology means that the depreciation rate increases to 5%. Repeat parts i and ii of part c.
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Let Y=10 * sqrt(K) * sqrt(L)
Suppose households save 10% of all
output. This savings is...
Suppose the per-capita production function is given by y=\k, where kis capital per person and y is output per person....
Suppose the per-capita production function is given by y=\k, where kis capital per person and y is output per person. Suppose that the savings rate in this economy is 50% and capital depreciates at the rate of 25% a year. The steady-state capital-to-labor ratio is: k-1 k 2 k-4 cannot be determined from the above information.
Q.2 Consider the Solow growth model. Suppose that F(K,N)=RºS No5 with d=0.1, s=0.2, n=0.01, and z=1...
Q.2 Consider the Solow growth model. Suppose that F(K,N)=RºS No5 with d=0.1, s=0.2, n=0.01, and z=1 and take a period to be one year. (15 marks) a. Determine capital per worker, income per capita, and consumption per capita in the steady state. Show the theoretical derivation and numerical solution. (7 marks) b. Now suppose that the economy is initially in the steady state that you calculated in part a, and savings increases to s=0.4. Determine capital per worker, income per...
0.5 , where y is output per worker and k Suppose that an economy has the...
0.5 , where y is output per worker and k Suppose that an economy has the per-worker production function given as: Y = 5k is capital per worker. In addition, national savings is given as: S = 0.1074, 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, k is 6.25. The steady-state value of output per...
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 the Solow growth model. Suppose that with d=0.1, s=0.2, n=0.01, and z=1 and take a...
Consider the Solow growth model. Suppose that with d=0.1, s=0.2, n=0.01, and
z=1 and take a period to be one year.
a. Determine capital per worker, income per capita, and consumption
per capita in the steady-state. Show the theoretical derivation and
numerical solution.
b. Now suppose that the economy is initially in the steady-state
that you calculated in part a, and savings increases to s=0.4.
Determine capital per worker, income per capita, and consumption
per capita in the new steady...
Solow Growth Model D. Consider an economy with production characterized by function Y = AVKL, per...
Solow Growth Model D. Consider an economy with production characterized by function Y = AVKL, per capita output y = AVkt with rate of depreciation of capital 8, investment it = sy. = sAvky, capital transition function kt+1 - k = SAVk - Okt, where s is savings ratio. 1. Putting per capita output (income) y on the y-axis and k on the x-axis, graph the curves for depre- ciation and investment. Label steady state capital k* and steady state...
1. Let the production function for an economy by given by Y=AK1/2L1/2 where Y is output,...
1. Let the production function for an economy by given by Y=AK1/2L1/2 where Y is output, K is capital, L is labor and A is “ideas.” a. If L=25, A=10, the savings rate is ¼ and the depreciation rate is ½, what will the steady-state values of output, capital and consumption be? b. On a graph, show what will happen to steady-state output and capital of there is a decrease in the depreciation rate. 2. As capital increases, the marginal...
Question 7 Suppose an economy begins in steady state which has a production function of Y...
Question 7 Suppose an economy begins in steady state which has a production function of Y = ĀK3L3. By what proportion does per capita GDP change in the long run (at the steady state) in response to each of the following changes? (a) The investment rate doubles. (b) The depreciation rate falls by 10%. (c) The productivity level rises by 10%. (d) An earthquake destroys 75% of the capital stock. (e) A more generous immigration policy leads the population to...
Consider the Solow growth model. Output at time t is given by the production function Y-AK3...
Consider the Solow growth model. Output at time t is given by the production function Y-AK3 Lš where K, is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation KH = (1-d) * Kit It: where d is the depreciation rate. Every person saves share s of his income and, therefore, aggregate saving is St-s...
When St=0.4Yt，k? y? c? Suppose that an economy has the per-worker production function given as: y...
When St=0.4Yt，k? y? c?
Suppose that an economy has the per-worker production function given as: y = 3405 where y is output per worker and k is capital per worker. In addition, national savings is given as: S = 0.37 where S is national savings and Y is total output Use the production and savings functions on your left and the depreciation and population growth rates below to answer the following questions. (Round all numerical responses to one decimal place)...
Suppose the per-capita production function is given by y=\k, where kis capital per person and y is output per person. Suppose that the savings rate in this economy is 50% and capital depreciates at the rate of 25% a year. The steady-state capital-to-labor ratio is: k-1 k 2 k-4 cannot be determined from the above information.
Q.2 Consider the Solow growth model. Suppose that F(K,N)=RºS No5 with d=0.1, s=0.2, n=0.01, and z=1 and take a period to be one year. (15 marks) a. Determine capital per worker, income per capita, and consumption per capita in the steady state. Show the theoretical derivation and numerical solution. (7 marks) b. Now suppose that the economy is initially in the steady state that you calculated in part a, and savings increases to s=0.4. Determine capital per worker, income per...
0.5 , where y is output per worker and k Suppose that an economy has the per-worker production function given as: Y = 5k is capital per worker. In addition, national savings is given as: S = 0.1074, 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, k is 6.25. The steady-state value of output per...
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 the Solow growth model. Suppose that with d=0.1, s=0.2, n=0.01, and
z=1 and take a period to be one year.
a. Determine capital per worker, income per capita, and consumption
per capita in the steady-state. Show the theoretical derivation and
numerical solution.
b. Now suppose that the economy is initially in the steady-state
that you calculated in part a, and savings increases to s=0.4.
Determine capital per worker, income per capita, and consumption
per capita in the new steady...
Solow Growth Model D. Consider an economy with production characterized by function Y = AVKL, per capita output y = AVkt with rate of depreciation of capital 8, investment it = sy. = sAvky, capital transition function kt+1 - k = SAVk - Okt, where s is savings ratio. 1. Putting per capita output (income) y on the y-axis and k on the x-axis, graph the curves for depre- ciation and investment. Label steady state capital k* and steady state...
Question 7 Suppose an economy begins in steady state which has a production function of Y = ĀK3L3. By what proportion does per capita GDP change in the long run (at the steady state) in response to each of the following changes? (a) The investment rate doubles. (b) The depreciation rate falls by 10%. (c) The productivity level rises by 10%. (d) An earthquake destroys 75% of the capital stock. (e) A more generous immigration policy leads the population to...
Consider the Solow growth model. Output at time t is given by the production function Y-AK3 Lš where K, is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation KH = (1-d) * Kit It: where d is the depreciation rate. Every person saves share s of his income and, therefore, aggregate saving is St-s...
When St=0.4Yt，k? y? c?
Suppose that an economy has the per-worker production function given as: y = 3405 where y is output per worker and k is capital per worker. In addition, national savings is given as: S = 0.37 where S is national savings and Y is total output Use the production and savings functions on your left and the depreciation and population growth rates below to answer the following questions. (Round all numerical responses to one decimal place)...
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