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Problem 3: Write each production function given below in terms of output per person y =...
1.The “per-person” versions of production functions: Write each production functiongiven below in terms of output per...
1.The “per-person” versions of production functions: Write each production functiongiven below in terms of output per persony≡Y /Land capital per personk≡K/L.Showwhat these “per person” versions look like in a graph withkon the horizontal axis andyonthe vertical axis. (Assume ̄A is some fixed positive number.)(a)Y=K1/3L2/3andY=K3/4L1/4(on the same graph) (b)Y=K (c)Y=K+ ̄AL (d)Y=K− ̄AL2.
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...
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....
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.
6. Suppose that the long run aggregate production function can be written as Y = A*F(K,...
6. Suppose that the long run aggregate production function can be written as Y = A*F(K, L), where Y is the value of aggregate supply of goods and services, A is a measure of the level of technological sophistication in the economy, K is the aggregate capital stock of machinery, and L represents the labor force in the economy. The production function, which relates inputs of K and L to output is represented by F(.). (15 total points) a) Depict...
Problem #3: Long-Run Labor Dernand and Factor Substitutability Suppose there are two inputs in the production...
Problem #3: Long-Run Labor Dernand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which can be combined to produe Y units of output according to the following production function Y = 30K + 10L The firm wants to produce 600 units of output 1. Draw the ot that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and K on the vertical...
Problem 1. Suppose that production function for the corporate sector is well presented by the Cobb-Douglas...
Problem 1. Suppose that production function for the corporate sector is well presented by the Cobb-Douglas production function: Y = K0.3L0.7 With this production function: MPL(K, L)=0.7K0.3L0.3 and MPK(K, L)=0.3K0.7L0.7 a) Suppose the capital stock of the firm is K¯ =10. Show that the demand for labor is given by: b) Find the amount of labor demanded for W P = 0.1,W P = 0.3, W P = 0.5, W P = 0.7 and W P = 0.9. Plot the...
Consider the Solow growth model. Output at time t is given by the production function Yt...
Consider the Solow growth model. Output at time t is given by the production function Yt = AK 1 3 t L 2 3 where Kt 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 Kt+1 = (1 − d) ∗ Kt + It , where d is the depreciation rate. Every person saves...
2. A country has the following production function: Y = 0.3L0.5p0.2 where Y is total output,...
2. A country has the following production function: Y = 0.3L0.5p0.2 where Y is total output, K is capital stock, L is population size and P is land size (P is a fixed number). The depreciation rate (8) is 0.05. The population growth rate (n) is 0. The saving rate is 0.2. We define: y = Y/L, K = K/L and p = P/L. Use: Ak = sy - (n + )k. a) Find out the steady state values of...
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. 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...
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.
6. Suppose that the long run aggregate production function can be written as Y = A*F(K, L), where Y is the value of aggregate supply of goods and services, A is a measure of the level of technological sophistication in the economy, K is the aggregate capital stock of machinery, and L represents the labor force in the economy. The production function, which relates inputs of K and L to output is represented by F(.). (15 total points) a) Depict...
Problem #3: Long-Run Labor Dernand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which can be combined to produe Y units of output according to the following production function Y = 30K + 10L The firm wants to produce 600 units of output 1. Draw the ot that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and K on the vertical...
2. A country has the following production function: Y = 0.3L0.5p0.2 where Y is total output, K is capital stock, L is population size and P is land size (P is a fixed number). The depreciation rate (8) is 0.05. The population growth rate (n) is 0. The saving rate is 0.2. We define: y = Y/L, K = K/L and p = P/L. Use: Ak = sy - (n + )k. a) Find out the steady state values of...
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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