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Work It Out. Consider an economy with the following Cobb-Douglas production function: Y= 5K/3L2/3 where L...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The economy has 27,000 units of capital and a labour force of 1,000 workers. a. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock. b. If the real wage can adjust to equilibrate labour supply and labour de- mand, what is the real wage? In this equilibrium, what are employment, output, and the total...
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of...
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of workers and k is units of capital.mrtslk is k/l. the wage rate is $900 per week, and a unit of capital costs $400 per week. assuming no fixed cost, what is the firm's total cost of production if it uses least-cost input combination to produce 675 units of output?
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of...
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of workers and k is units of capital.mrtslk is k/l. the wage rate is $900 per week, and a unit of capital costs $400 per week. what is the least cost input combination for producing 675 units of output?
1. Consider the following production functions. In each case determine if: • the function is Cobb...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
Athens is an agricultural economy with the following Cobb-Douglas production function that uses land (x) and...
Athens is an agricultural economy with the following Cobb-Douglas production function that uses land (x) and labor (L) as factor inputs to produce grain (V) as the real output. Y = 2x0.5 70.5 = 2/XVI Land stock is 25 units. Labor supply is 16 workers. Find real output per worker.
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:...
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: %...
Consider an economy having a Cobb Douglas production function, where the share of capital income in...
Consider an economy having a Cobb Douglas production function,
where the share of capital income in total income is 1/2. The
depreciation rate is , population growth rate is n = 0.02
A. The golden rule level of capital per worker is .
B. The golden rule level of investment per worker is .
C. The golden rule level of output per worker is .
D. The golden rule savings rate is X% where X equals .
QUESTION 2 20...
2. Consider a Solow growth model with Cobb-Douglas production function Y Ko (AN)-a with constant savings...
2. Consider a Solow growth model with Cobb-Douglas production function Y Ko (AN)-a with constant savings rate s, depreciation rate d and no growth in productivity or labor (gA = gN = 0) (a) Suppose A = 1, a = 1/3, s = 0.2 and 5 = 0.1 (annual). Calculate the steady state capital per worker and steady state output per worker (b) Suppose that the real wage w and real return to capital r are equal to the marginal...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form,...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form, Y = Ka (LE)1-a, where 0 < α < 1. The savings rate s s, the depreciation rate isỗ, and the growth rate of E is g and the growth rate of L is n. Denote y E and LE 1. The economy is at the steady state. Report the steady-state growth rates of y, k, Y, K, L' K' ?, an 2. Assume...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The economy has 27,000 units of capital and a labour force of 1,000 workers. a. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock. b. If the real wage can adjust to equilibrate labour supply and labour de- mand, what is the real wage? In this equilibrium, what are employment, output, and the total...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
Athens is an agricultural economy with the following Cobb-Douglas production function that uses land (x) and labor (L) as factor inputs to produce grain (V) as the real output. Y = 2x0.5 70.5 = 2/XVI Land stock is 25 units. Labor supply is 16 workers. Find real output per worker.
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:...
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: %...
Consider an economy having a Cobb Douglas production function,
where the share of capital income in total income is 1/2. The
depreciation rate is , population growth rate is n = 0.02
A. The golden rule level of capital per worker is .
B. The golden rule level of investment per worker is .
C. The golden rule level of output per worker is .
D. The golden rule savings rate is X% where X equals .
QUESTION 2 20...
2. Consider a Solow growth model with Cobb-Douglas production function Y Ko (AN)-a with constant savings rate s, depreciation rate d and no growth in productivity or labor (gA = gN = 0) (a) Suppose A = 1, a = 1/3, s = 0.2 and 5 = 0.1 (annual). Calculate the steady state capital per worker and steady state output per worker (b) Suppose that the real wage w and real return to capital r are equal to the marginal...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form, Y = Ka (LE)1-a, where 0 < α < 1. The savings rate s s, the depreciation rate isỗ, and the growth rate of E is g and the growth rate of L is n. Denote y E and LE 1. The economy is at the steady state. Report the steady-state growth rates of y, k, Y, K, L' K' ?, an 2. Assume...
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