Homework Answers
b) if labor per capital increases by 1 percentage then output per capital will increase by B2 percentage.
c) interpretation will be in per labor terms then. And the if capital per labor increases by 1 percentage then output per labor will increase by B3 percentage.
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8.5. Consider the Cobb-Douglas production function Y = BILB2 KB where Y= output, L = labor...
An economy has a Cobb Douglas production function, given by: a, (1-a) (1) YAK L Where...
An economy has a Cobb Douglas production function, given by: a, (1-a) (1) YAK L Where Yis equal to total production, K is equal to the capital input of production and L is equal to the labour input of production. The constant, A, represents technology in the economy and a the elasticity of capital. function exhibits, decreasing, increasing or constant returns to scale. [ 10 Marks A2. Carefully derive the marginal product of labour and explain how this might be...
A “Cobb–Douglas” production function relates production (Q) to factors of production, capital (K), labor (L), and...
A “Cobb–Douglas” production function relates production (Q) to factors of production, capital (K), labor (L), and raw materials (M), and an error term u using the equation: ? = ???1??2M?3? ?, where ?, ?1, ?2, and ?3 are production parameters. a) Suppose that you have data on production and the factors of production from a random sample of firms with the same Cobb–Douglas production function. How would you propose to use OLS regression analysis to estimate the above production parameters,...
Assume a Cobb-Douglas function such that ? where A=1, K=20, L=16, , and ?. Calculate Q....
Assume a Cobb-Douglas function such that
? where A=1, K=20, L=16,
, and
?. Calculate Q. Does the function show increasing, decreasing, or
constant returns to scale? Why? Calculate the marginal produce of K
and L. Let K increase to 21 ceteris paribus and calculate the
marginal product of K and L. Explain the results.
Q = ᎪK L°
Consider the Cobb-Douglas production function
Please help with part c. Thank you!Returns to scale Consider the Cobb-Douglas production function, Yt = KẠN L-a=b. This production function includes three inputs: capital (Kt), labor (Nt), and land (Lt). a) Under what conditions does the function exhibit decreasing returns to scale in Kt, Nt and Lt individually? b) Show that the function exhibits constant returns to scale in Kt, Nt and Ljointly. c) Define (lowercase) yt = *, ku = and lt = . Express Yt as a...
Suppose you have data on output quantity, labor input, and capital input for all the firms (N-50) in a given industry. Suppose we believe that the production function is Cobb-Douglas: (a) Transfo...
Suppose you have data on output quantity, labor input, and capital input for all the firms (N-50) in a given industry. Suppose we believe that the production function is Cobb-Douglas: (a) Transform this equation into a linear model so that the parameters can be (b) What is the null-hypothesis for testing whether the production function is (c) Derive the 95% confidence interval for testing the null-hypothesis against estimated by OLS. Give an interpretation of Bi constant returns to scale? the...
Show that the Cobb-Douglas production function has constant returns to scale.
Show that the Cobb-Douglas production function has constant returns to scale. [Hint: start by writing out \(F(z K, z L)=A(z K)^{\alpha}(z L)^{1-\alpha}\) and use your algebra to see where you can get from here. You will need to use the following rules: \((z K)^{\alpha}=z^{\alpha} K^{\alpha}\), and \(\left.z^{\alpha} z^{(1-\alpha)}=z^{(\alpha+1-\alpha)}=z\right]\).
Question 17 1 pts Which of the following characteristics below does the Cobb-Douglas production function Y...
Question 17 1 pts Which of the following characteristics below does the Cobb-Douglas production function Y = K L l-a-8X8 satisfy? (There may be more than one correct answer. Select all of them.) Increasing returns to scale. Decreasing returns to scale. Constant returns to scale. Constant labor share of income. It is an exact replication of a firm's production function. Question 18 1 pts The production function is given by Y K1/ 43/4. Moreover, K-81 and L-2.5. Calculate total output....
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production...
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production technology exhibit increasing, constant, or decreasing returns to scale? (b) Suppose that the rental rate of capital is r = 1, the wage rate is w = 1, and the ?rm wants to produce Q = 3. In the long-run, what combination of L and K should they use? (It would be good to practice doing this with the Lagrangian, even if you can...
The Labor Share and Data The production function is Cobb-Douglas, Y = F (K, L) =...
The Labor Share and Data The production function is Cobb-Douglas, Y = F (K, L) = ĀKαL1−α with Ā = 1, depreciation of δ = 0.07 savings rate of 20% and population growth of 1%. 1. Suppose you have data on the total payments to labor and GDP, take the ratio of labor payments over GDP, (wL)/Y, and show the parameter in the model this corresponds to. To answer this, you will have to use the perfect competition assumption that...
Consider the following Cobb-Douglas production function for a firm that uses labor hours (L), capital (K),...
Consider the following Cobb-Douglas production function for a firm that uses labor hours (L), capital (K), and energy (E) as inputs: Q = (0.0012L^0.45)(K^0.3)(E^0.2) Determine the labor, capital and energy production elasticities. Suppose that worker hours are increased by 2 percent holding other inputs constant. What would be the resulting percentage change in output? Suppose that capital is decreased by 3 percent holding other inputs constant. What would be the resulting percentage change in output? What type of returns to scale appears...
An economy has a Cobb Douglas production function, given by: a, (1-a) (1) YAK L Where Yis equal to total production, K is equal to the capital input of production and L is equal to the labour input of production. The constant, A, represents technology in the economy and a the elasticity of capital. function exhibits, decreasing, increasing or constant returns to scale. [ 10 Marks A2. Carefully derive the marginal product of labour and explain how this might be...
Assume a Cobb-Douglas function such that
? where A=1, K=20, L=16,
, and
?. Calculate Q. Does the function show increasing, decreasing, or
constant returns to scale? Why? Calculate the marginal produce of K
and L. Let K increase to 21 ceteris paribus and calculate the
marginal product of K and L. Explain the results.
Q = ᎪK L°
Please help with part c. Thank you!Returns to scale Consider the Cobb-Douglas production function, Yt = KẠN L-a=b. This production function includes three inputs: capital (Kt), labor (Nt), and land (Lt). a) Under what conditions does the function exhibit decreasing returns to scale in Kt, Nt and Lt individually? b) Show that the function exhibits constant returns to scale in Kt, Nt and Ljointly. c) Define (lowercase) yt = *, ku = and lt = . Express Yt as a...
Suppose you have data on output quantity, labor input, and capital input for all the firms (N-50) in a given industry. Suppose we believe that the production function is Cobb-Douglas: (a) Transform this equation into a linear model so that the parameters can be (b) What is the null-hypothesis for testing whether the production function is (c) Derive the 95% confidence interval for testing the null-hypothesis against estimated by OLS. Give an interpretation of Bi constant returns to scale? the...
Question 17 1 pts Which of the following characteristics below does the Cobb-Douglas production function Y = K L l-a-8X8 satisfy? (There may be more than one correct answer. Select all of them.) Increasing returns to scale. Decreasing returns to scale. Constant returns to scale. Constant labor share of income. It is an exact replication of a firm's production function. Question 18 1 pts The production function is given by Y K1/ 43/4. Moreover, K-81 and L-2.5. Calculate total output....
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