2. Consider an economy with many identical firms. Each firm produces according to a Cobb- Douglas...
2. Consider an economy with many identical firms. Each firm produces according to a Cobb- Douglas production function: y = AK α N 1−α where y is output, K is the amount of capital, N is the amount of labor and 0<α <1 is a parameter.
(a) What is the marginal product of labor (MPN)? (Take a partial derivative with respect to N )
(b) What is the marginal product of labor when A = K = 1 , N = 4 and α = 0.5 .
(c) What happens to the marginal product of labor when A goes up?
(d) What happens to the marginal product of labor when K goes up?
(e) What happens to the equilibrium amount of labor when K goes up? Use a graph to illustrate your answer. In the graph, use N' to denote the equilibrium amount of labor before K went up and N'' to denote the equilibrium amount of labor after the change in K. Is N'' larger or smaller than N'?
(f) What will happen to the full employment output when K goes up?
Homework Answers
Add Answer to:
2. Consider an economy with many identical firms. Each firm
produces according to a Cobb- Douglas...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
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 =...
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.
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by...
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between O and I a) Derive an analytical expression for the marginal product of capital (MPK),...
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...
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...
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by...
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. α and β are parameters whose values are between 0 and 1. a) Derive an analytical expression for the marginal product of capital (MPK),...
Work It Out. Consider an economy with the following Cobb-Douglas production function: Y= 5K/3L2/3 where L...
Work It Out. Consider an economy with the following Cobb-Douglas production function: Y= 5K/3L2/3 where L the wag the sect are will a. If w wh a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint: Review Chapter 3.) b. The economy has 27,000 units of capital and a labor force of 1,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage,...
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...
Consider the following production functions Y = AK1/2L1/2 Y=AK+3L a. Fixing total factor productivity (A) at...
Consider the following production functions Y = AK1/2L1/2 Y=AK+3L a. Fixing total factor productivity (A) at 2 and labor employment (L) at 16 units, what is the marginal product of capital when capital employment (K) is 25, 35, and 45 for each production function? Do these production functions exhibit diminishing returns to capital employment? Explain. b. Are labor and capital complements under these production functions? Explain. c. Is either production function a “Cobb-Douglas” function? Explain. 3. Describe the difference between...
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 =...
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.
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between O and I a) Derive an analytical expression for the marginal product of capital (MPK),...
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...
Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. α and β are parameters whose values are between 0 and 1. a) Derive an analytical expression for the marginal product of capital (MPK),...
Work It Out. Consider an economy with the following Cobb-Douglas production function: Y= 5K/3L2/3 where L the wag the sect are will a. If w wh a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint: Review Chapter 3.) b. The economy has 27,000 units of capital and a labor force of 1,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage,...
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...
Most questions answered within 3 hours.
-
The phylum Protista has often been referred to as a junk drawer
of classification. Explain what...
asked 5 minutes ago -
The average amount of money spent for lunch per person in the
college cafeteria is $7.09...
asked 7 minutes ago -
You follow the lab procedure and at the end of Part 4C, you used
an average...
asked 26 minutes ago -
Write 250-450 words, about the following: • Analyze how a
servant leader in your organization or...
asked 29 minutes ago -
3. American and Japanese workers can each produce 4 cars a
year. An American worker can...
asked 32 minutes ago -
On October 1, 20X1, a company purchased a piece of land by
agreeing to pay the...
asked 44 minutes ago -
Jamie is doing a survey at her school about whether the students
feel the cafeteria food...
asked 49 minutes ago -
What are the roles of 3' and 5' untranslated regions in
mRNAs?
asked 50 minutes ago -
A domestic television receives antenna delivers a sky noise
power of -105 dBm to a matched...
asked 49 minutes ago -
What do you think are the chemical reactions involved in the
breathalyzer tests administered to potentially...
asked 1 hour ago -
A random sample of 120 observations produces a mean of
38.2 from a population with a...
asked 1 hour ago -
The average area of land burned by forest fires every year in
Canada is 2.5 million...
asked 1 hour ago