Homework Answers
17. Constant returns to scale
Constant labor share of income
18. 5.96
Y= k^1/4L^3/4
K= 81, L= 2.5
Y= 81^1/4 * 2.5^3/4 = 3*1.99= 5.96
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Question 17 1 pts Which of the following characteristics below does the Cobb-Douglas production function Y...
a. Suppose that a firm has the Cobb-Douglas production function = 12K0.75 0.25. Because this function...
a. Suppose that a firm has the Cobb-Douglas production function = 12K0.75 0.25. Because this function exhibits returns to scale, the long-run average cost curve is , whereas the long-run total cost curve is upward-sloping, with slope. b. Now suppose that the firm's production function is = KL. Because this function exhibits returns to scale, the long-run average cost curve is upward-sloping , whereas the long-run total cost curve is upward-sloping, with slope. a. Suppose that a firm has the...
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...
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...
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...
Assume a Cobb-Douglas production function of the form: 10L023 K043 What type of returns to scale...
Assume a Cobb-Douglas production function of the form: 10L023 K043 What type of returns to scale does this production function exhibit? In this instance, r This production function exhibits returns to scale equal(Enter a numearic response using a real number rounded to two decimal places) a numenic O A. increasing returns to scale. O B. constant returns to scale. ⓔ C. initially decreasing but then constant returns to scale O D. decreasing retums to scale O E. iniially constant but...
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
Question-3 (Marginal Products and Returns to Scale) (30 points) Suppose the production function is Cobb-Douglas and...
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
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°
Assume the following Cobb-Douglas production function: Assume the following Cobb-Douglas production function: Y = AK 0.4...
Assume the following Cobb-Douglas production function:
Assume the following Cobb-Douglas production function: Y = AK 0.4 20.6 If Y=12; K=8; and L=95, answer the following questions (SHOW ALL YOUR WORK): - 1. What is total factor productivity? 2. With your answer in (1), assume L=95 and estimate the production function with respect to K 3. Estimate the marginal product of capital and demonstrate diminishing marginal product of capital 4. Estimate real capital income 5. Estimate the share of capital income...
SHOW ALL WORK!!! 2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for m...
SHOW ALL WORK!!!
2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
a. Suppose that a firm has the Cobb-Douglas production function = 12K0.75 0.25. Because this function exhibits returns to scale, the long-run average cost curve is , whereas the long-run total cost curve is upward-sloping, with slope. b. Now suppose that the firm's production function is = KL. Because this function exhibits returns to scale, the long-run average cost curve is upward-sloping , whereas the long-run total cost curve is upward-sloping, with slope. a. Suppose that a firm has the...
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...
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...
Assume a Cobb-Douglas production function of the form: 10L023 K043 What type of returns to scale does this production function exhibit? In this instance, r This production function exhibits returns to scale equal(Enter a numearic response using a real number rounded to two decimal places) a numenic O A. increasing returns to scale. O B. constant returns to scale. ⓔ C. initially decreasing but then constant returns to scale O D. decreasing retums to scale O E. iniially constant but...
2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
Question-3 (Marginal Products and Returns to Scale) (30 points)
Suppose the production function is Cobb-Douglas and f(x1; x2) =
x1^1/2 x2^3/2
1. Write an expression for the marginal product of x1.
2. Does marginal product of x1 increase for small increases in
x1, holding x2 fixed? Explain
3. Does an increase in the amount of x2 lead to decrease in the
marginal product of x1? Explain
4. What is the technical rate of substitution between x2 and
x1?
5. What...
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°
Assume the following Cobb-Douglas production function:
Assume the following Cobb-Douglas production function: Y = AK 0.4 20.6 If Y=12; K=8; and L=95, answer the following questions (SHOW ALL YOUR WORK): - 1. What is total factor productivity? 2. With your answer in (1), assume L=95 and estimate the production function with respect to K 3. Estimate the marginal product of capital and demonstrate diminishing marginal product of capital 4. Estimate real capital income 5. Estimate the share of capital income...
SHOW ALL WORK!!!
2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for marginal product of labor and marginal product of capital, MP, and MPK. b. Derive the expression for marginal rate of technical substitution, MRTS. C. Does this production function display constant, increasing, or decreasing returns to scale? Why? d. By how much would output increase if the firm increased each input by 50%?
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