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6. Suppose the production function takes on the following form: a) What is the marginal rate...
6. Suppose the production function takes on the following form: Q=K’L? a) What is the marginal...
6. Suppose the production function takes on the following form: Q=K’L? a) What is the marginal productivity of labor? Evaluate it at L = 5 and K = 7. (5 points) b) What is the Marginal Rate of Technical Substitution? Evaluate it at L = 5 and K = 7. (5 points)
3. Suppose the production function takes on the following form: Q = aK2L 2 a) What...
3. Suppose the production function takes on the following form: Q = aK2L 2 a) What is the marginal productivity of labor? Evaluate it at L = 2 and K = 4. b) What is the marginal productivity of capital? Evaluate it at L = 2 and K = 4. c) What is the Marginal Rate of Technical Substitution, and what does it mean? (Provide two interpretations of the MRTS) Evaluate the value of the MRTS at L = 2...
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...
(c) What is marginal rate of technical substitution? (d) What do we mean by returns to...
(c) What is marginal rate of technical substitution? (d) What do we mean by returns to scale? Give examples of Cobb-Douglas production functions exhibiting increasing, decreasing and constant returns to scale. [A Cobb-Douglas production function takes the following form: Q = AKalpha Lbeta, ; A > 0, Alpha > 0, Beta> 0:
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for the marginal product of 21 at the point (21,12). (b) Holding 22 fixed, for small increases in I, will the marginal product of 2 increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in ra? (d) Does an increase in the amount of 22 increase, leave unchanged or decrease the...
(1) Let's suppose that a firm's production technology is represented by the following production function. What...
(1) Let's suppose that a firm's production technology is represented by the following production function. What is the marginal product of labor (MPL)? a. -3 b. 1 c. 3 d. 1/3 What is the marginal product of capital (MPK)? a. -1 b. 1/3 c. 3 d. 1 What is the marginal rate of technical substitution (MRTS)? a. 1/3 b.3 c. -1/3 d. 1
Suppose a firm has a production function given by Q=2K+L, where L is labor, K is...
Suppose a firm has a production function given by Q=2K+L, where L is labor, K is capital and Q is the quantity of output. Which of the following statements is WRONG? A. The firm is exhibiting constant returns to scale B. The firm’s marginal product of capital is constant C. The firm’s marginal product of labor is constant D. The firm’s marginal rate of technical substitution depends on the amount of inputs
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution.
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution. Then answer the following for each: does this production function exhibit diminishing marginal product of labour? Does this production function exhibit diminishing marginal product of capital? Does this production function exhibit constant, decreasing, or increasing returns to scale? Show all your work.(a) \(Q=L+K\)(b) \(Q=2 L^{2}+K^{2}\)(c) \(Q=L^{1 / 2} K^{1 / 2}\)
Suppose the production function is Cobb-Douglas and f(x1, x2) = x^1/2 x^3/2 (e) What's the technical...
Suppose the production function is Cobb-Douglas and f(x1, x2) =
x^1/2 x^3/2
(e) What's the technical rate of substitution TRS (11, 12)? (f) Does this technology have diminishing technical rate of substitution? (g) Does this technology demonstrate increasing, constant or decreasing returns to scale?
6. Suppose the production function takes on the following form: Q=K’L? a) What is the marginal productivity of labor? Evaluate it at L = 5 and K = 7. (5 points) b) What is the Marginal Rate of Technical Substitution? Evaluate it at L = 5 and K = 7. (5 points)
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...
1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its...
1. Suppose the production function is Cobb-Douglas and f(11,12) = 21222 (a) Write an expression for the marginal product of 21 at the point (21,12). (b) Holding 22 fixed, for small increases in I, will the marginal product of 2 increase, decrease or remain constant? (c) What's the marginal product of factor 2? Will it increase, remain constant or decrease for small increases in ra? (d) Does an increase in the amount of 22 increase, leave unchanged or decrease the...
Suppose the production function is Cobb-Douglas and f(x1, x2) =
x^1/2 x^3/2
(e) What's the technical rate of substitution TRS (11, 12)? (f) Does this technology have diminishing technical rate of substitution? (g) Does this technology demonstrate increasing, constant or decreasing returns to scale?
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