1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.

Question

Question

1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.

1. Suppose f(K,L)=[L+K]³, what is the MRTS?

2. Suppose f(K,L)=K^(1/2)+L^(1/2) Find the marginal rate of technical substitution.

3. f(K,L)=K^(1/2)+L^(1/2) Find the marginal rate of technical substitution.

business economics

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

1- MPl = 3(L+K)^2

MPk= 3(L+K)^2

So,MRTS = MPl/MPk = 1

2. MPl= 1/2 L^ -1/2

MPk = 1/2 K^ -1/2

So,MRTS = MPl/MPk =( K/L )^1/2

2nd and 3rd question are same . Maybe you have done a typo while typing question.

Add a comment

Answer 2

Similar Homework Help Questions

Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...

Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.

Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor. a. Find marginal product of labor and marginal product of capital.b. Define what is marginal rate of technical substitution, MRTS. Calculate the MRTS for the above case.c. When K = 10, L = 16, what is the total output? Sketch this isoquant function on a diagram where K is the vertical axis and L is the horizontal axis.
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...

2) MRTS or Marginal rate of technical substitution (MRTS) for an isoquant is defined as Δ...

2) MRTS or Marginal rate of technical substitution (MRTS) for an isoquant is defined as Δ capital / Δ labor, which in turn means that, MRTS will be of higher value when labor is more productive than capital. Select one: True False 3) Regression techniques could involve the issue of 'heteroscedasticity' meaning unequal scatter. This issue is important only when regression is used for demand estimation and not when we use the technique for demand forecasting. Select one: True False...
3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of...

3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of technical substitution of labor for capital (MRTS ) is diminishing, constant, increasing, or none of these. a. Q=LK b. Q=LVK c. Q=L*K13 d. Q = 3L +K e. Q = min{3L, K} Show transcribed image text 3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of technical substitution of labor for capital...
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%?

1. A frequent assumption that economists make about production functions is that the marginal rate of...

1. A frequent assumption that economists make about production functions is that the marginal rate of technical substitution (MRTS) is diminishing. (a) Explain the intuition behind this assumption; is it a reasonable assumption to make? Why or why not? (b) Describe (or show) what an isoquant would look like if this assumption were violated. Interpret. (c) In the two-good production function q = f(k. 1), the assumption of a diminishing marginal rate of technical substitution can be expressed as SMRTS...
2. Find the technical rate of substitution (TRSKL) for the production function 9-(K +3L) A. ***

2. Find the technical rate of substitution (TRSKL) for the production function 9-(K +3L) A. ***
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...

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%?

1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.

Homework Answers

Add Answer to:
1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.

Post as a guest

Earn Coins

Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is...

Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.

3. Suppose the production function takes on the following form: Q = aK2L 2 a) What...

2) MRTS or Marginal rate of technical substitution (MRTS) for an isoquant is defined as Δ...

3. For each of the following production functions, graph a typical isoquant and determine whether the marginal rate of...

2. For the following Cobb-Douglas production function, q = f(L,K) = _0.45 0.7 a. Derive expressions...

1. A frequent assumption that economists make about production functions is that the marginal rate of...

2. Find the technical rate of substitution (TRSKL) for the production function 9-(K +3L) A. ***

1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP...

SHOW ALL WORK!!! 2. For the following Cobb-Douglas production function, q=f(L,K) = _0.45 0.7 a. Derive expressions for m...

1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.

Homework Answers

Add Answer to: 1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.

Post as a guest

Earn Coins

Add Answer to:
1. Suppose f(K,L)=[L+K]3, what is the MRTS? 2. Suppose f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution. 3. f(K,L)=K(1/2)+L(1/2) Find the marginal rate of technical substitution.