(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:
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(c) What is marginal rate of technical substitution?
(d) What do we mean by returns to...
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...
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?
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%?
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) \(Q=L^{1 / 2} K^{1 / 2}\)
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%?
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...
Q=100K^0.7L^0.4 Find the marginal product of labor Find the marginal product of capital Is there diminishing...
Q=100K^0.7L^0.4 Find the marginal product of labor Find the marginal product of capital Is there diminishing marginal rate of technical substitution? Explain. Does the production function exhibit constant, increasing, or decreasing returns to scale.
Returns to scale. A production function has constant returns to scale with
Returns to scale. A production function has constant returns to scale with respect to inputs with inputs K and L if for any z > 0: F(z · K, z ·L) = zF(K, L), For example, for a production function with constant returns to scale, doubling the amount of each input (i.e., setting z = 2) will lead to a doubling of the output from the production function. A production function has increasing returns to scale if for any z >1: F(z ·...
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...
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: a) What is the marginal rate of technical substitution? Evaluate it at L5 and K 7. (5 points) b) What are the returns to scale for this production technology? (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...
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?
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%?
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%?
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...
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...
6. Suppose the production function takes on the following form: a) What is the marginal rate of technical substitution? Evaluate it at L5 and K 7. (5 points) b) What are the returns to scale for this production technology? (5 Points)
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