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 function of kį and lt. When does this function exhibit decreasing, constant, and increasing returns to scale?
Homework Answers
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...
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...
Douglas production function F(x,, x)- xg, where X1, xl are Consider the Cobb- values of generic...
Douglas production function F(x,, x)- xg, where X1, xl are Consider the Cobb- values of generic inputs, while α marginal product of input i? For any i, for what parameter values is there diminishing marginal product of inpu increasing, constant, and decreasing returns to scale? While a general answer is preferable, you can answer these questions for 1-3. 2. a, are constant nt parameters. Forthe , t i? Under what parameter values does the production fu
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for...
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
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...
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...
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...
26. If the sum of the exponents of a Cobb-Douglas production function is equal to 1.2,...
26. If the sum of the exponents of a Cobb-Douglas production function is equal to 1.2, the production function exhibits: a) increasing average costs b) constant returns to scale. c) increasing returns to scale. d) declining productivity. e) none of the above 27. Dana, who is a trained yoga instructor, spends 4 hours on Monday baking and packing 10 boxes of cookies. She sells the cookies for $10 a box. Given that she can also teach yoga for $80 an...
Question 17 1 pts Which of the following characteristics below does the Cobb-Douglas production function Y...
Question 17 1 pts Which of the following characteristics below does the Cobb-Douglas production function Y = K L l-a-8X8 satisfy? (There may be more than one correct answer. Select all of them.) Increasing returns to scale. Decreasing returns to scale. Constant returns to scale. Constant labor share of income. It is an exact replication of a firm's production function. Question 18 1 pts The production function is given by Y K1/ 43/4. Moreover, K-81 and L-2.5. Calculate total output....
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?
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...
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...
Douglas production function F(x,, x)- xg, where X1, xl are Consider the Cobb- values of generic inputs, while α marginal product of input i? For any i, for what parameter values is there diminishing marginal product of inpu increasing, constant, and decreasing returns to scale? While a general answer is preferable, you can answer these questions for 1-3. 2. a, are constant nt parameters. Forthe , t i? Under what parameter values does the production fu
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
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...
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...
26. If the sum of the exponents of a Cobb-Douglas production function is equal to 1.2, the production function exhibits: a) increasing average costs b) constant returns to scale. c) increasing returns to scale. d) declining productivity. e) none of the above 27. Dana, who is a trained yoga instructor, spends 4 hours on Monday baking and packing 10 boxes of cookies. She sells the cookies for $10 a box. Given that she can also teach yoga for $80 an...
Question 17 1 pts Which of the following characteristics below does the Cobb-Douglas production function Y = K L l-a-8X8 satisfy? (There may be more than one correct answer. Select all of them.) Increasing returns to scale. Decreasing returns to scale. Constant returns to scale. Constant labor share of income. It is an exact replication of a firm's production function. Question 18 1 pts The production function is given by Y K1/ 43/4. Moreover, K-81 and L-2.5. Calculate total output....
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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