ZuoTi.Pro
Question

Show that the Cobb-Douglas production function has constant returns to scale.

Show that the Cobb-Douglas production function has constant returns to scale. [Hint: start by writing out \(F(z K, z L)=A(z K)^{\alpha}(z L)^{1-\alpha}\) and use your algebra to see where you can get from here. You will need to use the following rules: \((z K)^{\alpha}=z^{\alpha} K^{\alpha}\), and \(\left.z^{\alpha} z^{(1-\alpha)}=z^{(\alpha+1-\alpha)}=z\right]\).

business   economics   
3 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

0 0
Add a comment
Know the answer?
Add Answer to:
Show that the Cobb-Douglas production function has constant returns to scale.
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 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 ·...

  • If national production is given by a Cobb-Douglas production function with constant returns to scale, real...

    If national production is given by a Cobb-Douglas production function with constant returns to scale, real GDP is growing at 4%, the capital to labor ratio is constant, and the labor force is growing at 1.5%, what is the growth rate of the Solow residual? Assume α = 0.3. a) 1.5% b) 2.5% c) 5.5% d) 7.0% e) None of the above Please provide the solving process for this problem.

  • 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...

  • 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...

  • 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...

  • 6. What is the relationship between the Cobb-Douglas production function and returns to scale? (The following...

    6. What is the relationship between the Cobb-Douglas production function and returns to scale? (The following questions may require using an advanced textbook, such as Varian’s “Microeconomic Analysis”)

  • 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. 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...

  • 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....

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT