Is the following production function homogeneous? If so, find the degree of homogeneity and comment on...

Question

Question

Is the following production function homogeneous? If so, find the degree of homogeneity and comment on the returns to scale!

business economics

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

1) is homogeneous

2) degree : 9

3) increasing returns to scale

Let for all t> 1

Q(tL, tK) = 4*(tK)⁵* (tL)⁴

= t⁹*(4K⁵ L⁴)

= t⁹*Q(K,L)

Add a comment

Answer 2

Similar Homework Help Questions

Is the following production function homogeneous? If so, find the degree of homogeneity and comment on...

Is the following production function homogeneous? If so, find the degree of homogeneity and comment on the returns to scale. Q=3K*24 +Kº24 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. and the function exhibits increasing returns to scale. O A. This function is homogeneous. The degree of homogeneity is (Type a whole number.) and the function constant returns to scale. OB. This function is homogeneous. The degree of homogeneity is (Type...
If output is described by the production function , then the production function has: (a) degree...

If output is described by the production function , then the production function has: (a) degree of returns to scale that cannot be determined from the information given. (b) diminishing returns to scale (c) increasing returns to scale (d) constant returns to scale (e) None of the above
For the following functions, answer if the function is homogeneous in (x , y), and if...

For the following functions, answer if the function is homogeneous in (x , y), and if yes, what degree it is. a. b. c. Does any of these three production functions display constant returns to scale? F(z,y) %3D zy-y을 We were unable to transcribe this imageWe were unable to transcribe this image

A firm has the production function Q= 4LK. The marginal products are given by MPL =...

A firm has the production function Q= 4LK. The marginal products are given by MPL = 4K and MPK= 4L. Suppose that the prices of labour and capital are given by w and r. Solve for the quantities of L and K that minimize the cost of producing Q units of output. Provide an expression for the long run total cost function. What returns to scale are exhibited by this production function? What economies of scale are exhibited? Show the...
2) Assume that a firm faces the following production function: q(L, K) = {1/4K 3/4 a)...

2) Assume that a firm faces the following production function: q(L, K) = {1/4K 3/4 a) Does this function represent increasing, decreasing or constant return to scale? b) Do we have diminishing productivity for factors of production? c) Find short-run cost function if K=256, w=3 and r=4
Show that if the production function is homogeneous of degree 2, then the cost minimizing demand...

Show that if the production function is homogeneous of degree 2, then the cost minimizing demand for input i is given by: xi = h(w) √y, where y and w are output and input prices and h(w) is some function of input prices.

5. Prove that when the production function is homogeneous of degree one, it may be as...

5. Prove that when the production function is homogeneous of degree one, it may be as f(x) 2MP(x)x where MPi(x) is the marginal product of input i. Hint use Euler's Theorem. 6. Derive the cost function for the linear technology y f(xix2)-axi+bx 7. Given the production function fxi)aIxa In(x), derive the firm's supply function assuming an interior solution, assuming that a>0 and a 0. 8. Consider a duopoly facing an industry demand function, p-a-bQ, where Q tg respective cost functions...
For following two production functions: (1) Q = L1/4 K (2) Q = 2L + 4K...

For following two production functions: (1) Q = L1/4 K (2) Q = 2L + 4K a) Determine whether factor L is subject to diminishing marginal returns? What about K? b) Calculate the MRTS. c) Determine returns to scale: CRS, IRS or DRS. Show how you arrive at your answers. For function (2) also draw a few representative isoquants; fully label your graph.
Given the following long run production and cost functions: q=LPK1/4 C = 12L +4K (A) What...

Given the following long run production and cost functions: q=LPK1/4 C = 12L +4K (A) What input has diminishing marginal returns? (B) Does this production function display increasing, decreasing or constant returns to scale? (C) What is this firm's expansion path assuming input prices do not change? Clearly type out your answer to parts (A), (B) and (C) in the space provided. Retain all of your handwritten work for this question to be uploaded separately after you have completed the...

For the following rice production function: Q = 80 ( K 0.6 L 0.4) Beginning with...

For the following rice production function: Q = 80 ( K 0.6 L 0.4) Beginning with K=5 and L=37, find out if the marginal product of both K and L is decreasing. Show your work. Does the production function exhibit increasing, decreasing, or constant returns to scale? Show your work. Why does it matter to know about what you found in a. and b. above?

Is the following production function homogeneous? If so, find the degree of homogeneity and comment on...

Homework Answers