Under what conditions do the following production functions exhibit decreasing, constant, or...
Question:
Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale?
a. {eq}q = L + K {/eq}, a linear production function,
b. {eq}q = L^{\alpha}K^{\beta} {/eq}, a general Cobb-Douglas production function.
Returns to scale
Production function provides a frontier with inputs limits to be employed to reach the production combinations. Such production is maximized provided with certain input productivities. With changing productivities, production returns change, they may constantly rise, stay the same or fall. These are returns to scale.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer
a.
Linear production function:
If the linear production function is multiplied by a constant, say t, the output should also be multiplied by t.
{...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:

from
Chapter 3 / Lesson 71Understand the meaning of returns to scale in economics. Learn about increasing returns to scale, constant returns to scale and decreasing returns to scale.
Related to this Question
- Are the returns to scale of the following production functions increasing, decreasing, or constant? a) Q = KL/4 b) Q = K + L c) Q = Min(K/6, L/3)
- Do the following functions exhibit increasing, constant, or decreasing returns to scale? Explain your answers. A. The production function Q = M^{0.5}K^{0.5}L^{0.5}, where M is materials, K is capital, and L is labor. B. q = L + 0.5K C. q = 0.5LK^{0.25} D.
- Do the following production functions exhibit decreasing, constant, or increasing returns to scale? You must show calculations to justify your answers (a) Q = 0.5KL (b) Q = 2K + 3L (c) Q = L + L1/2
- List whether each of the following production functions has decreasing, increasing or constant returns to scale: a. Q = Min (2K, L) b . Q = L .5 K .8 c . Q = L .5 + K .5 d . Q = 10 + K + L
- Determine whether the following production function exhibits increasing, constant or decreasing returns to scale. Q = Min(2K, 2L)
- Determine whether the following production function exhibits increasing, constant or decreasing returns to scale. Q = K + L
- Suppose a firm has a production function given by Q = L*K. Does this production function exhibit increasing, constant or decreasing returns to scale?
- Determine whether the production function exhibits increasing, constant or decreasing returns to scale. Q = L^(0.5) K^(0.5)
- The following are different algebraic expressions of the production function. Decide whether each one has constant, increasing, or decreasing returns to scale. a. Q = 75L 0.25 K 0.75 b. Q = 75A 0.15
- Following are different algebraic expressions of the production function. Decide whether each one has constant, increasing, or decreasing returns to scale. a. Q = 75L 0.25 K 0.75 b. Q = 75A 0.15 B 0
- Determine if each of the following production functions exhibit decreasing, constant, or increasing returns to scale. a. q = 5L0.4K0.5 b. q = min(21, K)
- Suppose output is produced according to the production function: Q = M^0.5 K^0.5 L^0.5, where M is materials, K is capital and L is labor (inputs) used for the production. Does this production function exhibit decreasing, increasing, or constant returns t
- Does the production function q=100L- {50}/{K} exhibit increasing, decreasing, or constant returns to scale? This production function exhibits ____ returns to scale.
- A firm's production function is Q = 5L2/3K1/3. a) Does this production function exhibit constant, increasing, or decreasing returns to scale, and why? b) What is the marginal rate of technical substitution of L for K for this production function? c) Wh
- For each of the following production functions, determine whether it exhibits increasing, constant or decreasing returns to scale: a) Q = K + 4L b) Q = L + L/K c) Q = Min(K,L) d) Q = L*K
- With capital K and labor L input, there are five production functions in the following: I. Q = L + K II. Q = \sqrt{L \cdot K} III. Q = L \cdot K IV. Q = \sqrt[3]{L \cdot K} V. Q = L^2 + K^2 a. Which function(s) exhibit the constant returns to scale? b. Wh
- For each of the following production functions, determine whether it exhibits increasing, constant or decreasing returns to scale: a) Q = 2K + L b) Q = 3L + L/K c) Q = Min(2K,L) d) Q = L*K
- With capital K and labor L input, there are five production functions in the following: I. Q = L + K II. Q = sqrt{L * K} III. Q = L * K IV. Q = sqrt[3]{L * K} V. Q = L^2 + K^2 a. Which function(s) exhibit constant returns to scale? b. Which function(s) ex
- Show whether the following production functions exhibit decreasing returns to scale (DRS), constant returns to scale (CRS), or increasing returns to scale (IRS). A. q = 10L^{0.6}K^{0.5} B. q = L + K C. q = L^{0.6} + K^{0.5}
- Let a production function exist such that Q = (K^.30 L^.75). a) Does this production function exhibit increasing, decreasing, or constant returns to scale? b) Estimate the effect on Q of a 10% increas
- Let a production function exist such that Q = K^{0.35}L^{0.75}. A. Does this production function exhibit increasing, decreasing, or constant returns to scale? Explain. B. What is the effect on Q of a 10% increase in labor hours, keeping K constant? C. Wha
- Determine whether the production function below exhibits increasing, constant or decreasing returns to scale. Q = L + L/K
- Suppose the production function for a firm is as follows: q = min (3K, L). (a) Draw the isoquants for q = 3 and q = 6. (b.) Explain whether the production function exhibits constant, increasing or dec
- Determine whether the following production function have increasing, decreasing or constant returns to scale. a. Q=0.001M+50,000 b. Q=15K+0.5KL+30L
- State whether the following production functions exhibits constant, increasing or decreasing returns to scale. Assume in all cases {bar}() A is greater than 0. 1) Y = 1/2*K + L 2) Y = L^(3/2) + K^(5/
- Do the following production functions, where Q is total output, L is the quantity of labor employed, and K is the quantity of capital employed, exhibit constant, increasing, or decreasing returns to scale. Explain. a. Q=3LK^2 b. Q=8L+5K
- Following are different algebraic expressions of the production function. Decide whether each one has constant, increasing, or decreasing returns to scale. a. Q = 75L^{0.25}K^{0.75} b. Q = 75A^{0.15
- Do the following production functions exhibit decreasing, constant, or increasing returns to scale? Show calculations to justify your answers. (a) Q = 0.5KL (b) Q = 2K + 3L (c) Q = L + L1/2K1/2 + K
- Consider the production function: Q = K^(1/3) L^(2/3) where Q is quantity of output, K is capital, and L is labor. Does this function exhibit increasing, diminishing, or constant returns to scale?
- A firm has the production function q = f (L, K) = L + K2 This firm has: a) Decreasing returns to scale. b) Increasing returns to scale. c) Constant returns to scale. d) Increasing marginal product. e) None of the above.
- Suppose firms have the following production function This production function exhibits a. Increasing returns to scale b. Decreasing returns to scale. c. Constant returns to scale. d. The returns to sc
- State whether the following production functions exhibit decreasing returns to scale, increasing returns to scale or constant returns to scale, briefly explain.
- A production function can exhibit increasing, constant or decreasing returns to scale. Describe the meaning of this statement using a simple production function Y = F (K, L) , where K is capital and L
- A firm's production function is given by the equation Q = 100K0.3L0.8, where Q represents units of output, K units of capital, and L units of labor. a. Does this production function exhibit increasing, decreasing, or constant returns to scale? b. Suppose
- For each of the following production functions, are there Increasing returns to scale, constant returns to scale, decreasing returns to scale, or does the answer depend on output level: - A. B. C. D.
- Consider the following production function: q = 4LK. Which term describes this production function's returns to scale? A. increasing returns to scale B. decreasing returns to scale C. constant returns to scale
- Find the returns to scale for the following production function where q denotes output, and x_1, x_2, and x_3 are inputs. q = x_1^{1/4} x_2^{1/3} O decreasing returns to scale O constant returns to scale O increasing returns to scale
- Find the returns to scale for the following production function where q denotes output, and x_1, x_2, and x_3 are inputs. q = 4x_1^{1/4} x_2^{1/4} x_3^{1/4} O decreasing returns to scale O constant returns to scale O increasing returns to scale
- Determine whether this production function exhibits increasing, decreasing, or constant returns to scale.
- The production function q = 22K^{0.7}L^{0.1} exhibits A. increasing returns to scale. B. constant returns to scale. C. unknown returns to scale because the exponents are not equal. D. decreasing returns to scale.
- Check if the following production function is constant, decreasing, or increasing return to scale: a. q = K^1/2 L^3/4 b. q = K^1/2 L^4/6
- Determine whether the following production function exhibits constant increasing or decreasing returns to scale in capital and labor. A). Y = AK^\frac{3}{4} L^\frac{3}{4}
- Assume a production function can exhibit increasing, constant or decreasing returns to scale. Describe the meaning of this statement using a simple production function Y = F (K, L), where K is capital
- Which of the following production functions exhibit(s) constant returns to scale? I. Q = K + L II. Q = 2K + L III. Q = K0.810.2 a. I and II b. II and III c. I, II, and III d. III only
- Determine whether the production function T(L, K)=10L+2K, yields an increasing or decreasing returns to scale or a constant returns to scale.
- For both production functions below, determine: (1) if MPPL and MPPK are increasing, decreasing or constant (2) if the production function exhibits increasing, decreasing or constant returns to scal
- The production function f(K,L) = (max\begin{Bmatrix} K,L \end{Bmatrix})^\frac{1}{2} exhibits... \\ A. Decreasing returns to scale B. Constant returns to scale C. Increasing returns to scale D. None of the above
- Find the returns to scale for the following production function where q denotes output, and x_1 and x_2 are inputs. q = (0.3sqrt{x_1} + 0.7 sqrt{x_2})^{1/2} O decreasing returns to scale O constant returns to scale O increasing returns to scale
- The Cobb-Douglas production function and the steady state. Suppose that the economy's production function is given by Y = K^alpha} N^1 - alpha. a. Is this production function characterized by constant
- Does the production function: q = 100L - 20/k exhibit increasing, decreasing, or constant returns to scale?
- A firm's production function is f(K, L) = 10K1/2L. Which of the following statements is correct? a. The firm has constant returns to scale. b. The firm has decreasing returns to scale. c. The firm has increasing returns to scale.
- A production function Y=F(K,L) exhibits constant, decreasing, increasing returns to scale if for some positive number a, say a=2, we have: Constant returns: F(aK,aL)=aF(K,L)
- A firm faces the following production function: Q = - 0.1 L3 + 12 L2 + 480L. At what level of employment (L) does diminishing returns set in?
- Let a production function exist such that Q=(K0.30 L0.75) a) Does this production function exhibit Increasing, Decreasing or Constant Returns to Scale? Explain what your answer means and how you know.
- Given the production function q = 10K_{a}L^{B}, show that this exhibits constant returns to scale if a+B = 1.
- Find the returns to scale for the following production function where q denotes output, and x_1 and x_2 are inputs. q = ( min { x_1, 2x_2 } )^{1/4} O decreasing returns to scale O constant returns to scale O increasing returns to scale
- 2. determine the returns to scale for the following production functions: (a) Q=(L+K)2 (b) Q=(L(1/2)+K(1/2))2 3. A firm's production function is given by q = 5L2/3 K1/3 (a) Calculate APL and MPL. D
- A more general form of the Cobb Douglas production function is q = f(L, K) = AL^aK^b where A, a, b > 0 are constants. What is the MRTSL,K?
- Which of the following production functions displays decreasing returns to scale? a) Q = aL + bK^{2} b) Q = aL + bK c) Q = bLK d) Q = cL^{0.2} \times K^{0.5}
- a) Suppose two countries have the following production function: Y=F(K, L)=K^(0.3)L^(0.7). b) Is this production function constant returns to scale? Express the above production function in per worker
- A production function may exhibit _____. a. constant returns to scale and diminishing marginal productivities. b. increasing returns to scale and diminishing marginal productivities. c. decreasing returns to scale and diminishing marginal productivities.
- Suppose you have the following production function: Q = 10 K 0.5 L 0.5 Pl = $ 2 Pk = $ 3 P = $ 100 A) What kind of returns to scale are there? B) If the scale increases 10% in what percentage wi
- Consider the following production function: Q = 10L2K, where Q is the amount of production, L is the amount of labor, and K is the amount of capital. a. Does this production function exhibit the law of diminishing returns? Explain. b. Does this production
- List whether each of the following production function functions has diminishing marginal returns to labor (Y or N). a. Q = 50K + 30L - .5L2, MPL.= 30- L b. Q = L.5K.8 MPL = .5K.8/L.5 c. Q = 2L + K
- For which values of > 0 and > 0 do the followingproduction functions exhibit decreasing, constant or increasingreturns to scale? Explain your answer. a) Q = L + K (a linear production function) b) Q = AL K c) Q=L+L K +K
- Suppose you have two production functions where A is constant total factor productivity: (i) y = A(K + L), (ii) y = A + (K + L) Show/demonstrate that only one is a constant returns to scale production function. Also, show/demonstrate that the other
- If the slope of a long-run total cost function decreases as output increases, the firm's underlying production function exhibits: a. Constant returns to scale. b. Decreasing returns to scale. c. Decreasing returns to a factor input. d. Increasing returns
- The production function Y = (X^2)*(X^{0.5}) has returns to scale. a. increasing b. marginal c. decreasing d. constant
- Do the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L? (Assume bar A is some fixed positive number.)
- Find the returns to scale for the following production function where q denotes output, and x_1, x_2, and x_3 are inputs. q = (2x_1 + x_2)^{2/3} O decreasing returns to scale O constant returns to scale O increasing returns to scale
- For the following production function, please do the following: Y = aK + bL; a, b > 0 a. Find whether they have increasing, constant, or decreasing returns to scale b. Draw the isoquant map for two or
- With capital K and labor L input, there are five production functions in the following: I. Q = L+K II. Q = Square root L*K III. Q = L*K IV. Q = Cube root L*K V. Q = Lsquare +Ksquare a. Which function(s) exhibit the constant returns to scale? b. Which
- Consider the CES production function. This production function exhibits A. constant returns to scale. B. decreasing returns to scale. C. increasing returns to scale. D. either decreasing or constant returns to scale, but more information is needed
- Consider the Production Function, Y = 25K1/3L2/3 (a) Calculate the marginal product of labor and capital (b) Does this production function exhibit constant/increasing/decreasing returns to scale? (
- The production function q=100k^0.4L^0.8 exhibits: a. increasing returns to scale but diminishing marginal products for both k and l. b. decreasing returns to scale and diminishing marginal products for both k and l. c. increasing returns to scale but dim
- Show whether the following production functions exhibit constant returns to scale, decreasing returnsto scale or increasing returns to scale. Please do not just state your answer, but show mathematica
- Which of the following production functions exhibit decreasing returns to scale? In each case, q is output and K and L are inputs. (1) q=K^{1/3} L^{2/3}(2) q=K^{1/2} L^{1/2} (3) q=2K+3L a. 1,2,and 3 b. 2 and3 c. 1 and 3 d. 1 and 2 e. None of the func
- Suppose that a firm has a production function given by q = 10L0.5K0.6. The firm has 10 units of capital in the short run. Which of the following will describe the marginal product of labor (MPL) for this production function? a. increasing marginal returns
- Suppose you have a production function equal to Q= 10(0.7K2+0.3L2)0.5. Does this function exhibit a. increasing, b. decreasing, or c. constant returns to scale? Explain.
- A firm produces quantity Q of breakfast cereal using labor L and material M with the production function Q = 50 (ML)1/ 2 +M + L . a) Find out the marginal products of M and L. b) Are the returns to scale increasing, constant, or decreasing for this produc
- A labor intensive production process has the following production function: Q=L-L(2)/400. a labor intensive production process has the following production function: Q = L- L squared /400. The firm se
- Suppose the total cost function is TC(q) = f + cq^2. What levels of production are associated with increasing, decreasing and constant returns to scale?
- Suppose f(L, K) = K^2 + LK + L^1/2 K^1/2. Does this production function exhibit increasing, decreasing or constant returns to scale? Show your work.
- Suppose that a firms fixed proportion production function is given by: q = min (5K, 10L), and that r = 1, and w = 3. a. Does this function exhibit decreasing, constant, or increasing returns to scale
- A firm has the following weekly production function: Q = 20KL - 0.025KL^2. Suppose the firm is in the short-run with K fixed at 20. a. What is the equation for the marginal product? Explain whether the production function is consistent with the Law of Di
- Define returns to scale. Ascertain whether the given production function exhibit constant, diminishing, or increasing returns to scale.
- Suppose the production function for good q is given by q = 3K + 2L where K and L are capital and labor inputs. Consider three statements about this function: I. The function exhibits constant returns to scale. II. The function exhibits constant marginal p
- As its capital stock increases, a nation will: A. move rightward along a fixed production function. B. move leftward along a fixed production function. C. find its production function shifting upward. D. find its production function shifting downward. E.
- Different cost functions derived from a constant returns to scale Cobb-Douglas production function
- Suppose the production for good q is given by q=3k+2l, where k and l are capital and labor inputs. Consider three statements function about this function: I. the function exhibits constant returns to scale. II. the function exhibits diminishing marginal p
- Determine which of the following production functions exhibits constant returns to scale (CRS). a) Y=0.5K+0.3L b) Y=(K L)^1/2 c) Y=min{K,0.3 L} d) Y=K^0.3 L^0.5
- Suppose a firm has the Cobb-Douglas production function Q= f(K, L) = 2K^0.7L^0.8, where K is capital and L is labor. Using this function, show the following: (a) Does this production function exhibit
- Consider the production function q= sqrt(L) + 8K^3. Starting from the input combination (5,10), does the production function exhibit increasing, constant or decreasing returns to scale if inputs doubl
- If the slope of the total cost curve increases as output increases, the production function is exhibiting: a. increasing returns to scale b. constant returns to scale c. decreasing returns to scale d. decreasing returns to a factor input
- Let a production function exist such that Q= (K^{0.35} L^{0.60}). a) Does this production function exhibit Increasing, Decreasing or Constant returns to scale? Explain how you know. b) What is the effect on Q of a 10% increase in labor hours, keeping K
- If the equation Y = F(K,L) represents a constant returns to scale production function, then for any positive constant c the following must also hold: Select one: a. Y = F(cK,cL). b. cY = cF(K,L). c. c
- Show whether the following production functions exhibit decreasing returns to scale (DRS), constant returns to scale (CRS), or increasing returns to scale (IRS)?