Determine whether the following production function exhibits increasing, constant or decreasing...
Question:
Determine whether the following production function exhibits increasing, constant or decreasing returns to scale.
{eq}Q = K + L {/eq}
Returns to Scale:
Returns to scale is a concept in economics that illustrates how output increases in proportion with the increase in inputs. When the same factor is added to all inputs, outputs will change accordingly. The quantitative change in outputs depends on if the production function was constant, decreasing, or increasing returns to scale.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerGiven {eq}Q = K + L {/eq}
We increase inputs a proportional amount {eq}\lambda {/eq} for both {eq}K {/eq} and {eq}L {/eq} and compare with the...
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
- Determine whether the following production function exhibits increasing, constant or decreasing returns to scale. Q = Min(2K, 2L)
- Determine whether the production function below exhibits increasing, constant or decreasing returns to scale. Q = L + L/K
- 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)
- Determine whether the production function exhibits increasing, constant or decreasing returns to scale. Q = L^(0.5) K^(0.5)
- 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 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
- 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
- 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
- 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 have increasing, decreasing or constant returns to scale. a. Q=0.001M+50,000 b. Q=15K+0.5KL+30L
- Suppose a firm has a production function given by Q = L*K. Does this production function exhibit increasing, constant or decreasing returns to scale?
- Does the production function: q = 100L - 20/k exhibit increasing, decreasing, or constant returns to scale?
- 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}
- Determine whether this production function exhibits increasing, decreasing, or constant returns to scale.
- 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
- 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.
- 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.)
- 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.
- 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}
- 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 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
- 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.
- 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
- 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
- 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
- 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
- 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
- Determine whether the production function T(L, K)=10L+2K, yields an increasing or decreasing returns to scale or a constant returns to scale.
- 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
- 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
- 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}
- 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
- 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?
- 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
- 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 the production function Q = K^0.5L^0. 5, if K and L are both 4 and K increases to 9, output will increase by _____ units.
- 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
- 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
- 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
- Consider the following production function: Q = L^AK^0.45. If this production technology exhibits constant returns to scale, what must be the value of A?
- Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale? a. q = L + K, a linear production function, b. q = L^{\alpha}K^{\beta}, a general Cobb-Douglas production function.
- Suppose production is described as Q = 50K + 5KL. Is production increasing returns to scale (IRS), constant returns to scale (CRS), or decreasing returns to scale (DRS)?
- 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
- State whether the following production functions exhibit decreasing returns to scale, increasing returns to scale or constant returns to scale, briefly explain.
- 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 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 a production function given by: Q = 27K^{2}L^{0.5} - 2K^{4} A. Let L = 16. Find the level of K at which the marginal product of capital reaches a maximum B. Let L = 16. Find the level of K
- 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.
- 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.
- 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
- 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
- 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
- Suppose you have two production functions: (i) y = A(K + L) (ii) y = A + (K + L) Demonstrate how one function is a constant return to scale and the other is not.
- 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
- 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.
- Given the production function q = 10K_{a}L^{B}, show that this exhibits constant returns to scale if a+B = 1.
- 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 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
- Does the production function q=100L- {50}/{K} exhibit increasing, decreasing, or constant returns to scale? This production function exhibits ____ returns to scale.
- 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
- 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
- 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
- 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
- Determine which statement is true in regards to the two production functions shown below. 1. Q = K^{0.75}L^{0.75} 2. Q = K^{0.25}L^{0.25} A. The first exhibits decreasing returns to scale, while the second exhibits increasing returns to scale. B. Both fun
- 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
- 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
- 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
- Find the returns to scale for the following production functions. Q=X1^.34 X2^.34 Q= (2X1+3X2)^.5 Q=[0.3X1^.5+0.7X2^.5]^2 Q=[min(X1,2X2)]^2
- 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
- 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
- Show whether the following production functions exhibit decreasing returns to scale (DRS), constant returns to scale (CRS), or increasing returns to scale (IRS)?
- Define returns to scale. Ascertain whether the given production function exhibit constant, diminishing, or increasing returns to scale.
- Suppose that a production function can be written Q = 9KL^2 -L^3. a) Assuming K=1, complete the following table: |L|Q|MP|AP |0| | | |1 | | | |2 | | | |3 | | | |4 | | | |5 | | | |6 | | | |7 | | | |8 | | | |9 | | | b) Graph the production function for K=1
- Consider the following production function q = 4\sqrt(LK), where q is the quantity of output produced, and L and K respectively denote the quantity of labor and capital used. Given this production fu
- Consider the production function Y=\frac{X-500}{20}, where Y is output and X represents inputs. Graph this production function. Does it display decreasing, constant, or increasing returns to scale?
- Which of the following four production functions exhibit constant returns to scale? In each case, y is output and K and L are inputs. (Select all that apply.) a. y = K1/2L1/3 b. y = 3K1/2L1/2 c. y = K1/2 + L1/2 d. y = 2K + 3L
- 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
- 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
- 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
- Suppose you are given the following function: C(w,r,Q)=2w^(1/2)*r^(1/2)*Q^(3/2), where 'w' is the wage rate for labor, 'r' is the rental of capital and 'q' is the output level. a) Does output increase
- 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
- If output is produced according to Q = (KL)3/4, then this production process exhibits: a. first decreasing and then increasing returns to scale b. first increasing and then decreasing returns to scale c. increasing returns to scale d. decreasing returns t
- The production function Y = (X^2)*(X^{0.5}) has returns to scale. a. increasing b. marginal c. decreasing d. constant
- 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
- 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 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)
- Consider the following production function: Q = AL^aK^b. Assume A is greater than 0. Further assume 0 is less than a is less than 1, and 0 is less than b is less than 1. a. What is the Marginal Produ
- 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 = 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
- Which of the following production functions exhibit constant marginal product of capital, K? In each case y is output and K and L are inputs. a. y=K*L^{2/3} b. y=3K^{1/2}*L^{1/2} c. y=K^{1/2}+L^{1/2} d. y=2K+3L
- Determine which of the following production functions exhibit constant returns to scale (CRS). Hint: Using scale up to double the inputs used, does the output double, less than double, or more than do
- Suppose the production function is q = 20K^0.5L^0.5. Calculate the RTS (-MPL/MPK) when: a) K = 200, L = 300 b) K = 50, L = 400
- Let the production function be q = AL^aK^b. The function exhibits increasing returns to scale if A. a + b is less than 1. B. a + b = 1. C. a + b is greater than 1. D. Cannot be determined with the information given.
- 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
- 1) Starting with the production function, q = L^{(1/3)}*K^{(2/3)} where r = 2 and w = 1, what is the Expansion Path (L as a function of K)? 2) Starting with the production function, q = L^{(1/3)}*K^{
- Which of the following production functions exhibit constant returns to scale? (a) F(K, L) = KL/10 (b) F(K, L) = KL (c) F(K, L) = (KL)^2 (d) F(K, L) = K + L
- Provide a graph and an explanation to show that the production function Q = L0.5K0.5 has a diminishing marginal product of labor but has constant returns to scale.