Determine whether the following production function exhibits constant increasing or decreasing...
Question:
Determine whether the following production function exhibits constant increasing or decreasing returns to scale in capital and labor.
A) {eq}Y = AK^\frac{3}{4} L^\frac{3}{4} {/eq}
Production function:
The production function shows the relationship between input and output. It has three returns to scale that are increasing, decreasing, or constant return to scale. In constant return to scale, as the input increases by double amount then output also increases by double amount.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer
Production function exhibits increasing return to scale. It shows that the sum of the exponent is greater than one. It means the more output is...
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 11 / Lesson 27Learn about the production function. Read the production function definition in economics, learn the production function formula. Plus, see graphs and examples.
Related to this Question
- 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
- Determine whether this production function exhibits increasing, decreasing, or constant returns to scale.
- 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? (
- 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.
- 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
- 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
- Determine whether the production function T(L, K)=10L+2K, yields an increasing or decreasing returns to scale or a constant returns to scale.
- Determine whether the following production function exhibits increasing, constant or decreasing returns to scale. Q = K + L
- Determine whether the following production function exhibits increasing, constant or decreasing returns to scale. Q = Min(2K, 2L)
- Determine whether the production function exhibits increasing, constant or decreasing returns to scale. Q = L^(0.5) K^(0.5)
- 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/
- Consider a production function \text Y = \text z \text F(\text K, \text N^d). Which of the following properties we assume for F? 1. Constant returns to scale. 2. Output increases with increase in either the labor input or the capital input. 3. The margina
- 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)
- 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?
- 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
- Determine whether the production function below exhibits increasing, constant or decreasing returns to scale. Q = L + L/K
- 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
- 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
- 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
- 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.
- Do these functions exhibit increasing, decreasing or constant returns to capital and labor? a) F(K, L) = 3K+5L b) F(K, L) = 2KL c) F(K, L) = 3K^2L^{0.5} d) F(K, L) = K^{0.3}L^{0.5} e) F(K, L) = 6K^{0.5}L^{0.5}
- State whether the following production functions exhibit decreasing returns to scale, increasing returns to scale or constant returns to scale, briefly explain.
- 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.
- Does the production function q=100L- {50}/{K} exhibit increasing, decreasing, or constant returns to scale? This production function exhibits ____ returns to scale.
- 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?
- 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 firm, that has production function, f(L,K)=3L^2/3K^1/3. Does this production function satisfy the law of decreasing marginal returns of capital?
- 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
- 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
- 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)
- 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 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.
- 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}
- Show whether the following production functions exhibit decreasing returns to scale (DRS), constant returns to scale (CRS), or increasing returns to scale (IRS)?
- 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
- 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
- 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
- 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
- Define returns to scale. Ascertain whether the given production function exhibit constant, diminishing, or increasing returns to scale.
- 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
- 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
- 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
- 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
- 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.
- 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
- Suppose a firm has a production function given by Q = L*K. Does this production function exhibit increasing, constant or decreasing returns to scale?
- If a 10% increase in both capital and labor causes output to increase by less than 10%, the production function is said to exhibit decreasing returns to scale. If it causes output to increase by more
- 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
- 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
- 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
- Consider an economy with the following production function: Y = AK^{0.5} L^{0.5} The labor force is constant. The rate of depreciation is 0.1, the savings rate is s = 0.3 a) Has this production function constant returns to scale? Why? b) Write the pro
- 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.
- The production function Y = (X^2)*(X^{0.5}) has returns to scale. a. increasing b. marginal c. decreasing d. constant
- 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.
- 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
- Assume that production is a function of capital and labor, and that the rate of savings and depreciation are constant. Furthermore, assume that the production function can be described by the function
- 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.)
- Consider two goods, x and y, each produced using two inputs, labor l and capital k. Which of the following statements is correct? a. If production functions exhibit diminishing returns to scale, the
- 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
- Suppose that a firm's technology is given by the following production function: f(k,l) = 6k^{1/6} L^{1/6 } a. Prove that this production function exhibits diminishing marginal product in both k and l. This is not the same thing as decreasing returns
- 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
- 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 an economy with the following production function: Y = AK^{.5}L^{.5} The labor force is constant. The rate of depreciation is δ = .1, the savings rate is s = .3. a. Has this production function constant returns to scale? Why? b. Write t
- 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?
- 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
- Assume Knappy Knickers has the following production function and marginal product of labor: Y = L^{1/3} and MPL= 1/3L^{2/3} Use levels of labor equal to 10, 11 and 12 to show that this function exhibits diminishing marginal returns to labor. Clearly use
- Why is it sensible to assume that the production function exhibits constant returns to scale and diminishing returns to capital?
- 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
- 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.
- 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
- For each of the following production functions, determine if the technology exhibits increasing, decreasing, or constant returns to scale. A) f(L,K) = 2L + K B) f(L,K)= L+ K C) f(L,K) = LK + L + K
- 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
- 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
- Consider the following production functions: 1. Q=9L+3K 2. Q=10 K0.6L0.4 3. Q=10 min (K, 2L) Which of these production functions exhibits constant returns to scale?s: 1. Q = 9L + 3K 2. Q = 10 K0.6L0.4 3. Q = 10 min (K, 2L) Which of these production functi
- 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
- Given the following production functions, test if they exhibit constant returns to scale. Be sure to mathematically prove your answer and show your work. A) Y = 2K + 15L B) Y = 2(K + L) ^0.5 C)
- The marginal product of capital _____ as additional units of capital are added, holding the labor force constant, causing the production function to become _____. a. increases; steeper b. increases; flatter c. decreases; steeper d. decreases; flatter
- Consider the production function Q = (0.5K^{1/3} + 0.5L^{1/3})^3 . a. Prove that this production function exhibits constant returns to scale. b. Suppose the firms want to minimize the cost of produc
- Derive the steady state capital per effective worker and output per effective worker given the production function Y =F(K,AN) where the saving rate is s, the depreciation rate is , the growth rate of
- Suppose an economy has the following production function, Y = K^{1/3} (AL)^{2/3}. Furthermore, suppose that that the growth rate of capital is 3%, the growth rate of the population is 4% and the growt
- 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
- Does the production function: q = 100L - 20/k exhibit increasing, decreasing, or constant returns to scale?
- Assume that the aggregate production function for an economy is described by: where 0 < a < 1. a. Show the production function has the property of constant returns to scale. b. Obtain the per capita
- 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
- Suppose that the production function for output in an economy is given by 2.\sqrt{N}.\sqrt{K} The number of workers, N, is constant. The saving rate is s, and the depreciation rate of physical capital
- The production function takes the following formY = F(K,N) = zK^0.3N^0.7 (a) Write the expressions for marginal product of labor and marginal product of capital.
- 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
- Consider the following production function: Q = F(L, K) = L^4 * K^7. A) Does this production function exhibit diminishing or increasing marginal rate of technical substitution of labor for capital? Show your work. B) Find the elasticity of substitution fo
- Consider an economy described by the following production function: Y(K,L) = K^{0.4}L^{0.6} And the depreciation rate is 10 percent. What is the per worker production function? Assume that the L is
- Suppose a country has the following production function: Y = F(K, L) = K0.4L0.6. Does this production function have constant returns to scale? Explain.
- In order to use the Solow growth model, putting production functions in per-worker tersm, when all inputs used in production are increased by 2%, output must equal: A - increase by 2% or more B - in
- 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
- 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 an economy described by the production function: Y = F (K, L ) = K1/3L2/3. (a) Find the steady-state capital stock per worker as a function of the savings, population growth, rate of technol
- Consider the production function: f(L;K) =L+K(LK)^2= 1 f(L;K)has diminishing MPL and diminishing MPk, but does not have diminishing MRTS. Provide the evidence for this function. Consider the isoquant