# Give an example of a production function that exhibits increasing returns to scale and...

## Question:

Give an example of a production function that exhibits increasing returns to scale and diminishing marginal product of labor at the same time. Prove that the function has these properties.

## Production Function:

Production Function shows the relationship between the inputs used in the production with the outputs of the production. The production function is a functional mathematical relationship between the factors and the output of production.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answerOne example of a production function which shows increasing returns to scale and diminishing marginal product of labor will be :

Y = 10 * L^0.5...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search 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

- Show that increasing returns to scale can co-exist with diminishing marginal productivity. To do so, provide an example of a production function with IRTS and diminishing marginal returns.
- 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
- 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
- For each production function below, determine: (1) Whether there are diminishing marginal returns to labor in the short run, and (2) the returns to scale. 1. f(L, K) = 2L + 3K 2. f(L, K) = 4LK 3. f(L, K) = min{L, K}
- Suppose that the production function z F(K, N) exhibits increasing returns to scale, to the extent that the marginal product of labour increases when the quantity of labour input increases. Given this production function, what will be the representative f
- Consider the following production function F(K, L) = { KL } / {K + L } (a) Does it satisfy the Constant Returns to Scale Assumption? Explain. (b) Are marginal products diminishing? Explain. (If you can't find marginal products mathematically, you can com
- 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.
- Graphically derive a marginal product of labor function from a total product function for a firm that experiences an increasing rate of returns (faster than proportional) up to an output of 60 units o
- According to the law of diminishing returns, over some range of output: a. Every production function exhibits diminishing returns to scale. b. Total product will decrease as the quantity of variable input employed increases. c. Marginal product will event
- 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?
- A firm has the production function: q = 10L^{0.5}K^{0.5}, the price of labor is w = 10 and the price of capital is r = 20 a) demonstrate that this function has constant returns to scale. b) derive the short-run marginal and average variable cost functio
- Does the production function q=100L- {50}/{K} exhibit increasing, decreasing, or constant returns to scale? This production function exhibits ____ returns to scale.
- If the production function for a certain good exhibits constant returns to scale, does this mean that the law of diminishing marginal returns does not apply?
- 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
- A firm has the production function f(x, y) = x^1.40y^1. This firm has: a. decreasing returns to scale and diminishing marginal products for factor x. b. increasing returns to scale and decreasing marginal product of factor x. c. decreasing returns to scal
- 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.
- Diminishing marginal returns means that: a. as more capital is used in production, but the labour input is held constant, MPK falls. b. as labour increases and capital decreases for a given level of output, the marginal product of labour divided by the
- MARGINAL PRODUCT IS BETWEEN ROWS (32 IS BETWEEN ROW 3 AND 4) A) Does the production function exhibit diminishing marginal returns? B). If so, where do they "set in"? C) Intuitively, what will happe
- The production function of an economy is: Y = A * K^{0.3} * H^{0.7} a. What is real output when K = 20, H = 50 and A = 2? b. Does this production function exhibit diminishing marginal productivity of capital? Calculate MPK if K increases from 50 to 60 a
- The concept of the production function implies that a firm using resources inefficiently will: A. obtain more output than the theoretical production function shows. B. not be subject to diminishing marginal product. C. obtain exactly the amount that the
- 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
- Define returns to scale. Ascertain whether the given production function exhibit constant, diminishing, or increasing 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.
- 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.
- 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
- Suppose that aggregate production function in a particular economy is given by Y = (N/ 60) [5080 - N], where N is the size of the labor force. Show formally that the production function exhibits a diminishing marginal product of labor. Begin by providing
- Increasing marginal returns to labor: a. occur only when there are increasing marginal returns to capital. b. are the result of specialization and division of labor in the production process. c. describe the portion of a total product curve where the marg
- The law of diminishing marginal returns (a) does not hold when the marginal product is always positive (b) has to hold when an additional unit of capital produces more extra output than an additional unit of labor (c) has to hold when increasing 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
- For a production function with a diminishing, but positive, marginal product of labor: a. Output increases at an increasing rate as more workers are employed. b. Output increases at a decreasing rate as more workers are employed. c. Output declines as
- Suppose that a firm's production function is given by Q = K^0.33L^0.67, where MPK = 0.33K - 0.67L^0.67 and MPL = 0.67K^0.33L - 0.33. As L increases, what happens to the marginal product of labor? What
- 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 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
- Solow-function transformations Y_t=K_{t}^{a}(A_tL_t)^{1-a} K_{t+1}=(1-delta)K_t+I_t I_t=S_t=sY_t a. Show that the production function above has returns to scale. b. Transform the production function i
- A firm's production function is given by q = f(L, K) = LK + 2L^2 K - L^3. Suppose the firm is operating in the short-run with K = 9. A) What is the marginal product of labor function? B) For what values of labor does increasing marginal product exist? C)
- 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
- 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
- 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
- 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?
- 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
- When an economy faces diminishing returns: A) the slope of the per-worker production function becomes flatter as capital per hour worked increases. B) the per-worker production function shifts to the left. C) the per-worker production function shifts to t
- Consider a production function of the form: q = L^.5 K^.6 Determine the elasticity of output with respect to labor and the elasticity of output with respect to capital. Show that marginal products
- The principle of diminishing returns doesn't apply to labor in the long run because: a. a firm can build an additional production facility, so each worker's share of the facility doesn't necessarily decrease. b. eventually the marginal product of labor wi
- Explain how a firm's production function is related to its marginal product of labor.
- The production function Y = (X^2)*(X^{0.5}) has returns to scale. a. increasing b. marginal c. decreasing d. constant
- 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
- Marginal utility: a. is the extra output a firm obtains when it adds another unit of labor b. explains why product supply curves slope upward c. typically rises as successive units of a good are consumed d. is the extra satisfaction from the consumption o
- If output is produced with two factors of production and with increasing returns to scale, a) there cannot be a diminishing marginal rate of substitution. b) all inputs must have increasing marginal products. c) on a graph of production isoquants, moving
- How does a diminishing marginal product affect the shape of the production function? a. The slope of the production function increases as the quantity of input increases. b. The slope of the production function becomes more positive with diminishing margi
- Determine whether this production function exhibits increasing, decreasing, or constant 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?
- The production function: a. is an economic relationship between revenue and cost. b. always shows increasing marginal product of labor. c. shows the relationship between input prices and amount of input used. d. shows the maximum level of output for a giv
- The production function for a product is given by q = K1/2L1/4 where K is capital, L is labor and q is output. a. Find the marginal products of labor and capital. b. Is the marginal product of labor increasing or decreasing with labor? Is the marginal p
- The marginal product of capital {Blank} as additional units of capital are added, holding the labor force constant, causing the production function to become {Blank}. A. increases; steeper B. increases; flatter C. decreases; steeper D. decreases; flatter
- The production function is the: a.) increase in the amount of output from an additional unit of labor. b.) marginal product of input times the price of output. c.) relationship between the number o
- 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.
- A firm's production is given by: q = 5L^{2/3} K^{1/3} (a) Calculate APL and MPL. Determine if the production function exhibits the law of diminishing marginal returns. Calculate the output (production) elasticity with respect to labor. (b) Calculate MRTS.
- What happens with no diminishing returns? Consider a Solow model where the production function no longer exhibits diminishing returns to capital accumulation. More specifically assume that the product
- 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
- Draw a graph and provide 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.
- A production function with constant returns to scale for capital alone implies that: A. there are increasing returns to scale for all factors of production taken together. B. if all inputs are doubled then output will more than double. C. technological ad
- 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
- If a firm doubles its usage of all inputs and output also doubles, the production function is said to exhibit: a. increasing returns to scale. b. decreasing returns to scale. c. constant returns to scale. d. increasing marginal returns to a fixed factor o
- Suppose a firm's production function is given by f(k,l) = kl - 0.8k^2 - 0.2l^2 1. Fixing capital at k = 10, graph the marginal physical product of labour (MP_l), as a function of l. At what l does MP
- 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
- Suppose the production function is given by Y=AK^{1/3}L^{2/3} (a) What is the marginal product of capital given the production function? (b) Given your answer to part (a), why might an investor exp
- 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
- 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
- If a firm doubles its usage of all inputs and output more than doubles, the production function is said to exhibit: a. increasing returns to scale. b. decreasing returns to scale. c. constant returns to scale. d. increasing marginal returns to a fixed fac
- Consider the linear production function q=f(K,L)=2L+K . a. What is the short-run production function given that capital is fixed at K=100? b. What is the marginal product of labor?
- In the case of one variable input, complete the following table and explain whether this production function exhibits diminishing marginal product of labor.
- Suppose a firm's production function is given by Q= L^1/2 * K^1/2.The marginal product of labor and the marginal product of capital is given by: MPL= K^1/2 /2L^1/2 and MPk= L^1/2/2K^ 1/2. Suppose the price of labor is w = 24 and the price of capital is r
- 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
- 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
- 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
- The law of diminishing marginal product states that: a. Successive equal-sized increases in a fixed factor of production added to variable factors of production will result in smaller and smaller increases in output, b. Successive equal-sized increases i
- The production function for a firm is given by q = L^{.75} K^{.25} where q denotes output; Land K labor and capital inputs. (a) Determine marginal product of labor. Show whether or not the above production function exhibits diminishing marginal produ
- Determine whether the production function T(L, K)=10L+2K, yields an increasing or decreasing returns to scale or a constant returns to scale.
- Suppose a firm has a production function given by Q = L*K. Does this production function exhibit increasing, constant or decreasing returns to scale?
- The production function for cups uses a variable amount of labor and a fixed a mount of capital to produce output. The production function exhibits diminishing returns to labor. Suppose the techonology in producing cups improves. Show how this will affect
- Suppose a firm's production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = (K^1/2)/(2L^1/2), and MPK =(L^1/2)/(2K^1/2). a) S
- 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
- The law of diminishing returns assumes: a) There are no fixed factors of production. b) There are no variable factors of production. c) Utility is maximized when marginal product falls. d) Some factors of production are fixed.
- 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 a firm doubles its usage of all inputs and output less than doubles, the production function is said to exhibit: a. increasing returns to scale. b. decreasing returns to scale. c. constant returns to scale. d. decreasing marginal returns to a fixed fac
- 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
- 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
- The law of diminishing returns implies that, with the use of capital fixed, as the use of labor rises, A. the marginal product of labor will fall eventually. B. total product will fall eventually. C. the production process will become technologically inef
- The marginal product of labor in manufacturing slopes downward because of: A. diseconomies to scale B. discontinuities in the production function C. diminishing returns D. gross substitution with the food sector E. None of the above.
- Explain how a firm's production function is related to its marginal product of labor. Use Samsung as an example.
- 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
- State whether the following production functions exhibit decreasing returns to scale, increasing returns to scale or constant returns to scale, briefly explain.
- Consider the following short-run production function: q = 4L2 - (2/3)L3. a. At what level of L do diminishing marginal returns begin? Show your derivation. b. At what level of L do diminishing returns begin? Show your derivation.