A firm has carefully estimated its production function to be: Q = K^0.4L^ 0.6 , where Q = units...
Question:
A firm has carefully estimated its production function to be: Q = K0.4L 0.6 , where Q = units of output, K = units of capital, and L = units of labor. If both capital and labor were increases by 10%, how much would output increase (in percentage terms)? What sort of returns to scale does the firm face? Explain.
Returns To Scale:
The term "returns to scale" refers to the way in which a firm's output changes as its inputs change by equal percentages. If a firm increases all its inputs by the same percentage and the change in its output is less than proportional, then the firm experiences decreasing returns to scale. If the change in output is more than proportional, the firm experiences increasing returns to scale. Finally, if the change in output is proportional, the firm experiences constant returns to scale.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerAnswer: The firm faces constant returns to scale.
Given:
- {eq}Q = K^{0.4}L^{0.6} {/eq}
Our task here is to determine the percentage change in output...
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:
Get access to this video and our entire Q&A library
Returns to Scale in Economics: Definition & Examples
from
Chapter 3 / Lesson 71
225K
Understand 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
- Suppose that the production function of a firm is given by the equation Q = 2K1/2L1/2, where Q represents units of output, K units of capital, and L units of labor. What is the marginal product of labor and the marginal product of capital at K = 40 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
- A firm has the production function: Q = 30 + 10 L + 5 K^2 - 5 K. If the firm has 4 units of capital (K) they plan to use, how much labor is needed to produce 300 units of output?
- Suppose the production function is given by Q = 5 K + 3 L. What is the average product of capital when 10 units of capital and 10 units of labor are employed? a) 5. b) 8. c) 3. d) 30.
- A firm estimates its long-run production function to be Q = -0.0050K^3L^3 + 15K^2L^2. Suppose the firm employs 10 units of capital. At units of labor, marginal product of labor begins to diminish. a. 66.67 b. 100 c. 150 d. 200 e. 1000
- A firm's production function is given by Q=2L^1}/{2+4K^1}/{2 }] where Q, L, and K denote the number of units of output, labor, and capital, respectively. Labor costs are $2 per unit, capital
- The long-run production function for widgets is: Q=L^.6K^.4, where Q is total output, L is the quantity of labor employed, and K is the physical quantity of capital in place. a. Determine the short-run production function, if capital is fixed at 240 units
- Suppose a firm's production function is given by Q = LK^2. Suppose the firm is producing 16 units of output by using 1 units of Labor and 4 units of Capital. What is the slope of the isoquant at this
- A firm's production function is given by the equation Q=10K0.3L0.7 where Q represents units of output, K units of capital, and L units of labor. a. What are the returns to scale? b. What is the output elasticity of labor?
- A firm has the following production function: Q = 7*K1/2*L1/2a) Calculate the amount of output the firm should expect if it uses 25 units of capital and 50 units of labor. b) Suppose the firm wants to produce the same amount of output from a), but only h
- A firm production function is given by q(l,k) = l^{0.5}k^{0.5}, where q is number of units of output produced, l the number of units of labor input used and k the number of units of capital input used
- Suppose that a production function of a firm is given by Q= min{2L,K}, where Q denotes output, K capital, and L labor. Currently the wage is w=$10, and the rental rate of capital is r=$15. a. What is the cost and method of producing Q=20 units of capital
- Suppose the production function is q = 12L0.25K0.75. Determine the long-run capital-to-labor ratio \frac{K}{L} if the cost of a unit of capital ''(r)'' is three times the cost of a unit of labor ''(w)''.
- Suppose the production function is q = 12 L^{0.25} K^{0.75}. Determine the long-run capital-to-labor ratio (K/L) if the cost a unit of capital (r) is three times the cost of a unit of labor (w).
- A production function Q = 100 L 0.4 K ? 0.6 relates to output, Q, to the number of labour units, L, and capital units K. A) Derive the equation for the marginal and the average products of labour an
- The production function is given by Q = K^1/4L^1/4. a. Derive the marginal product of capital. Consider a production manager who must produce 200 units. b. Given this, express labor in terms of the needed output (200) and capital (K). c. From this, derive
- Capital and labor, denoted by K and L restively, are used to produce output denoted by q, so firm's production function is equal to q = min {K, 2L} The price of capital is $5 and the price of labor is
- A firm produces according to the following production function: Q = K^{0.5}L^{0.5} where Q = units of output, K = units of capital, and L = units of labor. Suppose that in the short run K = 100. Moreover, wage of labor is W = 5 and price of the product is
- Suppose a firm with a production function given by Q = 30K^0.5L^0.5 produces 3,000 units of output. The firm pays a wage of $40 per unit and pays a rental rate of capital of $640 per unit. How many units of labor and capital should the firm employ to mini
- Suppose a firm with a production function given by Q = 30 K^{0.5}L^{0.5} produces 1,500 units of output. The firm pays a wage of $40 per unit and pays a rental rate of capital of $640 per unit. How many units of labor and capital should the firm employ to
- A firm has a production function Q = F(K,L) with constant returns to scale, where K is units of capital and L is units of labour. Input prices are r = $2 per unit of K and w = $1 per unit of L. When i
- Suppose a firm with a production function given by Q = 30 K^{0.5}L^{0.5} produces 1,500 units of output. The firm pays a wage of $40 per unit and pays a rental rate of capital of $640 per unit. How
- Consider a firm with the production function f(L,K)=L^{1/5}K^{4/5}. Assume that the price of capital r=3 and the price of labor w=2. If L^* and K^* are the amounts used by the firm to produce q units of output when both L and K are variable, then what is
- Consider a firm with production function f(L,K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the average cost of producing q units is what?
- A firm can manufacture a product according to the production function Q = 2(K)^{\frac{1}{2(L)^{\frac{1}{2 where K represents capital equipment and L is labor. The company has already spent $10,000 on the 4 units capital. a. Calculate the average pro
- A firm has the following production function: Q = 7*K1/2*L1/2 a) Calculate the amount of output the firm should expect if it uses 25 units of capital and 50 units of labor. b) Suppose the firm wants to produce the same amount of output from a), but only h
- Suppose that a firm's production function is q = 10L1/2K1/2. The cost of a unit of labor is $20 and the cost of a unit of capital is $80. a. Derive the long-run total cost curve function TC(q). b. The firm is currently producing 100 units of output. Find
- A firm's production function is given by Q = 2L - L^2 + K. The price of labor is w > 0 and the price of capital is r > 0. Assuming the firm uses both labor and capital, derive the long-run total cost function.
- A. Suppose that a firm's production function is Q = 2L^0.5K^0.5, Derive the isoquant associated with Q = 12 units of output. B. If L = 1, what must K be in order to produce Q = 12 units of output? C
- Consider a firm with production function f(L,K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the variable cost of producing q units is what?
- Assume that a firm's production function Q = K1/2L1/2. Assume that the firm currently employs 200 units of capital and 100 units of labor. Determine the Average Product of Capital, Average Product of Labor, Marginal Product of Capital, and Marginal Produ
- Suppose a firm's production function is Q = 4K0.5 L0.5. Its level of capital is fixed at 4 units, the price of labor is PL = $16 per unit, and the price of capital is PK = $20 per unit. The firms aver
- A firm uses labor, denoted by L, and capital, denoted by K, to produce skateboards, denoted by q. The firm's production function is q = K^{1/2}L^{1/2}. The price of capital and labor are both equal to
- 1. Suppose that a firm's production function is q = 10L^{1/2}K^{1/2}. The cost of a unit of labor is $20 and the cost of a unit of capital is $80.a. If the firm wishes to produce 100 units of output,
- A firm produces according to the following production function: Q = k^.5L^.5 where q = units of output, k = units of capital, and L= units of labor. suppose that in the short run k = 100. Moreover, the wage of labor is w = 5, and the price of the produ
- Suppose the production function is given by Q = 3K + 4L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?
- Suppose a production function is given by Q = 4K + 3L. What is the marginal product of capital when 10 units of capital and 10 units of labor are employed?
- A firms production function is given be Q=f(L,K)=L^1/2K^1/2. The prices of labor (w) and of capital (r) are $2.5/unit and $5/unit, respectively. Suppose that the firm has a capital employment of 25 un
- If the production function is Q = K^{1/2} L^{1/2} and labor is fixed at 36 units, then the average product of capital when k = 25 is?
- Consider a firm with production function f(L,K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the average fixed cost of producing q units is what?
- A firm has a production function given by Q = 10(K^{.25})(L^{.25}). Suppose that each unit of capital costs R and each unit of labor costs W. a.) Derive the long-run demands for capital and labor. b.) Derive the total cost curve for this firm. c.) Deri
- Suppose the production function is given by Q = 2K + 5L. What is the marginal product of labor when 15 units of capital and 10 units of labor are employed?
- Suppose that a firm that produced buttons had a production function given by q = 4L^{0.5}K^{0.5}. The firm has 16 units of capital in the short run. Determine the amount of labor required to produce 64 units of output.
- Suppose a firm with a production function given by Q = K^{0.25}L^{0.75} produces 1,500 units of output. The firm pays a wage of $50 per unit and pays a rental rate of the capital of $50 per unit. To produce 1,500 units of output, the firm should use: a. 1
- 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 a firms production function is Q = 2K0.5 L0.5. Its level of capital is fixed at 9 units, the price of labor is PL = $12 per unit, and the price of capital is PK = $10 per unit. The firms avera
- A firm is producing output Q using a mix of capital K and labor L. The production function is given by . A unit of capital costs $3 and a unit of labor costs $9. The firm wants to minimize the total c
- Suppose that a firm's production function is q = 10L^{0.5}K^{0.5} . The cost of a unit of labor is $10/hour and the cost of capital is $40/hour, and the firm is currently producing q=1000 units
- Suppose the production function is Q = 20(K^0.5 L^0.5) and the value of capital is 100. A.) Calculate the total product for the following values of labor input: 1, 5, 10, 20, 40, 50, 80, 100, 150, 200
- 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
- How much labor does a firm require to produce q = 1000 when capital is fixed at 5 and they have a production function equal to q = 200L0.5K0.5? a. L = 200 b. L = 2.5 c. L = 5 d. L = 2.25
- 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?
- Assume that a firm produces 90 units of output Q using 9 units of labor and 9 units of capital (K). The firm's technological possibilities can be represented by the production function q = 10 L^1/2 K^
- 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
- A firm produces output according to a production function: Q = F(K,L) = min {6K,6L}. How much output is produced when K = 2 and L = 3? If the wage rate is $60 per hour and the rental rate on capital i
- A firm produces Q = K^{1/2}L^{1/4} units of its output good when it uses K units capital and L units of labor. The firm sells its output at the price of $16 per unit of output; it pays $4 per unit of capital and $2 per unit of labor. a. Is Q homogenous in
- Suppose a firm with a production function Q = KL is producing 125 units of output by using 5 workers (L) and 25 units of capital (K). The wage rate (W) per worker is $10 and the rental rate (price) pe
- A firm's product function is Q = 5L^{0.5}K^{0.5}. Labor costs $40 per unit and capital costs $10 per unit. K = 16 in the short run. Suppose the production of a firm is Q = 5 + 2K + L. Which of the following statements is correct? A. The firm's production
- Firm Alpha uses capital K and labor L to produce output q. The firm's production function is F(K,L)= 5K^{0.4}\times L^{0.6}. The prices of capital and labor are r = 4 and w=4, respectively. Moreover,
- Suppose capital is fixed at 4 units in the production function Q = KL. Draw the total, marginal, and average product curves for the labor input.
- Suppose the production function for a firm is given by q = 4L0.75K0.25. If the firm currently has 10 units of capital (K) and 10 units of labor (L), then calculate the marginal rate of technical substitution (MRTSLK).
- Suppose a firm's production function is given by the equation Q = 12L^.5K^.5 . This firm operates in the short run where capital (K) is fixed at a quantity of 16. If the price per unit of the good is $1.9 and labor costs $10 per unit. Then the profit-maxi
- Starting with the general production function Q=FK,L, which states that output Q is a function of or depends on the quantity of labor L and capital K used in production, derive the expression for the
- A firm has the production function q = 0.2LK + 5L^2K - 0.1L^3K. Assume that K is fixed at 10 in the short run. A. What is the short-run production function? B. What is the marginal product of labor and the average product of labor in the short run? C. Whe
- A firm produces a product with labor and capital. Its production function is described by Q = 2L + 3K. Let w and r be the prices of labor and capital, respectively. (a) Find the equation for the firm's long-run total cost curves as a function of quantity
- The production function for a certain firm is given by Q = 20K^(0.7)L^(0.3), where Q is the firm's annual output, K is the firm's capital input and L is the firm's labor input. The price per unit of c
- Suppose in the short run a firm's production function is given by Q = L1/2K1/2, and K is fixed at K = 36. If the price of labor, w = $12 per unit of labor, what is the firm's marginal cost of production when the firm is producing 48 units of output?
- Suppose the following production function: Q = 10 (K)^{1/3} (L)^{2/3} subject to; W *L + r * K = Cost. a. Suppose that K the amount of capital is K = 8. If this company hires 64 workers (L), calculate the value of Q. b. Determine if this production func
- The following cubic equation is a long-run production function for a firm: Q= -0.0032K^3L^3 + 8K^2 L^2 where Q is the number of units produced per year. Suppose the firm employs 25 units of capital.
- Suppose the production function is Q = 20(K^0.5 L^0.5) and the value of capital is 100. A.) Calculate the total product for the following values of labour input: 1, 5, 10, 20, 40, 50, 80, 100, 150, 2
- Suppose the production function for a firm is given by q = 4L + 2K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the marginal rate of technical substitution (MRTSLK).
- Suppose the production function for a firm is given by q = 8L + 2K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS_(LK)).
- If the production function is Q = K^(1/2) L^(1/2) and capital is fixed at 100 units, then the marginal product of labor (MPL) will be?
- A firm has a production function F(L,K), where K is a fixed amount of capital, and L is the variable amount of labor hired. The equation w= pF_{L}(L,K) determines the amount of labor that the firm hir
- Consider the production function: Q = 12L - 2L^2 where Q is quantity of output, and L is labor. What is the average product?
- Suppose a firm's short-run production function is given by Q = 4L^{0.8}. If the production function is Q = L^{0.8} K^{0.2}, how many units of capital is it using?
- The long-run production function for a firm's product is given by q = f(K; L) = 5 K L. The price of capital is $10 and the price of labor is $15. a. Suppose the firm wishes to produce an output of 500. List 5 combinations of capital and labor that the fi
- Suppose a firm can use either capital (K) or labor (L) in a production process. The firms production function is given by Q = 5L + 15K. The price of capital is $20 per unit and the price of labor is $8 per unit. a. What is the firm's total cost function?
- Suppose that a firm's short-run production function has been estimated as Q = 2L + 0.4L2 - 0.002L3, where Q is units of output and L is labor hours. a. What is the firm's marginal product of labor equation? b. What is the firm's average product of labor e
- Suppose a firm with a production function given by Q = K0.25L0.75 spends $6000. The firm pays a wage of $30 per units and pays a rental rate of capital of $10 per unit. The maximum output that can be
- A firm's product function is Q = 5L^{0.5}K^{0.5}. Labor costs $40 per unit and capital costs $10 per unit. K = 16 in the short run. Suppose the production function of a firm is Q = 5 + 2K + L. Which of the following statements is correct? A. The firm's LA
- In the production function, Q = 10L1/2 K1/2. Calculate the slope of the isoquant when the entrepreneur is producing efficiently with 9 laborers and 16 units of capital. (Hint: The slope of the isoquant = the ratio of the marginal product of labor to the m
- If the aggregate production function of firms in an economy is Q=F(L,K). Where L is labor employed and K is the quantity of capital in the economy, with Q as output, with the usual properties, includi
- Suppose that a firm's production function is q = 5x^{0.5} in the short run, where there are fixed costs of $1,000, and x is the variable input whose cost is$1250 per unit. The total cost of producing a level of output q is C(q) = 1,000 + \frac{1250q^2}{25
- Suppose a firms production function is Q = 0.2K0.5 L0.5. Its level of capital is fixed at 25 units, the price of labor is PL = $8 per unit, and the price of capital is PK = $4 per unit. The firms aver
- A firm produces output according to a production function: Q = F(K,L) = min {3K,6L}, where K is capital, and L is labor. a) How much output is produced when K = 2 and L = 3? b) If the wage rate is $55
- A firm employs labor L and capital K = 10 to produce using the production function q = 60K^2L^2 - K^3L^3. Derive the total product of labor curve.
- Output is produced according to Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. The price of K is $10 and the price of L is $5. Determine the cost minimizing co
- 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
- Assume that a firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. Given that the production function is given by: Q = 10L - L^2+ 60K -1.5K^2, where Q is total output, L is labor, and K is c
- A manufacturing firm's production function is Q = KL + K +L. For this production function, MPL = K + 1 and MPK = L + 1. Suppose that the price r of capital services is equal to 1, and let w denote the price of the labor services. If the firm is required t
- Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firms Production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of Labor is $
- Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firm's Production function is given by Q = 5L+ 15K. The price of Capital is $20 per unit and the price of Labor is
- A firm produces output according to a production function: Q = F(K,L) = min(4K,4L). a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $50 per hour and the rental rate on capi
- Suppose a firm's production function is Q = 2K0.5L0.5. If the level of capital is fixed at 25 units, then what is the firm's short-run production function?
- A firm produces output according to a production function: Q = F(K,L) = min(6K,6L). a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $35 per hour and the rental rate on capi
- A firm produces output according to a production function: Q = F(K,L) = min(9K,3L) a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capit
- A firm produces output according to the production function Q = F(K, L) = 4K + 8L. 1. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing capital and labor for producing 32 units of output? 2. If th
- A firm has the production function Q=K^(0.1)L^(0.9), where Q measures output, K represents machine hours, and L measures labor hours. Suppose that the wage rate is $45 and the firm wants to produce 10
- A firm produces according to the following production function: Q = K0.25L0.75. The price of K is $4 per unit, and the price of L is $6 per unit. a. What is the optimal capital/labor ratio? b. Derive the amount of capital and labor required to produce 400
Explore our homework questions and answers library
Browse
by subject