# A firm has the following production function: Q = 7*K1/2*L1/2a) Calculate the amount of output...

## Question:

A firm has the following production function: {eq}Q=7*K^{\frac{1}{2}}*L^{\frac{1}{2}} {/eq}

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 has 15 units of capital. How much labor will it need to hire?

c) Suppose that a unit of capital costs $50, and a unit of labor costs $20. What is the cost of producing that quantity in part a) and in part b)?

## Production Function:

The production function of a firm represents the relationship between the factors of production employed and the resultant output produced in production activity. It is a mathematical function that allows the calculation of the units of a good or service which can be produced using a certain combination of factor inputs, primarily labor and capital.

## Answer and Explanation: 1

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

View this answer**Ans. a)**

To calculate the output expected when the firm uses 25 units of capital and 50 units of labor, we will substitute the values in the...

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 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

- 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 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 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
- A firm has carefully estimated its production function to be: Q = K^0.4L^ 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%,
- 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
- 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
- Consider a firm that uses labor (L) and capital (K) to produce a general output (q) using the following production function: \\ q = K^{0.9}L^{0.1} \\ The firm seeks to produce q = 60 units for sale and faces prices for labor of w = 5 and capital of r = 6.
- 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.
- A firm has the following production function: Q = 50K + 20L. Each unit of capital costs $4 to employ and each unit of labor costs $1 to employ. Labor and capital are this firm's only costs of production. The firm is currently producing 250 units of output
- 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
- 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
- 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 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
- 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
- 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
- Suppose that a company produces output according to the following production function: Q = 0.5L^2 a) Define and calculate the marginal product of labor. b) Define and calculate the average product of
- Suppose you have the following production function: Q = L^25 K^75, where Q is production, L is the amount of labor used in production, K is the amount of capital. The marginal product of labor is mathematically defined as: partial Q/ partial L. If K is fi
- 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
- Production A firm has the following short-run production function:Q = 50L + 6L^2 = 0.5L^3 Where Q = Quantity of output per week and L = Labor (number of workers)
- 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 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
- 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
- Suppose a production function for a firm takes the following algebraic form Q = 4KL - 0.3L^2, where Q is the output of sweaters per day. Now suppose the firm is operating with 7 units of capital (K = 7) and 9 units of labor (L = 9). What is the output of
- 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
- 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
- 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
- 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 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
- 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?
- 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,
- Assume that a firm's long-run average total cost (ATC) is constant. Which of the following functions, where Q is output; L is labor input; K is capital input, is more likely to represent the firm s production? Please explain briefly about your choice. (a
- 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
- 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
- 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 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
- 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
- Calculate a firm's labor demand for the following production functions. Assume that output is 100 and the rental cost of capital is 1. In each of the following cases, calculate the amount of labor
- 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
- 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
- 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 has the following short-run production function: Q = 50L + 6L2 - 0.5L3, where Q = quantity of output per week, L = labor (number of workers). \\(a.) When does the law of diminishing returns tak
- 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 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
- 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
- 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
- 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
- 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 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
- 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
- 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
- Firm GHI Corp. has the following short run production function: Q = 60 * L + 6 * L^2 - 0.5 * L^3 Where Q is output, and L units of labor input. At how many unit of labor input does the law of dimini
- 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
- 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
- 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?
- 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 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
- Consider a profit-maximizing firm that uses labor, L, as an input to produce its output, Q, according to the production function Q = L^1/2. Labor is paid an hourly wage w. The firm's total revenue is
- A firm's production function Q = 20L^{0.5}K^{0.4}. Labour costs $100 per unit and capital costs $100. The firm sets a production target of 100 units. a. Show or explain whether the production function
- 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^
- 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
- 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
- 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 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
- A firm's production process uses labor, L, and capital, K, and materials, M, to produce an output, Q according to the function Q= KLM, where the marginal products of the three inputs are MP_L= KM, MP_K = LM, and MP_M= KL. The wage rate for labor is w = 2
- 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
- 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?
- 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?
- The production function of a company is given by the following expression: q (K;L) = 10K^{1/3} . L^{3/4} In short term there s only 9 units of capital (K = 9). The price per unit of capital is 8 and the price each unit of work is 5. Get the cost fun
- 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
- A firm has the following production function: Q=2K L. Capital is fixed at 16 units. (a) calculate the average product of labor when 16 units of labor are utilized (b) calculate the marginal product
- 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
- Assume a firm has a production function Q = 2 S L 5 K 5 and the price of labor is $3 and the price of capital is $12. a) What is the minimum cost of producing 1,250 units of output? b) Now show t
- Assume a firm has a production function Q = 25 L 5 K 5 and the price of labor is $3 and the price of capital is $12. a) What is the minimum cost of producing 1,250 units of output? b) Now show tha
- Production function: Q = f(L,K) = L sqrt{K}. Supposed that the firm operates in the short run with 16 units of capital. a. Obtain the firm's short-run production function. b. Obtain the firm's average product (AP). c. Obtain the firm's marginal product (M
- Suppose you are given the following production process: labor capital output MPL MPK APL APK VMPL VMPK 08 18 210 310 512 812 1412 where the Production Function is Q =L^1/2 K^1/2, where Q is output; L,
- 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 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).
- 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)''.
- 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
- 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.
- Using the production function (ie: q = (K^{1/2} + L^{1/2})^2) suppose that the firm is now operating in the long-run. a) Solve for the long-run cost function (i.e. total costs as a function of input
- 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 the production function for a competitive firm is Q = K^.75L^.25. The firm sells its output at a price of $32 and can hire labor at a wage rate of $2. Capital is fixed at 1 unit. a. What is the profit-maximizing quantity of labor? b. If the price
- 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
- 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
- If a firm's production function has the form Q=A*K \alpha L\beta, where Q is total output, K is capital, and L is labor, then a change in which of the following is an indicator of technical progress?
- 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?
- A firm has the following short-run production function: Q = 50 L + 6 L^2 - 0.5 L^3, where Q = quantity of output per week, L = number of workers employed. A) When does the law of diminishing returns take effect? B) Calculate the range of values for labor
- 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?
- 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
- Suppose in the short run a firm's production function is given by Q = L^(1/2) x K^(1/2), and that K is fixed at K = 9. 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
- A factory produces output (Q) using capital (K) and labor (L) according to the production function Y(K,L)=K^{1/5}L^{4/5}. Let r denote the price per unit capital, and w denote the price per unit labor, so that the total expenditure on these factors is r_K
- 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?
- Let L represent the amount of labor that a firm employs and let Q represent the quantity of the firm's output. The firm's production function is: Q = f(L) = 100 \ln(2L + 1). a. Let z = 2L + 1. Then Q = 100 \ln(z). Use the chain rule for derivatives to to
- Suppose a firm has a production function given by Q = L1/2K1/2. The firm can purchase labor, L, at a price w = 8, and capital, K, at a price of r = 2. a) What is the firm's total cost function, TC(Q)? b) What is the firm's marginal cost of production?
- Let L represent the number of workers hired by a firm, and let Q represent that firm's quantity of output. Assume two points on the firm's production function are (L=6, Q=147) and (L=7, Q=174). The ma
- 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 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 capital is fixed at 4 units in the production function Q = KL. Draw the total, marginal, and average product curves for the labor input.