Suppose a factory produces 120 units of output per month and it is deciding how much labor and...
Question:
Suppose a factory produces 120 units of output per month and it is deciding how much labor and capital it should hire. If labor costs $230 per unit and capital costs $440 per unit, which combination of labor and capital should the firm use to produce the 120 units of output?
Labor capital mix
Almost every firm has to choose its labor capital mix when deciding how to organize its production. The key considerations are cost of labor and capital and their relative productivities.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerOutput is 120 units per month. Labor cost is 230 per unit of labor and capital cost is 440 per unit of capital.
We will assume L units of labor and C...
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
Using the Production Possibility Curve to Illustrate Economic Conditions
from
Chapter 3 / Lesson 8
18K
The production possibility curve demonstrates the potential profit from a given economic condition. See how this illustrates different economic conditions through evaluating scarcity, production factors, efficiency, and opportunity costs.
Related to this Question
- Suppose a factory produces 100 units of output per month and it is deciding how much labor and capital it should hire. If labor costs $200 per unit and capital costs $400 per unit, which of the following combinations of labor and capital should the firm u
- Suppose a firm spends $ 300,000 per month on production. Its two inputs are labor and capital. The hourly rate for labor (L) IS $25, and the price per unit of capital (K) is $100. a) Using isoquants a
- a. Suppose the firm can produce 5,000 units of output this year by combining its fixed capital with 100 units of labor and 450 units of raw materials. What are the total cost and average total cost of producing the 5,000 units of output?
- Suppose the hourly wage is $2, the price of each unit of capital is $4, and the price of output is $8 per unit. Assume that the firm cannot affect any of these prices. The production function of the firm is f(E, K) = KE^1/2. If the current capital stocked
- A firm produces output with capital and labor. Suppose currently the marginal product of labor is 21 and the marginal product of capital is 6. Each unit of labor costs $12 and each unit of capital co
- Suppose the hourly wage is $2, the price of each unit of capital is $4, and the price of output is $8 per unit. Assume that the firm cannot affect any of these prices. The production function of the firm is f(E, K) = KE^1/2. Now let s think about the long
- Suppose input prices are w = 4, and r = 1, and Q=4K^{0.5}L^{0.5} , where, w is the wage rate, r is the cost of capital, Q is output, K is capital and L is labor. (a.) What is the least cost input combination required to produce 40 units of output? (b.)
- Assume that the isoquant represents an output level of 50 units. If the firm chooses to produce 50 units of output, its least-cost combination of labor and capital is at a point: 1. A 2. B 3. C 4. D
- 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
- Consider a firm using labor and capital as its only inputs. The price of capital is $40 where the price of labor (wage) is $60. Using 500 units of labor and 500 units of capital the firm is producing
- Suppose that capital costs $10 per unit and labour costs $4 per unit. If the marginal product of capital is 50 and the marginal product of labour is 50, then in the long run the firm should in order to minimize its costs of producing its output. A) emplo
- 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 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 firm has a fixed-proportions production function that uses two units of labor combined with one unit of capital to produce one unit of output. a) If the firm has 10 units of capital, draw the short-run production. That is, draw the total product
- 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 you are thinking of starting a new business. You will need to give up your current job that pays you $20,000. You will pay $10,000 for labor costs and $12,000 for capital costs. These are your only costs. You can produce 30 units that you can sell
- Suppose the hourly wage is $10, the price of each unit of capital is $270, and the price of output is $20 per unit. Assume that the firm cannot affect any of these prices. The production function of t
- Suppose that a firm can hire a unit of labor for $5 per hour and a unit of capital for $10 per hour, regardless of how rmany units of labor or capital they hire. Initially, the firm is hiring 8 units of labor and 8 units of capital each hour, and is produ
- Consider a firm that uses capital and labor as inputs and sells 20000 units of output per year at the going market price of 15 Also assume that total labor costs to the firm are 248500 annually
- The production function of a firm is y = min {2l, k} where y, l and k rest denote output, labor, and capital. The firm has to produce 10 units of output and the wage rate is 2 and the price of capital
- A firm faces the following costs: total cost of capital = $1,500; price paid for labor = $12 per labor unit; and price paid for raw materials = $4 per raw-material unit. Suppose the firm can produce 5,500 units of output this year by combining its fixed c
- 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. If K is not fixed, determine the lease cost combination of L and K to produce 1000 units of Q.
- Suppose a firm with a production function given by Q=4K^0.25L^0.75 produces 100 units of output. The firm pays a wage of $30 per units and pays a rental rate of capital $10 per unit. The minimum cost
- A firm faces the following costs: Total cost of capital = $1500; price paid for labor = $14 per labor unit; and price paid for raw materials = $5 per raw-material unit. a. Suppose the firm can produce 5500 units of output this year by combining its fixed
- 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 uses labor and capital, (L, K), to produce and output. The hourly cost of labor is $10 and the hourly cost of capital is $50. Which of the following combinations of labor and capital hours of use represent points on the firm's $100,000 isocost line
- In order to hire the least-cost combination of labor and capital, the firm must do which of the following? A. Find the combination of labor and capital where the marginal product of labor is equal to the marginal product of capital. B. Find the combinatio
- 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)''.
- 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
- Suppose the price of each unit of labor is $25 and the price of each unit of capital is $100. The firm's total costs are $10,000 and it is producing 30 units of output. a. In the long run, if the fir
- Consider a firm with a production function of: q - 1000t^1/2 k^1/2. Suppose that the monthly rental rate on capital is v = 12000 per machine and the monthly wage rate for labor is w = 3000 per worker.
- 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
- 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
- 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
- A firm uses labor and capital (L, K), to produce an output. The hourly cost of labor is $10 and the hourly cost of capital is $50. Which combinations of labor and capital hours of use represent points
- 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
- 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?
- Suppose a firm finds that the marginal product of capital is 60, and the marginal product of labor is 20. If the price of capital is $6, and the price of labor is $2.50, describe how the firm should adjust its mix of capital and labor. What will be the re
- Consider a firm that can produce 1850 units of output by using 4 units of labor and 20 units of capital, or alternatively 2000 units of output by using 5 units of labor and 20 units of capital. If the
- 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?
- A firm uses labor and capital to make cupcakes according to the production function Suppose the price of labor is =$5 per unit and the price of capital was =$10 per unit. 1. In the short run, capital
- Suppose that a firm has only one variable input, labor, and firm output is zero when labor is zero. When the firm hires 6 workers the firm produces 90 units of output. Fixed costs of production are $6 and the variable cost per unit of labor is $10. The ma
- A company's production function is y = f(K,L) = (K^1/2)(L^1/2); and, the cost of a unit of capital and a unit of labor are denoted w and r, respectively. a. Suppose K = 100. Derive the short run cost
- A firm is employing 100 units of labor and 50 units of capital to produce 200 widgets. Labor costs $10 per unit and capital $5 per unit. For the quantities of inputs employed. MPL = 7 and MPx = 5. In this situation, the firm A. is producing the maximum ou
- Suppose the production function in an economy is Y = 3 K^1/3L^2/3, where K is the amount of capital and L is the amount of labor. The economy begins with 64 units of capital and 125 units of labor. a. What are the rate of wage and rate of rent? b. What a
- A firm is producing 1,000 units of output with 40 units of labor and 30 unit of capital. The marginal product of the last units of labor and capital are, respectively, MPL = 60 and MPK = 120. The prices of labor and capital are, respectively, w = 30 and r
- A firm faces the following costs: total cost of capital = $1,500; price paid for labor = $12 per labor unit; and price paid for raw materials = $4 per raw-material unit. Now assume the firm improves its production process so that it can produce 6,500 unit
- 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
- 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
- Consider a firm where production depends on two inputs: labor and capital. The firm starts using a production process that causes it to use much less labor as a fraction of its costs. How do you predi
- Firm A can produce a unit of output with 10 hours of labor and 5 units of capital. Firm B can produce a unit of output with 5 hours of labor and 10 units of capital. Firm C can produce a unit of output with 10 hours of labor and 10 units of capital. If th
- Firm A can produce a unit of output with 10 hours of labour and 5 units of capital. Firm B can produce a unit of output with 5 hours of labour and 10 units of capital. Firm C can produce a unit of output with 10 hours of labour and 10 units of capital. If
- 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
- Suppose a firm follows the production function f(E,K) = E^{1/2} K^{1/2}. The hourly wage of hiring one worker is $10 and the price of each unit of capital is $50. The price of output is constant at $100 per unit. a. Write out the function for the margina
- Suppose in a particular production process that capital and labor are perfect substitutes so that three units of labor are equivalent to one unit of capital. If the price of capital is $4 per unit and the price of labor is $1 per unit, the firm should (1)
- 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 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 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
- 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 f(L, K) = KL^9 w = 1; r = 2: MPL = 9L^8K; MPK = L^9. How much labor and capital should the firm hire if it wants to produce 10 units of output while minimizing its cost of production? Show your work.
- Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit and can hire labor at $50 per unit, how many units of labor should the firm hire in order to maximize profits?
- 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
- Hiring a unit of labour costs $10 while hiring a unit of capital costs $20. The marginal product of capital is equal to 200. A cost-minimizing manager will hire labour until its marginal product falls to: a) 50 b) 100 c) 200 d) 400
- A firm has a production function given by Q=10K^{0.5}L^{0.5}. 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. Derive the lon
- A firm has the following production function f(K,L)=K^{1/2}L^{2/3}, where K is capital and L is labor. It will produce 80 units of output and faces prices for labor and capital as follows: w_K =15, w_L+ 10. Find the cost minimizing bundle of labor and cap
- 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) = 2L + 6K. Assume that capital is fixed at K = 6. Also assume that the price of capital r = 10 and the price of labor w = 2. Then, what is the marginal
- 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 company currently employs 2,000 workers and produces 5 million units of output per month. Labor is its only variable input, and the company pays each worker the same monthly wage. The c
- 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
- Consider a firm using labor and capital as its only inputs. The price of capital is $40 and the price of labor (the wage) is $60. Using 500 units of labor and 500 units of capital the firm is producin
- If a firm chooses to produce 100 units of output for $150 with 10 units of labor and 12 units of capital when they could produce the same 100 units for $120 with 10 units of labor and 8 units of capital, the firm is technologically and economically. a. ef
- A firm uses labor and capital. To tell if the firm is technologically efficient, you A. do not need to know the cost of labor or the cost of capital. B. need to know the cost of capital but not the cost of labor. C. need to know the cost of labor but not
- 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
- The short-run production function of a profit maximizer firm is given by f(L) = 6L^(2/3), where L is the amount of labor it uses. The cost per labor unit is w = 6, and the price per unit of output is p = 3. 1) How many units of labor will the firm hire?
- 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
- If production is Q=(a^c) min (K, L) where a is greater than 0, c is greater than 1 , price of capital, (r) = 10 and price of labor, (w) = 10 what is the optimal combination of capital and labor? Does
- Suppose a firm is currently using 500 laborers and 325 units of capital to produce its product. The wage rate is 425, and the price of capital is $130. The last laborer adds 25 units to total output, while the last unit of capital adds 65 units to total o
- Assume a firm uses labor and capital to make cupcakes according to the production function of y = f(x_1 x_2) = x_1 x_2. Suppose the price of labor is w_1 = $4 per unit and the price of capital is also
- Assume a firm is currently employing 20 units of capital and 100 units of labor in its production process. Assume also that the marginal product of the 20th unit of capital is 40 units of output, the marginal product of the 100th unit of labor is 10 units
- A business incurs the following costs per unit: Labor $125/unit; Materials $45/unit and rent $250,000/month. If the firm produces 1,000,000 units a month, the total variable costs equal what?
- In the graph below, the price of capital is $500 per unit. How many units of labor should a firm use in order to produce 30,000 units of output at the lowest possible cost? a. 300 units of labor b. 320 units of labor c. 500 units of labor d. 800 units
- 1. A firm's production function is: Q=20L^{0.6}K^{0.4}. Labor costs $100 per unit and capital costs $50. The firm sets a production target of 1000 units. a. Show or explain whether the production fun
- Consider the following production function: q = 100 L^(0.5) K^(0.5). Currently the wage rate (w) is $20.00 and the price of capital (r) is $5.00. If the firm is using 100 units of capital in production and the production price is $10, how much labor shoul
- 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 the production function for Hannah and Sam's home painting business is Q=F(L, K) = 10L^{0.2}K^{0.3}. If the wage rate is $1500 per week and the cost of renting a unit of capital is $1000 per week, what is the least-cost input combination for
- Now assume the firm improves its production process so that it can produce 6,000 units of output this year by combining its fixed capital with 100 units of labor and 450 units of raw materials. What are the total cost and average total cost of producing t
- A firm's production function is X = 6LK. Name five input combinations that would allow the firm to produce 180 units of output. In each case, what is the firm's capital-labor ratio? If the wage rate is $15 per unit and the rental rate on capital is $25 pe
- Suppose in the short run a firm's production function is given by Q = L^{1/2}K^{1/2}, and that 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 ou
- Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two inputs of production; each unit of labor is paid the market wage (w), and each unit of capital is rented at the rental price of capital (v). Output (Y) is, therefor
- Consider a firm that produces using only labor and capital. It can produce 1,850 units of output by using 4 units of labor and 20 units of capital, or alternatively 2,000 units of output by using 5 un
- Assume a firm is currently employing 20 units of capital and 100 units of labor in its production process. Assume also that the marginal product of the 20th unit of capital is 40 units of output, the
- Suppose that hiring one more worker increases output by 10 units. Hiring that worker costs $10. One more unit of capital increases output by 30 units, but costs $15. How should this firm change their input mix? A. It should hire more labor. B. It should h
- 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 the production function for iPods is Q=20K^0.5L^0.5. Suppose that labor can be hired for $6, and capital can be hired for $9. When the firm is producing 49 units at lowest cost, what will
- A firm produces output according to the production function: Q = F(K,L) = 4K + 8L. b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? c. If the wage r
- 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 that a firm has the following production function: Q(K, L) = 2LK^{1/2} a. If the price of labour is $2/unit and the price of capital is $4/unit, what is the optimal ratio of capital to labou
Explore our homework questions and answers library
Browse
by subject