In order to hire the least-cost combination of labor and capital, the firm must do which of the...
Question:
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 combination of labor and capital where the ratio of the marginal product of labor to the marginal product of capital is equal to one.
C. Find the combination of labor and capital where the marginal product of labor divided by the price of labor is equal to the marginal product of capital divided by the price of capital.
D. Find the combination of labor and capital where the price of labor is equal to the price of capital.
E. Find the combination of labor and capital where the marginal revenue product of labor is equal to the marginal revenue product of capital.
Cost Minimization:
The total cost function shows that, for any set of input costs and for any output level, the minimum total cost incurred by the firm is C = C(w, v, y) where w = wage rate, v= rental rate and y= output. For achieving this level of output, the firm needs to equate MRTS to w/v.
Answer and Explanation:
Become a Study.com member to unlock this answer! Create your account
View this answerSee full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:

from
Chapter 20 / Lesson 13Learn about the cost function formula. Discover how to find cost function. Explore average cost function and marginal cost function. See examples of finding the cost.
Related to this Question
- Suppose the marginal product of labor is 10 and the marginal product of capital is 8. If the wage rate is $5 and the price of capital is $2, then in order to minimize costs the firm should use: A. more capital and less labor. B. more labor and less capita
- Suppose the marginal product of labor is 12 and the marginal product of capital is 24. If the wage rate is $4 and the price of capital is $6, then in order to minimize costs, the firm should use: a. more labor and less capital. b. more capital and less la
- 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 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
- A firm using two inputs (call them "capital" and "labor") has an efficient combination of capital and labor levels when: the marginal product of capital and the marginal product of labor are equal. th
- 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
- Suppose we are given a Firm's Marginal product of capital and the marginal product of labor at the combination of labor and capital that the firm currently uses. Can we determine the Firm's marginal rate of technical substitution of labor for capital at t
- If the price of capital is $24, the price of labor is $15, and the marginal product of capital is 16, the least costly combination of capital and labor requires adjusting the amount of labor until its marginal product is equal to _________.
- If the price of capital is higher than the price of labor, a firm should use: a. capital and labor, making sure that the marginal product of capital is larger than the marginal product of labor. b. capital and labor, making sure that the ratio of the aver
- 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
- The marginal product of labor is 5 units of output per hour and the wage is $10. Capital can be rented at $8 per hours. At the optimal input combination, what is the marginal product of capital? If capital is cheaper per hour, why not only use capital?
- Your firm must produce a specified output level. The firm uses capital and labor as inputs. If the price of capital is $40, the price of labor is $100, the marginal product of capital is 20, and the marginal product of labor is 40, then: - the firm is mi
- 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
- Consider the following scenario: the firm estimates that currently, its marginal product of labor is 80, while the marginal product of capital is 160. The firm pays $40 in the rental price of capital
- If the marginal product of labor is MPL = 100k - L and the marginal product of capital is MPk = 100L - K, what is the maximum combination of labor and capital that would be employed? The producer has
- consider a firm that operates with the following production function: q = 2K^2L a. calculate the marginal products of labor and capital (MP_L AND MP_k) b. calculate the marginal rate of technical substitution of labor for capital, MRTS_{LK} Firm faces m
- 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
- If the price of capital is higher than the price of labor, a firm should use: A) Capital and labor, making sure the marginal product of capital is larger than the marginal product of labor. B) Capital and labor, making sure the ratio of the average prod
- The marginal product of labor is 10 and the marginal product of capital is 20. If the wage rate is $10 and the price of capital is $5, is the firm using the right balance of capital and labor? Explain
- 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
- The company you work for hires labor and capital in competitive factor markets. Currently the wage rate is $10 per hour and capital is rented at $21 per hour. If the marginal product of labor is 30 units of output per hour and the marginal product of capi
- Suppose that the marginal product of labor is 20, the marginal product of capital is 2, the price of output is $10, and the wage rate for labor is $5. Then we can deduce that the rental rate for capital is _____.
- If the marginal product of labor is 2, the marginal product of capital is 4, the wage rate is $3, the rental price of capital is $6, and the price of output is $1.50, then the firm should: a. increase output by hiring more labor, more capital, or both. b.
- If the marginal product of labor is 3, the marginal product of capital is 4, the wage rate is $4.50, the rental price of capital is $6, and the price of output is $1.50, then the firm should: A. increase output by hiring more labor, more capital, or both
- Suppose, in the long run, for a firm, the marginal product of labor is 100, the marginal product of capital is 120. The wage rate (per unit of labor) is W = 20, and the rental price (per unit of capital) is R = 24. Then which of the following is true? A.
- 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
- Fill in the blanks (_) and explain your answer: If a firm is using a lot of capital and just a little labor, the marginal product of labor is (_) relative to the marginal product of capital making it
- A firm has a production function of y = f(L, k) = ( sqrtL + sqrtk)^2 a) Find expressions for the marginal product of labor and capital (b) Find the cost function
- Suppose two firms have the respective production functions: Firm 1: q=LK Firm 2: q=0.9LK a. Find the marginal product of labor and capital for each firm. b. For a particular level of labor and capit
- 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
- 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 uses capital and labor to produce gadgets. If the firm profit maximizing combination of capital and labor is 2 and 3 respectively and each machine costs $50 an hour and each worker $20 an hour. What is the firm's production costs in an hour?
- Assume that a purely competitive firm uses two resources, labor (L)and capital (C), to produce a product. The market price of this product is $1.00. The Marginal Product (MP) and prices of the resourc
- 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 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
- When labor is the only input a firm uses, the marginal cost of a unit of output can be defined as: a. Wage divided by number of workers, b. Marginal product of labor multiplied by wage, c. Wage divided by marginal product of labor, d. Marginal product of
- To minimize the cost of a particular level of output, a firm should produce where: a. labor input equal capital input. b. (MPl/MPk)=r/w (MP stands for marginal product, w is the wage rate, and r is the unit cost of capital). c. (MPl/MPk)=r/w. d. labor
- 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.
- 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
- Adding a variable input (labor) to a fixed input (capital) will result in an increase in output: A. Until the marginal product of labor is maximized. B. Until the marginal product of labor begins to d
- 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
- 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 the following production function: Q = 10KL. If w = 25, r = 75, and c = 1200, find the minimum cost combination of capital and labor to produce a given level of output.
- This firm has a wage of $100 per worker, according to the following output schedule, the marginal cost when the firm is producing 15 units. Marginal cost is Labor Output 1 5 2 15 3 20 4 24
- 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.)
- The additional cost associated with the hiring of one more unit of labor is known as the: A. marginal utility of labor. B. marginal factor cost of labor. C. marginal revenue product of labor. D. marginal physical product of labor.
- If a firm wants to maximize its profits, it should: a. equate the marginal revenue product for each input to the price of the input. b. hire unskilled labor rather than skilled labor since unskilled labor is cheaper. c. hire lots of capital and very lit
- Consider a firm which produces according to the following production function by using labor and capital: f(l,k) = k1/2 * l1/2 (a) Solve the cost minimization problem of this firm for the given wage
- 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
- A firm is employing 100 workers (w = $15/hour) and 50 units of capital (r = $30/hour). At these levels, the marginal product of labor (MPL) is 45 and the marginal product of capital (MPK) is 60. Answe
- A firm hires capital and labor to produce grapefruits. Currently the marginal product of the last unit of labor input is 40 and the marginal product of the last unit of capital input is 60. the market wage is $20, if the firm is using the optimal combinat
- Consider a firm where, in the long-run, K and L are imperfect substitutes. The firm is currently production 1000 units of output with K = 10 and L = 2. A this mixture of inputs, the MRTS is 8. The cost of labor is 8 and the cost of capital is 24. (a) Is
- If the price of labor decreases, in order to minimize the costs of producing a given level of output, the firm manager should use: A. less of labor and more of capital. B. less of labor and less of capital. C. more of labor and more of capital. D. more of
- Fill in the blanks: Suppose this firm is using capital and labour such that the MP_K = 90 and the MP_L = 180 If the prices per unit of capital and labour are $5 and $30, respectively, this firm ____________
- 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 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
- Consider a firm with two inputs, capital (K) and labor (L), with the price of capital Pk and the price of labor PL. The firm's production function is q(K, L) = 25KL. a. Write the firm's cost (as a function of K, L, Pk, PL). b. From the production function
- Assume that at the current level of production, MP of labor is 5 and marginal product of capital is 10. The wage rate is $20 and the rental rate on capital is $50. Is the firm choosing the cost minim
- 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 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
- A firm uses capital and labor to produce a single output good. The production function is given by F(K, L) = K L^{0.5} where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, r
- Consider a firm using two inputs; capital (K) and labor (L) in production. The firm's production technology is characterized by the following production function: Q = F(K, L) = 100KL Price of labor is $100 per worker and the price of capital is $400 per
- Assume that both the product and labor markets are perfectly competitive. It would be profitable for a firm to hire additional labor if the ratio of the wage to the marginal produce of labor is a. les
- A firm produces 1,000 units of output with a particular combination of labor and capital such that the MRP of labor is $30 and MRP of capital is $40. If you know that this firm is maximizing profits,
- 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 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.
- "The optimal mix of labor and capital in producing output Q0 depends on the costs and marginal products of the inputs." What does this statement mean?
- When the opportunity cost of capital is matched with the benefits from adding to the capital stock, the marginal product of capital, we have: a. the optimal production function. b. the optimal stock of capital. c. the optimal combination of primary factor
- A firm is currently producing 200 units of output using 60 hours of labor and 80 hours of capital. The marginal product of labor is 12 units of output per hour, and the marginal product of capital is 15 units of output per hour. If the wage rate is $6 per
- 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
- What is the role of diminishing marginal product in determination of ideal labour-capital combination of a firm?
- Suppose the combination of capital (K) and labor (L) lies to the right of the firm's cost line. This means that the combination is: A. insufficient, given the budget B. undesirable C. inferior to the points within the contrast in terms of production D. un
- Suppose a firm produces hybrid, eco-friendly automobiles using a combination of capital (K) and labor (L). The firm knows its TC is $1,000, and the prices per unit of capital and labor are $20 and $10, respectively. a. Write the isocost equation. b. Draw
- 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?
- Assume all workers get paid the same wage rate of w = $80. Assume that there are no costs associated with capital (TFC = 0). The lowest marginal cost of output is associated with how many workers employed? a) 4 workers b) 5 workers c) 6 workers d) 7 worke
- Suppose that capital and labor are perfect complements in a one-to-one ratio in a firm's production function. The firm is currently at an efficient production level, employing an equal number of machines and workers. Suppose the cost of labor were to doub
- 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
- Consider the following production function: *Q=100K.4L.6 a) Derive expression for the marginal product of capital, and for the marginal product of capital. b) Compute the marginal products of capit
- 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
- 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
- The wage for qualified workers is $12 per hour and capital is rented at $8 per hour. The marginal product of labor is 60 units of output per labor hour, and the marginal product of capital is 48 units of output per hour of capital rental. The marginal pro
- 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
- Assume a firm uses two inputs, capital and labor. All else constant, an increase in the price of labor would create an incentive for the firm to: A) substitute labor for capital in its production function. B) substitute capital for labor in its production
- From a firms short run production function, the marginal product of labor and the average product of labor may be determined. The marginal product of labor is the: A. total output divided by the numb
- A monopsonist that faces a labor supply curve of the form L' 4w and has a constant marginal revenue product of 50 per unit of labor will opt for the following (w, L) combination: a. w 10 I- 40 w 25 L
- Refer to the figure below. What is the combination of inputs that produce 200 gooseberry pies at the lowest cost? Select one: a. Combination e: 10 hours of labor and 48 units of capital, b. Combination g: 60 hours of labor and 14 units of capital, c. Co
- Consider the following information about how a firm's output Y is related to the amount of labor it hires, L (holding the amount of capital, K, constant). A. Compute the marginal product of labor associated with each additional unit of labor hired. B. Plo
- 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
- The marginal product of labor is the change in total product from a one-unit increase in A. the wage rate. B. both the quantity of labor and the quantity of capital employed. C. the quantity of labor employed, holding the quantity of capital constant. D.
- 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.
- Consider a firm competing in a perfectly competitive market where capital and labor are paid constant wages. A. Fill in the table above. B. How much does each unit of capital cost? C. At what level of labor utilization does the law of diminishing returns
- If the marginal product per dollar spent on capital is more than the marginal product per dollar spent on labor, then to minimize costs, the firm should use? a) less capital and more labor. b) less labor and more capital. c) less labor and less capital. d
- 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
- 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
- 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 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
- An isoquant shows the various combinations of labor and capital that: a. the firm will choose to employ in the long run. b. yield the same total cost. c. can produce some fixed level of output. d. minimize the firm's average cost of production.
- Suppose that in order to produce any positive amount of output, a firm must build an operating facility which costs $40. The Variable Cost of production is equal to 6q, where q is the quantity of outp
- Please show how to setup and solve. Assume a firm produces 500 units of a good by using two inputs, capital and labor, whose per unit prices are $10 and $4. Assume also that the marginal physical prod