# A manager hires labor and rents capital equipment in a very competitive market. Currently, the...

## Question:

A manager hires labor and rents capital equipment in a very competitive market. Currently, the wage rate is $10/hour and the capital rental price is $5/hour. If the marginal product of labor is 50 units of output per hour and the marginal product of capital is 40 units of output per hour, is the firm using the cost-minimizing combination of labor and capital? If not, should the firm increase or decrease the amount of capital (labor) used in its production process?

## Optimum utilization of factor combinations

Suppose a producer uses two factors of production in the production process: Labor (L) and Capital (K). The total production can be maximized at the point where, Marginal Rate of Technical Substitution of L and K (MRTS of L and K) = Wage / Rent.

## Answer and Explanation: 1

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

View this answergiven, w = 10 , r = 5

The cost minimization rule is,

MRTS of L and K = w / r, or

MP of L / MP of K = w / r

Here, MP of L / MP of K = 50 / 40 =...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 3 / Lesson 51Learn how to calculate the marginal rate of substitution and its application in economics. View examples of the formula in use with real world application.

#### Related to this Question

- A manager hires labor and rents capital equipment in a very competitive market. Currently, the wage rate is $12 per hour and capital is rented at $9 per hour. If the marginal product of labor is 40 units of output per hour and the marginal product of capi
- A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $10 per hour and capital is rented at $12 per hour. If the marginal product of labor is 40 un
- A manager hires labor and rents capital equipment in a very competitive market. Currently, the wage rate is $12 per hour and capital is rented at $8 per hour. If the marginal product of labor is 60 un
- A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $ 12 per hour and capital is rented at $ 8 per hour. If the marginal product of labor is 60 u
- A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $8 per hour and capital is rented at $15 per hour. If the marginal product of labor is 50 uni
- 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
- 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
- A manager hires labor and rents capital equipment in a very competitive market for his firm to produce a certain quantity of output. Currently the wage rate is $10 per hour and capital is rented at $1
- 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
- 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
- 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?
- A firm is producing optimally (maximizing profits) when the price level=$1. It pays a wage rate of $10 per hour to labor and rents capital for $8 per hour. It sells its product for $20 per unit. At it
- 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
- 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.
- 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 _____.
- 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's product sells for $4 per unit in a highly competitive market. The firm produces output using capital (which it rents at $25 per hour) and labor (which is paid a wage of $30 per hour under a c
- 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 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 is currently producing their profit maximizing quantity of 600 units of output using 150 hours of labor and 50 hours of capital. The marginal product of labor is 10 units of output per hour and
- A firm is producing optimally (maximizing profits) when the price level = $1. It pays a wage rate of $10 per hour to labor and rents capital for $8 per hour. It sells its product for $20 per unit. At
- 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
- 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
- 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?
- 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 makes each unit of output using 2 workers and 1 machine (per hour). The hourly production function is Q = min(K, 2L). The hourly wage is w = 4 and the hourly rental rate of capital is r = 2. Fi
- A firm uses 80 hours of labor and 6 units of capital to produce 10,000 gadgets per day. Labor's marginal product is 4 gadgets per hour and the marginal product of capital is 20 gadgets per hour. Each
- 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
- 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
- Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function is f(E,K) = E�K �, so that the marginal product of
- If the last worker employed ($15/hour) produces 45 additional units of output per hour and the last unit of capital employed ($200/hour) produces 1,000 units of output per hour, how can the firm minimize the cost of its current output? a) hire more labor
- If the last worker employed ($10/hour) produces 50 additional units of output per hour and the last unit of capital employed ($500/hour) produces 2,500 units of output per hour, how can the firm minimize the cost of its current output? a) hire more labor
- 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 firm in a competitive industry faces a market price for output of $20 and a wage rate of $500. At the current level of employment (50 units of labor), the marginal product of labor is 30. In order to maximize profit, the firm should: a. hire less labor
- 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 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
- 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
- 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
- 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
- It is profitable to hire units of labor as long as the value of marginal product: a. is less than wage. b. exceeds average product. c. equals price. d. exceeds wage.
- 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
- 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 produces output according to the production function Q = F (K, L) = K + 10L. If the wage rate is $50 per hour and the rental rate on capital is $4 per hour, what is the cost-minimizing input m
- 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
- 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
- Suppose a firm follows the production function f(E,K) = E K . 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 uni
- If the wage rate is $10 per hour and one worker can produce 2 units of output per hour, then the marginal cost of production is: a. $5. b. $10. c. $20. d. The answer cannot be determined from the information given.
- 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
- Holding capital fixed at K=2 units, the firm's production table shows when labor units (L) = 1, output (Q)=5; L=2, Q=11; L=3, Q=16; L=4, Q=20; L=5, Q=22. Also, the firm can sell each unit of output at a price of P=$2. If so, the marginal product of labor
- 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
- 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
- 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
- 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 labor that is hired for $18 per hour. If the last hour of labor hired produces 8 units of output which sells for $10 per unit, that labor hour's marginal revenue product is: A) $1.20 B) $4.44 C) $64 D) $80 E) $144
- A firm that wants to employ workers should a) hire workers as long as the wage is greater than the value of the marginal product. b) hire workers as long as the wage is less than the value of the marginal product. c) not hire workers if the value of the
- 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
- 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.
- The current market wage rate is $10, the rental rate of land is $1,000 per unit, and the rental rate of capital is $500. Production managers at a firm find that under their current allocation of factors of production, the marginal physical product of labo
- 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
- The marginal product of labor is the increase in total product from a A. one-dollar increase in the wage rate, while holding the price of capital constant. B. one unit increase in the quantity of labor, while also increasing the quantity of capital by one
- The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution between hours of labor and hours of machine time is 1/4. What is the marginal product of capital?
- 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
- 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
- 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
- Figure 28-7 Labor Total Product 0 0 1 3 2 18 3 43 4 55 In Figure 28-7, assume that the resource and output markets are perfectly competitive. If the wage rate is $60 per unit of labor and the output price is $5 a unit, the MRP of the third laborer
- A firm is producing 100 units of its product. At this level of output the AVC=$60, and the ATC=$80. The firm is a price taker and the price for its product is $100. Assuming that the firm is maximizing profits and that labor is the only variable input. Fr
- Labor productivity and the price of the good being produced are two variables that contribute to: a. whether or not a union forms. b. the marginal product. c. the demand for the product. d. the wage rate.
- Labor productivity and the price of the good being produced are two variables that contribute to: a. whether or not a union forms. b. the marginal product. c. the demand for the product. e. the wage rate.
- 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 has the production function f(k, l) = 2k sqrt l. Let the price of capital be r = 1, the price labor be w = 2, and the price of output be p. Find the marginal products of capital and labor. Does the firm have constant returns to scale?
- In an economy with production function Y = 1.5K^{0.3}L^{0.7}, K = 343, and L = 512. If factor markets are in equilibrium, then the rental price of capital is (approximately) ________, and the real wage is (approximately) ________. (Show work.)
- If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 6 units of output?
- 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
- 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
- A firm's production function is q=5L^0.5K^0.5. The firm's capital is fixed at K=400 units, in the short run. The rental rate of a unit of capital is $9, and the wage rate is $100 in the short run. De
- 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 _________.
- Firm 1 can produce a unit of output with 10 hours of labor and 5 units of material. Firm 2 can produce a unit of output with 5 hours of labor and 10 units of material. Firm 3 can produce a unit of output with 10 hours of labor and 10 units of material. If
- For a given output level, a firm's short run average product of labor is 4 while its marginal product of labor is 5. Assume that the wage rate is $20. What is the short run average variable cost?
- 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
- 1) The long-run aggregate supply curve shows the output level that an economy can produce when: a) Labor is fully employed. b) Capital is fully employed. c) Both capital and labor are fully employed.
- There are 2 firms in the market and each of them plans the production as Q = K1/3L1/3, where K is capital and L is labor. Given K = 8, capital rental rate R = 0.5, and wage W = 8, what is the cost of producing more units of good if the market demand funct
- is the value of output per hour of labor input. a. Labor productivity b. GDP per capita c. Human capital d. Investment
- You are the CEO of Lewis Co,. Ltd., a firm that uses only two inputs, capital and labor, to produce output. The wage rate is $5/hour and the firm can rent as much capital as it wants at a price of $50
- 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
- Firm A can produce a unit of output with 10 hours of labor and 5 units of material. Firm B can produce a unit of output with 5 hours of labor and 10 units of material. Firm C can produce a unit of output with 10 hours of labor and 10 units of material. If
- 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 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?
- A firm produces output according to the production function: Q = F(K, L) = 4 K + 8 L. 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 capital is $20 per hour, what is the cost-minimizing inpu
- Suppose a firm has the following production function: q= (K*L)^1/2 and its associated MRTS of L for K=K/L. The hourly wage rate is $100 per hour, and the hourly rental rate for capital is $70 per hour
- If a firm hires labor in a competitive market, and the wage paid to labor is designated by ''W'', then the average variable cost of the firm is equivalent to: A) W times the marginal product of labor B) W divided by the average product of labor C) W d
- A firm's production function of output (y) is y = (0.1)K^{1/2}L^{3/4}, where K is number of hours of capital (machines) input and L is the number of hours of labor input. The price of capital, w_K, is $6 per machine-hour, and price of labor, w_L, is $4 pe
- A firm's production function of output (y) is y = (0.1)K1/2L3/4, where K is the number of hours of capital (machines) input and L is the number of hours of labor input. The price of capital, wK, is $6 per machine-hour, and the price of labor, wL, is $4 pe
- 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
- A price-taking firm (p = 100) chooses an amount of labor to employ that maximizes its profits. It has a fixed amount of capital (K= 100) and a constant return to scale Cobb-Douglass production function: q(L, K) = L^(1/2) K^(1/2). The wage rate and rental
- 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
- 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
- There are 2 firms in the market and each of them plans the production as Q = K1/3L1/3, where K is capital and L is labor. Given K = 8, capital rental rate R = 0.5, and wage W = 8, in equilibrium, what is the supply function of a firm if the market demand
- A firm has production function Y = KL + L^2. The firm faces costs of $10 wages and $1 rental rate of capital. Find the cost function, average total cost, average viable cost, and marginal cost functions.