# Consider a firm competing in a perfectly competitive market where capital and labor are paid...

## Question:

Consider a firm competing in a perfectly competitive market where capital and labor are paid constant wages.

L | K | Q | VC | FC | TC | ATC | MC | MPL |
---|---|---|---|---|---|---|---|---|

0 | 20 | 0 | 100 | - | - | - | ||

1 | 20 | 5 | 100 | 100 | ||||

2 | 20 | 100 | 10 | |||||

3 | 20 | 65 | 100 | |||||

4 | 20 | 100 | 16 | |||||

5 | 20 | 105 | 2,100 |

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 first appear?

## Law of Diminishing Return:

The Law of Diminishing Return is also known as the Law of Increasing Cost. It is a significant law under microeconomics, which states that an additional amount of a single factor of production will result to a decreasing marginal output of production.

## Answer and Explanation: 1

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

View this answer**For Requirement A**

To easily solve the following requirements, we must complete the table first. The following operations will help us solve 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 10 / Lesson 8Learn about the law of diminishing returns, or diminishing marginal returns. See the point of diminishing returns graphed and how to calculate it with examples.

#### Related to this Question

- Consider a competitive labor market with 800 identical firms. Each firm has the production function f(l) = \sqrt{l}, where l denotes the amount of labor employed by the firm. The price of a unit of ou
- Refer to the table below. This firm sells output in a competitive product market at an equilibrium price of $3. If the competitive wage for a unit of labor is $45, how many units of labor will be employed? a. 2 b. 3 c. 8 d. 5 e. 4 |Units of Labor |Margin
- 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
- 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
- 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 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 for which production depends on two normal inputs, labor, and capital, that are not perfect complements. Initially, the firm faces market prices of w = 10 and r = 8, for labor and capital. These prices then shift to w = 7 and r = 7. a) In
- 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 where production depends on two inputs, labor and capital, with prices w and r, respectively. The firm is a price taker in all input markets; initially the firm faces market prices of
- 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 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
- 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 a competitive firm can sell its output for $9 per unit. The following table gives the firm's short run production function. [TABLE] In the table below, you will determine several points on the firm's demand curve for labor. Determine how many work
- 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.
- All else constant, the choice of whether to use a labor-intensive production process or a capital-intensive one depends on: a) the absolute prices of capital and labor. b) the relative prices of capital and labor. c) the type of market in which the firm
- 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 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
- Refer to the table below. If this profit-maximizing firm sells its output in a competitive market for $3 per unit and hires labor in a competitive market for $8/hour, then this firm should hire. a. one worker b. two workers c. three workers d. four worker
- Suppose a competitive firm can sell its output for $7 per unit. The following table gives the firms short run production function. In the table below, you will determine several points on the firm's demand curve for labor. To do this, you must determine h
- Consider a firm that faces a constant per unit price of $1,200 for its output. The firm hires workers, E, from a union at a daily wage of w to produce output q. Given the production function, the marg
- 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
- 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 ____________
- 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
- Suppose a competitive firm can sell its output for $9 per unit. The following table gives the firm's short run production function. In the table below, you will determine several points on the firm?s demand curve for labor. To do this, you must determi
- 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 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
- 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 MP of the last unit of capital hired equals 12 and the MP of the last unit of labor hired equals 16. If the price of capital is $8 per unit and the price of labor is $8 per unit, then the firm should do what?
- Suppose that labor is the only input used by a perfectly competitive firm. The firm can hire workers for $30 per day. Each unit sells for $6. The firm's production function is as follows: a) Complete this table, filling in the value of the marginal produc
- Suppose a competitive firm can sell its output for $11 per unit. The following table gives the firm s short run production function. In the table below, you will determine several points on the firm's demand curve for labor. To do this, you must determine
- 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
- Suppose a competitive firm can sell its output for $5 per unit. The following table gives the firm's short run production function. [TABLE] In the table below, you will determine several points on the firm's demand curve for labor. To do this, you must
- Suppose a firm's production function is given by Q= L^1/2 * K^1/2.The marginal product of labor and the marginal product of capital is given by: MPL= K^1/2 /2L^1/2 and MPk= L^1/2/2K^ 1/2. Suppose the price of labor is w = 24 and the price of capital is r
- Suppose a competitive firm can sell its output for $7 per unit. The following table gives the firm's short-run production function. In the table below, you will determine several points on the firm's demand curve for labor. To do this, you must determi
- 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 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
- Refer to the table below. Suppose we know that the value of the marginal product of the seventh unit of labor is $15. If the firm operates in a competitive product market, what is the price of the good being produced by this labor? a) $2.50 b) $2 c) $6 d)
- 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
- Consider a firm that uses only labor and capital as inputs. At the present use of labor and capital, the MP of labor is four times the MP of capital, and the price of labor is twice the price of capital. In order to minimize its costs, the firm should A)
- A firm incurs a cost C of hiring new workers. Production is: Y = 10 L - L2 /4. The labor supply function is LS=4. -If C is a constant, find the demand for labor, the market clearing wage rate, outpu
- Consider the table above. Assume that the resource and output markets are both perfectly competitive. The equilibrium price of the resource is $25 and the equilibrium price of the product is $1.00. How many units of the resource will be hired by a profit
- 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
- 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
- Assume that an economy's production function is Y = 1000L^1/2, so that when the marginal product of capital is equated to the real wage the labor demand curve is L = 250, 000 (P/W)^2. The labor supply
- 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
- Suppose a competitive firm is paying a wage of $12 an hour and sells its product at $3 per unit. Assume that labor is the only input. If the last worker hired increases output by 3 units per hour, then to maximize profits, the firm should: A. lay off some
- 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
- 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
- Consider an economy in which the marginal product of labor is MPN=700-4N, where N is the amount of labor used. The amount of labor supply is given by 20+12w+4T, where w is the real wage, and T is a lu
- Using the perfectly competitive labor demand and labor supply model, what would happen, all else being equal, to the real wage and the number of workers if there is an increase in the amount of physical capital as a result of positive net investment in th
- Suppose a competitive firm can sell its output for $7 per unit. The following table gives the firm's short-run production function. In the table below, you will determine several points on the firm's demand curve for labor. Complete the table below.
- Assume the price of labor (W) equals $10 and the price of capital (C) equals $36. Also suppose that at the current mix of labor and capital, MPL = 5 and MPK = 12. Using the rule for cost minimization, which of the following correctly describes what the fi
- 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
- Consider a firm with the production function f(L,K) = L^{0.5}K^{0.5}. The wage rate and rental rate on capital are w and r, respectively. a. Use the Lagrangian for cost minimization to do derive the long-run cost function for this firm. b. Suppose the
- 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
- 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
- In a perfectly competitive labor market, each firm can hire: A. larger quantities of labor at going market wages per worker. B. all the labor it wants, but only by outbidding its competitors. C. larger quantities of labor at rising wages per worker. D. on
- Suppose that a firm faces the production function Q = 3K^{0.2}L^{0.3}, where the cost of labor and capital are w and r. What are the demand curves for labor and capital?
- In table above, assume all workers get paid the same wage rate of w = $60. Assume that there are no costs associated with capital (TFC = 0). Which of the following is true? Hint: You can add the MC column to the table and use MC = w/MPL to fill it in. A)
- Suppose a firm uses capital (K) and Labor (L) to produce milk. The production function is Q=K^{0.25}L^{0.25}. The price of capital is 1 and the price of labor is 4. The market price of milk is 32. a. In the short run, suppose the capital the firm has is 4
- Suppose low skilled labor and capital are substitutes but highly skilled labor and capital are complements. Over the past 45 years, the price of capital has dropped substantially because of the computer revolution. a. Draw and explain 2 labor market diag
- Consider a firm where production depends on two inputs, labor and capital with prices w and r, respectively. The firm is a price taker in all input markets; initially the firm faces market prices of w
- 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
- Consider a technology exhibiting diminishing MRTS. If capital is fixed, but a firm varies labor A) the firm stays on the same isoquant. B) the firm moves to a new isoquant. C) the firm might move to a new isoquant, depending on how much labor is added.
- Consider a firm with production function f(L,K)=L^1/7K^6/7 (cost minimization for this firm is characterized by the tangency rule). Assume also that the price of capital r=3 and the price of labor w=2
- 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
- Consider a technology exhibiting diminishing MRTS. If capital is fixed, but a firm varies labor, A. the firm stays on the same isoquant. B. the firm moves to a new isoquant. C. the firm might move to a new isoquant, depending on how much labor is added. D
- 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 contract for 20 hours of labor services). Identify the f
- 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
- 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
- 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
- Consider the following production function: q = 100L^{0.8}k^{0.4} Currently the wage rate (w) is $1.00 and the price of capital (r) is $2.00. If the firm is using 200 units of capital in producti
- In a labor market dominated by a monopsonist, wages and employment are usually lower than in a competitive labor market. This is because a monopsonist A. employs workers up to the point where the marginal revenue product of labor is equal to the wage rate
- Consider a firm whose production function is given by q(L, K) = LK where MPL = L and K and MPK = L. The per unit price of labour is w = $2 while the per unit price of capital is r = $1. (a)What is th
- 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 _____.
- 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
- 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 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
- 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
- Recall that the total cost for a firm is calculated as C = wL + rK. Suppose the firm has total costs of $1000, with wage rates of $25 and capital rents equal to $50. a. If the firm employs 24 units of labor, how many capital units are they employing? b.
- 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
- Assume a firm is currently employing labor and capital in such a way that the cost minimizing equality is: 100 $10=200 $20 with the left side of the equality representing the MPL/PL and the right side
- Consider a grain processing firm for which its labor and capital have a marginal revenue product of MRP_L = $22/hour and MRP_K = $35,000/machine, respectively. a. Suppose that wages for the kind of labor hired by the grain processor are $14/hour and the
- 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
- 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
- Assume of a sample case with the following production function: Y = 12K^(1/3)L^(2/3) where both the level of capital and labor in the economy is 1000. Compute the Equilibrium real wage.
- Assume supply is described by Q_S = 40 + 6P - 8W + 10F where W is the wage and F is the number of competing firms. The current wage rate is $20 and there are 60 competitors, what is the equation of the supply function?
- Consider the following production function. q = 100L^{0.8}K^{0.4} Currently, the wage rate (w) is $15.00 and the price of capital (r) is $5.00. If the firm is using 100 units of capital in production, how much should be employed to minimize costs?
- Consider the following firm with the production functionQ = F(L) = 2L^\frac12 L = labor, Wage w=12. Fixed cost is FC = 500 (sunk cost). a. Derive the short run
- Suppose a firm must pay labor (L) a wage rate (w) of $10 per unit, and the rental rate (r) on capital (K) is $20 per unit. A. Write the equation for the isocost line. What is the slope? B. Draw a gr
- The economy has 160,000 units of capital and a labor force of 10,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage, total output, and the total
- A firm has the production function: q = 10L^{0.5}K^{0.5}, the price of labor is w = 10 and the price of capital is r = 20 a) demonstrate that this function has constant returns to scale. b) derive the short-run marginal and average variable cost functio
- When will the scale effect of a wage increase cause a reduction in the quantity of labor demanded? a. Always. b. When labor is not a regressive factor. c. When labor and capital are substitutes in production. d. When labor and capital are complements
- Consider a firm which produces according to the following production function just by using labor f(l)=ln(l) a) Solve the cost minimization problem of this firm for the given wage rate, w. b) Derive t
- 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
- Consider the following table for a profit-max, perfectly competitive firm that produces using only labor and capital. Calculate the values for the table cells with letters in them. |Labor Used |Quant
- 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
- 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
- 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.
- 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 $