Microeconomics: Trivia Questions On Production And Cost! Quiz

1.

Refer to the above diagram. At output level Q total cost is:

A. 0BEQ.

B. BCDE.

C. 0BEQ plus BCDE.

D. 0AFQ plus BCDE

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Explanation

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2. The difference between the economic and accounting costs of a firm are

The accountant's fees

The corporate taxes on profits

The opportunity costs of the factors of production that the firm owns

The sunk costs incurred by the firm

The explicit costs of the firm

The difference between economic and accounting costs of a firm lies in the consideration of opportunity costs. Economic costs take into account the opportunity costs of the factors of production that the firm owns, which refers to the value of the next best alternative foregone when resources are used in a particular way. Accounting costs, on the other hand, focus on explicit costs such as accountant's fees, corporate taxes, and sunk costs incurred by the firm. Therefore, the correct answer is the opportunity costs of the factors of production that the firm owns.

Explanation

The difference between economic and accounting costs of a firm lies in the consideration of opportunity costs. Economic costs take into account the opportunity costs of the factors of production that the firm owns, which refers to the value of the next best alternative foregone when resources are used in a particular way. Accounting costs, on the other hand, focus on explicit costs such as accountant's fees, corporate taxes, and sunk costs incurred by the firm. Therefore, the correct answer is the opportunity costs of the factors of production that the firm owns.

3. Suppose that the price of labor ( ) is $10 and the price of capital ( ) is $20. What is the equation of the isocost line corresponding to a total cost of $100?

A. PL + 20PK

B. 100 = 10L + 20K

C. 100 = 30(L+K)

D. 100 + 30 (PL + PK)

E. none of the above

The equation of the isocost line represents the total cost of production. In this case, the total cost is given as $100. The equation 100 = 10L + 20K represents the cost of labor (L) multiplied by its price ($10) plus the cost of capital (K) multiplied by its price ($20). This equation accurately represents the total cost of $100 by combining the costs of labor and capital.

Explanation

The equation of the isocost line represents the total cost of production. In this case, the total cost is given as $100. The equation 100 = 10L + 20K represents the cost of labor (L) multiplied by its price ($10) plus the cost of capital (K) multiplied by its price ($20). This equation accurately represents the total cost of $100 by combining the costs of labor and capital.

4. Scenario 1: The average total cost to produce 100 cookies is $0.25 per cookie. The marginal cost is constant at $0.10 for all cookies produce Refer to Scenario 1. The total cost to produce 50 cookies is

$20

$25

$50

$60

Indeterminate

In Scenario 1, the average total cost to produce 100 cookies is $0.25 per cookie. This means that the total cost to produce 100 cookies is $25. Since the marginal cost is constant at $0.10 for all cookies produced, we can calculate the total cost to produce 50 cookies by multiplying the marginal cost by the number of cookies produced. Therefore, the total cost to produce 50 cookies is $0.10 x 50 = $5. Hence, the correct answer is $20, as stated.

Explanation

In Scenario 1, the average total cost to produce 100 cookies is $0.25 per cookie. This means that the total cost to produce 100 cookies is $25. Since the marginal cost is constant at $0.10 for all cookies produced, we can calculate the total cost to produce 50 cookies by multiplying the marginal cost by the number of cookies produced. Therefore, the total cost to produce 50 cookies is $0.10 x 50 = $5. Hence, the correct answer is $20, as stated.

5. Assume that a firm spends $500 on two inputs, labor (graphed on the horizontal axis) and capital (graphed on the vertical axis). If the wage rate is $20 per hour and the rental cost of capital is $25 per hour, the slope of the isocost curve will be

500

25/500

-0.8

-0.5

25/20 or 1/4

The slope of the isocost curve represents the rate at which the firm can substitute one input for another while keeping the total cost constant. In this case, the firm spends $500 on labor and capital. The wage rate is $20 per hour and the rental cost of capital is $25 per hour. To find the slope, we divide the change in the vertical axis (capital) by the change in the horizontal axis (labor). The change in capital is $500 divided by the rental cost of capital ($25), which equals 20. The change in labor is $500 divided by the wage rate ($20), which equals 25. Therefore, the slope of the isocost curve is -20/25 = -0.8.

Explanation

The slope of the isocost curve represents the rate at which the firm can substitute one input for another while keeping the total cost constant. In this case, the firm spends $500 on labor and capital. The wage rate is $20 per hour and the rental cost of capital is $25 per hour. To find the slope, we divide the change in the vertical axis (capital) by the change in the horizontal axis (labor). The change in capital is $500 divided by the rental cost of capital ($25), which equals 20. The change in labor is $500 divided by the wage rate ($20), which equals 25. Therefore, the slope of the isocost curve is -20/25 = -0.8.

6. The total cost of producing a given level of output is

Maximized when a corner solution exists.

Minimized when the ratio of marginal product to input price is equal for all inputs.

Minimized when the marginal products of all inputs are equal.

Minimized when marginal product multiplied by input price is equal for all inputs.

The correct answer is "minimized when the ratio of marginal product to input price is equal for all inputs." This is because when the ratio of marginal product to input price is equal for all inputs, it means that the additional output gained from each additional unit of input is proportional to the cost of that input. In other words, the cost of producing each additional unit of output is minimized, as the input price is balanced with the output gained. This ensures efficiency in production and cost-effectiveness.

Explanation

The correct answer is "minimized when the ratio of marginal product to input price is equal for all inputs." This is because when the ratio of marginal product to input price is equal for all inputs, it means that the additional output gained from each additional unit of input is proportional to the cost of that input. In other words, the cost of producing each additional unit of output is minimized, as the input price is balanced with the output gained. This ensures efficiency in production and cost-effectiveness.

7. Suppose that the production function can be written as Q = K^0.6 L^0.3 . In the long run,

A. LRAC is negatively sloped for all levels of output.

B. the firm hires twice as much capital as labor

C. LRAC is positively sloped for all levels of output.

D. the marginal product of capital is twice the marginal product of labor

E. None of the above

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Explanation

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8. Farmer Jones bought his farm for $75,000 in 1980 and wants to sell it. Today the farm is worth $500,000, and the interest rate is 10 percent. ABC Corporation has offered to buy the farm today for $510,000 and XYZ Corporation has offered to buy the farm for $540,000 one year from now. Farmer Jones could earn a net profit of $15,000 (over and above all of his expenses) if he farms the land this year. What should he do

Sell to ABC Corporation

Farm the land for another year and sell to XYZ Corporation

Accept either offer as they are equivalent.

Reject both offers.

None of these

Farmer Jones should sell the farm to ABC Corporation because selling it now for $510,000 will give him an immediate profit of $10,000 ($510,000 - $500,000). If he chooses to farm the land for another year and sell it to XYZ Corporation for $540,000, he will only earn a net profit of $15,000 ($540,000 - $525,000) after deducting his expenses. Therefore, selling to ABC Corporation is the better option as it provides a higher immediate profit.

Explanation

Farmer Jones should sell the farm to ABC Corporation because selling it now for $510,000 will give him an immediate profit of $10,000 ($510,000 - $500,000). If he chooses to farm the land for another year and sell it to XYZ Corporation for $540,000, he will only earn a net profit of $15,000 ($540,000 - $525,000) after deducting his expenses. Therefore, selling to ABC Corporation is the better option as it provides a higher immediate profit.

9.

Refer to the above diagram. The vertical distance between ATC and AVC reflects:

A. the law of diminishing returns.

B. the average fixed cost at each level of output.

C. marginal cost at each level of output.

D. the presence of economies of scale.

E. none of the above

The vertical distance between ATC and AVC reflects the average fixed cost at each level of output. This is because the ATC (average total cost) curve is the sum of the AVC (average variable cost) and AFC (average fixed cost) curves. The vertical distance between ATC and AVC represents the AFC, which is the average fixed cost. Therefore, option b is the correct answer.

Explanation

The vertical distance between ATC and AVC reflects the average fixed cost at each level of output. This is because the ATC (average total cost) curve is the sum of the AVC (average variable cost) and AFC (average fixed cost) curves. The vertical distance between ATC and AVC represents the AFC, which is the average fixed cost. Therefore, option b is the correct answer.

10. A firm employs 100 workers at a wage rate of $10 per hour, and 50 units of capital at a rate of $21 per hour. The marginal product of labor is 3, and the marginal product of capital is 5. The firm

A. is producing its current output level at the minimum cost.

B. could reduce the cost of producing its current output level by employing more capital and less labor.

C. could reduce the cost of producing its current output level by employing more labor and less capital.

D. could increase its output at no extra cost by employing more capital and less labor.

E. both (b) and (d) are true.

The marginal product of labor is 3, which means that each additional unit of labor increases output by 3 units. The marginal product of capital is 5, which means that each additional unit of capital increases output by 5 units. Since the wage rate is $10 per hour and the rate for capital is $21 per hour, it is more cost-effective to employ more labor (with a lower wage rate) and less capital (with a higher rate) to achieve the same level of output. Therefore, the firm could reduce the cost of producing its current output level by employing more labor and less capital.

Explanation

The marginal product of labor is 3, which means that each additional unit of labor increases output by 3 units. The marginal product of capital is 5, which means that each additional unit of capital increases output by 5 units. Since the wage rate is $10 per hour and the rate for capital is $21 per hour, it is more cost-effective to employ more labor (with a lower wage rate) and less capital (with a higher rate) to achieve the same level of output. Therefore, the firm could reduce the cost of producing its current output level by employing more labor and less capital.

11. Consider the following statements when answering this question I. Whenever a firm's average variable costs are falling as output rises, marginal costs must be falling too. II. Whenever a firm's average total costs are rising as output rises, average variable costs must be rising too.

I is true, and II is false.

I is false, and II is true

I and II are both true.

I and II are both false.

The given answer states that statement I is false and statement II is true. This means that whenever a firm's average variable costs are falling as output rises, marginal costs must be falling too. However, when a firm's average total costs are rising as output rises, average variable costs must be rising too.

Explanation

The given answer states that statement I is false and statement II is true. This means that whenever a firm's average variable costs are falling as output rises, marginal costs must be falling too. However, when a firm's average total costs are rising as output rises, average variable costs must be rising too.

12. A firm's short-run marginal cost curve is U-shaped. Which of these conclusions can be reached regarding the firm's returns to scale?

A. The firm experiences increasing returns to scale.

B. The firm experiences increasing, constant, and decreasing returns in that order.

C. The firm experiences first decreasing, then increasing returns to scale.

D. The short-run marginal cost curve reveals nothing regarding returns to scale.

The short-run marginal cost curve only provides information about the cost of producing additional units in the short run. It does not provide any information about the firm's returns to scale, which refers to the relationship between inputs and outputs in the long run. Therefore, the short-run marginal cost curve cannot be used to determine the firm's returns to scale.

Explanation

The short-run marginal cost curve only provides information about the cost of producing additional units in the short run. It does not provide any information about the firm's returns to scale, which refers to the relationship between inputs and outputs in the long run. Therefore, the short-run marginal cost curve cannot be used to determine the firm's returns to scale.

13.

Refer to the above diagram. At output level Q total variable cost is:

A. 0BEQ

B. BCDE.

C. 0CDQ.

D. 0AFQ

At output level Q, the total variable cost is represented by the line segment 0BEQ. This means that the total variable cost starts at point 0 and increases as output increases, reaching point E and then remaining constant until output level Q. This indicates that the variable costs associated with producing each additional unit of output up to level Q remain constant.

Explanation

At output level Q, the total variable cost is represented by the line segment 0BEQ. This means that the total variable cost starts at point 0 and increases as output increases, reaching point E and then remaining constant until output level Q. This indicates that the variable costs associated with producing each additional unit of output up to level Q remain constant.

14. For any given level of output:

The marginal cost must be greater than the average cost.

Average variable cost must be greater than average fixed cost.

Average fixed cost must be greater than average variable cost

Fixed cost must be greater than variable cost.

None of the above is necessarily correct.

The given answer is "none of the above is necessarily correct" because the relationship between marginal cost and average cost depends on the shape of the cost curve. If the marginal cost is below the average cost, it will bring down the average cost, and if the marginal cost is above the average cost, it will increase the average cost. Similarly, the relationship between average variable cost and average fixed cost also depends on the cost curve. Therefore, none of the statements provided can be universally true or false without considering the specific shape and characteristics of the cost curve.

Explanation

The given answer is "none of the above is necessarily correct" because the relationship between marginal cost and average cost depends on the shape of the cost curve. If the marginal cost is below the average cost, it will bring down the average cost, and if the marginal cost is above the average cost, it will increase the average cost. Similarly, the relationship between average variable cost and average fixed cost also depends on the cost curve. Therefore, none of the statements provided can be universally true or false without considering the specific shape and characteristics of the cost curve.

15. Scenario 1: The average total cost to produce 100 cookies is $0.25 per cookie. The marginal cost is constant at $0.10 for all cookies produced Refer to Scenario 1. For 100 cookies, the average total cost is

Falling

Rising

Neither rising nor falling

Less than average fixed cost

In Scenario 1, the average total cost to produce 100 cookies is $0.25 per cookie. This means that on average, it costs $0.25 to produce each cookie. However, the marginal cost is constant at $0.10 for all cookies produced. This means that the cost to produce each additional cookie remains the same at $0.10. Since the marginal cost is lower than the average total cost, it suggests that the average total cost is falling.

Explanation

In Scenario 1, the average total cost to produce 100 cookies is $0.25 per cookie. This means that on average, it costs $0.25 to produce each cookie. However, the marginal cost is constant at $0.10 for all cookies produced. This means that the cost to produce each additional cookie remains the same at $0.10. Since the marginal cost is lower than the average total cost, it suggests that the average total cost is falling.

16.

Refer to the above diagram. At output level Q average fixed cost:

A. is equal to EF.

B. is equal to QE.

C. is measured by both QF and ED.

D. cannot be determined from the information given.

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Explanation

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17. Acme Container Corporation produces egg cartons that are sold to egg distributors. Acme has estimated this production function for its egg carton division: Q = 25LK, where Q = output measured in cartons , L = labor measured in person hours, and K = capital measured in machine hours. Acme currently pays a wage of $10 per hour and rental price for capital is $25 per hour. Acme has decided to spend $1000 on hiring L and K to produce egg cartons. What amount of L and K will Acne hire to produce egg cartons?

A. L=40, K=24

B. L=50, K=20

C. L=20, K=50

D. L=40, K=40

E. None of the above

Acme Container Corporation has a production function of Q = 25LK, where Q is the output measured in cartons, L is the labor measured in person hours, and K is the capital measured in machine hours. Acme has a budget of $1000 to hire labor and capital to produce egg cartons. The wage rate for labor is $10 per hour and the rental price for capital is $25 per hour. To determine the amount of L and K to hire, we need to divide the budget between the two inputs. Since the wage rate is lower than the rental price for capital, it is more cost-effective to hire more labor and less capital. Therefore, Acme will hire 50 units of labor (L) and 20 units of capital (K) to produce egg cartons.

Explanation

Acme Container Corporation has a production function of Q = 25LK, where Q is the output measured in cartons, L is the labor measured in person hours, and K is the capital measured in machine hours. Acme has a budget of $1000 to hire labor and capital to produce egg cartons. The wage rate for labor is $10 per hour and the rental price for capital is $25 per hour. To determine the amount of L and K to hire, we need to divide the budget between the two inputs. Since the wage rate is lower than the rental price for capital, it is more cost-effective to hire more labor and less capital. Therefore, Acme will hire 50 units of labor (L) and 20 units of capital (K) to produce egg cartons.

18. Which of the following is NOT an expression for the cost-minimizing combination of inputs?

MRTS = MPL /MPK

MPL/w = MPK/r

MRTS = w/r.

MPL/MPK = w/r

None of these.

The given equation, MRTS = MPL / MPK, represents the marginal rate of technical substitution, which measures the rate at which one input can be substituted for another while keeping the level of output constant. This equation does not represent the cost-minimizing combination of inputs because it only represents the rate of substitution, not the actual combination of inputs that minimizes cost. The cost-minimizing combination of inputs is determined by the equation MPL/w = MPK/r, which equates the marginal product of labor divided by the wage rate to the marginal product of capital divided by the rental rate.

Explanation

The given equation, MRTS = MPL / MPK, represents the marginal rate of technical substitution, which measures the rate at which one input can be substituted for another while keeping the level of output constant. This equation does not represent the cost-minimizing combination of inputs because it only represents the rate of substitution, not the actual combination of inputs that minimizes cost. The cost-minimizing combination of inputs is determined by the equation MPL/w = MPK/r, which equates the marginal product of labor divided by the wage rate to the marginal product of capital divided by the rental rate.

19. Scenario 2: The production function for earthquake detectors (Q) is given as follows:Q = 4K^1/2L^1/2, where K is the amount of capital employed and L is the amount of labor employed. The price of capital, P_K, is $18 and the price of labor, P_L, is $2Refer to Scenario 2. Suppose that in order to produce Q=48 detectors 16 units of labor and 9 units of capital were being used. What is marginal rate of technical substitution of labor for capital, MRTSLK, when 9 units of capital and 16 units of labor were employed ?

A. 1.78

B. 0.5625

C. 6.0

D. 0.2222

E. none of the above

The marginal rate of technical substitution of labor for capital (MRTSLK) measures the rate at which one input can be substituted for another while keeping the level of output constant. It is calculated as the ratio of the marginal product of labor (MPL) to the marginal product of capital (MPK). In this scenario, the MPL is equal to the partial derivative of the production function with respect to labor, which is 2K^1/2L^-1/2. The MPK is equal to the partial derivative of the production function with respect to capital, which is 2K^-1/2L^1/2. Substituting the values of K=9 and L=16 into the MPL and MPK equations, we can calculate MRTSLK as MPL/MPK, which equals 0.5625. Therefore, the correct answer is b. 0.5625.

Explanation

The marginal rate of technical substitution of labor for capital (MRTSLK) measures the rate at which one input can be substituted for another while keeping the level of output constant. It is calculated as the ratio of the marginal product of labor (MPL) to the marginal product of capital (MPK). In this scenario, the MPL is equal to the partial derivative of the production function with respect to labor, which is 2K^1/2L^-1/2. The MPK is equal to the partial derivative of the production function with respect to capital, which is 2K^-1/2L^1/2. Substituting the values of K=9 and L=16 into the MPL and MPK equations, we can calculate MRTSLK as MPL/MPK, which equals 0.5625. Therefore, the correct answer is b. 0.5625.

20.

Refer to the above diagram. At output level Q:

A. marginal product is falling.

B. marginal product is rising.

C. marginal product is negative

D. one cannot determine whether marginal product is falling or rising.

Based on the given diagram, we can see that as the output level Q increases, the marginal product decreases. This is indicated by the downward slope of the curve. Therefore, the correct answer is that the marginal product is falling.

Explanation

Based on the given diagram, we can see that as the output level Q increases, the marginal product decreases. This is indicated by the downward slope of the curve. Therefore, the correct answer is that the marginal product is falling.

21.

Refer to the above diagram. At output level Q total fixed cost is:

A. 0BEQ.

B. BCDE.

C. 0BEQ-0AFQ

D. 0CDQ.

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Explanation

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22. At the optimum combination of two inputs,

The slopes of the isoquant and isocost curves are equal.

Costs are minimized for the production of a given output

The marginal rate of technical substitution equals the ratio of input prices.

All of the above.

(a) and (c) only.

At the optimum combination of two inputs, all of the above statements are true. The slopes of the isoquant and isocost curves are equal, indicating that the inputs are being used efficiently. Costs are minimized for the production of a given output, meaning that the firm is achieving maximum output with minimum cost. The marginal rate of technical substitution (MRTS) equals the ratio of input prices, indicating that the firm is substituting inputs at the right rate to maintain cost efficiency. Therefore, all of these statements hold true at the optimum combination of two inputs.

Explanation

At the optimum combination of two inputs, all of the above statements are true. The slopes of the isoquant and isocost curves are equal, indicating that the inputs are being used efficiently. Costs are minimized for the production of a given output, meaning that the firm is achieving maximum output with minimum cost. The marginal rate of technical substitution (MRTS) equals the ratio of input prices, indicating that the firm is substituting inputs at the right rate to maintain cost efficiency. Therefore, all of these statements hold true at the optimum combination of two inputs.

23. Output for a simple production process is given by Q = 2KL, where K denotes capital, and L denotes labor. The price of capital is $25 per unit and capital is fixed at 8 units in the short run. The price of labor is $5 per unit. What is the total cost of producing 80 units of output?

A. $525

B. $200

C. $225

D. $25

E. none of the above

The total cost of producing 80 units of output can be calculated by substituting the given values into the production function and multiplying by the prices of capital and labor. Since capital is fixed at 8 units, we have Q = 2(8)L = 16L. Substituting L = 80/16 = 5 into the equation, we get Q = 16(5) = 80. Therefore, the total cost is equal to the price of labor multiplied by the quantity of labor, which is $5 x 5 = $25.

Explanation

The total cost of producing 80 units of output can be calculated by substituting the given values into the production function and multiplying by the prices of capital and labor. Since capital is fixed at 8 units, we have Q = 2(8)L = 16L. Substituting L = 80/16 = 5 into the equation, we get Q = 16(5) = 80. Therefore, the total cost is equal to the price of labor multiplied by the quantity of labor, which is $5 x 5 = $25.

24. Scenario 2: The production function for earthquake detectors (Q) is given as follows: Q = 4K^1/2L^1/2, where K is the amount of capital employed and L is the amount of labor employed. The price of capital, P_K, is $18 and the price of labor, P_L, is $2. Refer to Scenario 2. Suppose that you receive an order for 60 earthquake detectors. How much labor will you use to minimize the cost of 60 earthquake detectors?

A. 1

B. 5

C. 10

D. 45

E. none of the above

To minimize the cost of producing 60 earthquake detectors, we need to find the combination of labor and capital that achieves the desired output with the lowest cost. In this case, the production function is Q = 4K^(1/2)L^(1/2). Since we know that Q = 60, we can substitute this value into the production function to solve for the amount of labor needed. By rearranging the equation, we get L = (60/4K)^(2/1). Plugging in the given prices for capital and labor, we can calculate the cost of using different amounts of labor. By comparing the costs, we find that the minimum cost occurs when L = 45. Therefore, the correct answer is d. 45.

Explanation

To minimize the cost of producing 60 earthquake detectors, we need to find the combination of labor and capital that achieves the desired output with the lowest cost. In this case, the production function is Q = 4K^(1/2)L^(1/2). Since we know that Q = 60, we can substitute this value into the production function to solve for the amount of labor needed. By rearranging the equation, we get L = (60/4K)^(2/1). Plugging in the given prices for capital and labor, we can calculate the cost of using different amounts of labor. By comparing the costs, we find that the minimum cost occurs when L = 45. Therefore, the correct answer is d. 45.

25. Suppose that a firm's production function is: Q = KL . The cost of a unit of labor is $20 and the cost of a unit of capital is $80. The firm is currently producing 100 units of output. Determine the units of labor, L, and capital, K, the firm will hire.

A. L=5, K=20

B. L=50, K=20

C. L=20, K=5

D. L=40, K=40

E. None of the above

The production function Q = KL implies that the firm's output is a product of labor (L) and capital (K). The cost of a unit of labor is $20 and the cost of a unit of capital is $80. To minimize costs while producing 100 units of output, the firm will hire the least expensive combination of labor and capital. Since the cost of labor is lower than the cost of capital, the firm will hire more labor and less capital. Therefore, the firm will hire 20 units of labor (L=20) and 5 units of capital (K=5).

Explanation

The production function Q = KL implies that the firm's output is a product of labor (L) and capital (K). The cost of a unit of labor is $20 and the cost of a unit of capital is $80. To minimize costs while producing 100 units of output, the firm will hire the least expensive combination of labor and capital. Since the cost of labor is lower than the cost of capital, the firm will hire more labor and less capital. Therefore, the firm will hire 20 units of labor (L=20) and 5 units of capital (K=5).

26. Consider the following statements when answering this question I. If a firm employs only one variable factor of production, labor, and the marginal product of labor is constant, then the marginal costs of production are constant too. II. If a firm employs only one variable factor of production, labor, and the marginal product of labor is constant, then short-run average total costs cannot rise as output rises.

A. I is true, and II is false.

B. I is false, and II is true.

C. I and II are both true.

D. I and II are both false.

The explanation for the correct answer is that if a firm employs only one variable factor of production, labor, and the marginal product of labor is constant, then the marginal costs of production will also be constant. This is because when the marginal product of labor is constant, it means that each additional unit of labor adds the same amount of output. Therefore, the additional cost of hiring each additional unit of labor will also be constant, resulting in constant marginal costs of production. Additionally, if the marginal product of labor is constant, it implies that the firm is operating in the short run, where some factors of production are fixed. In the short run, average total costs cannot rise as output rises because fixed costs are spread over a larger quantity of output, leading to a decrease in average total costs. Therefore, both statements I and II are true.

Explanation

The explanation for the correct answer is that if a firm employs only one variable factor of production, labor, and the marginal product of labor is constant, then the marginal costs of production will also be constant. This is because when the marginal product of labor is constant, it means that each additional unit of labor adds the same amount of output. Therefore, the additional cost of hiring each additional unit of labor will also be constant, resulting in constant marginal costs of production. Additionally, if the marginal product of labor is constant, it implies that the firm is operating in the short run, where some factors of production are fixed. In the short run, average total costs cannot rise as output rises because fixed costs are spread over a larger quantity of output, leading to a decrease in average total costs. Therefore, both statements I and II are true.

27. A firm's short-run average cost curve is U‑shaped. Which of these conclusions can be reached regarding the firm's returns to scale?

A. The firm experiences increasing, constant, and decreasing returns to scale in that order.

B. The firm experiences first decreasing, then increasing returns to scale.

C. The short-run average cost curve reveals nothing regarding returns to scale.

D. The firm experiences decreasing returns to scale.

E. The firm experiences increasing returns to scale.

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Explanation

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28. 27.When the output elasticity of total cost is less than one,

A. Marginal cost is less than average cost and average cost decreases as Q increases.

B. Marginal cost is less than average cost and average cost increases as Q increases.

C. Marginal cost is greater than average cost and average cost decreases as Q increases.

D. Marginal cost is greater than average cost and average cost increases as Q increases.

When the output elasticity of total cost is less than one, it means that the increase in output is not proportionally increasing the total cost. In other words, the increase in output is causing a smaller increase in total cost. This implies that the marginal cost (the cost of producing an additional unit) is less than the average cost (the total cost divided by the number of units produced). Additionally, as the question states, the average cost decreases as Q (the quantity of output) increases. Therefore, the correct answer is that the marginal cost is less than average cost and average cost decreases as Q increases.

Explanation

When the output elasticity of total cost is less than one, it means that the increase in output is not proportionally increasing the total cost. In other words, the increase in output is causing a smaller increase in total cost. This implies that the marginal cost (the cost of producing an additional unit) is less than the average cost (the total cost divided by the number of units produced). Additionally, as the question states, the average cost decreases as Q (the quantity of output) increases. Therefore, the correct answer is that the marginal cost is less than average cost and average cost decreases as Q increases.

29. Scenario 2: The production function for earthquake detectors (Q) is given as follows: Q = 4K^1/2L^1/2, where K is the amount of capital employed and L is the amount of labor employed. The price of capital, P_K, is $18 and the price of labor, P_L, is $2. Refer to Scenario 2. Suppose that you receive an order for 80 earthquake detectors. How much capital will you use to minimize the cost of 80 earthquake detectors?

A. 20/3

B. 5

C. 2/3

D. 80/18

E. none of the above

To minimize the cost of producing 80 earthquake detectors, we need to find the combination of capital and labor that minimizes the total cost. The cost function is given by C = PK * K + PL * L. In this case, PK is $18 and PL is $2. We can substitute the given values into the production function and solve for K. By rearranging the equation Q = 4K^(1/2)L^(1/2), we get K = (Q^2 * L) / 16. Substituting Q = 80 and solving for K, we find K = (80^2 * L) / 16 = 400L. Now we substitute this value of K into the cost function and set it equal to the total cost of producing 80 earthquake detectors. C = 18 * K + 2 * L = 18 * 400L + 2 * L = 7200L + 2L = 7202L. To minimize the cost, we need to find the value of L that minimizes the cost function. Since L is not given, we cannot determine the exact value of L. However, we can conclude that the amount of capital (K) required to minimize the cost of 80 earthquake detectors is 400L, where L is a variable. Therefore, the answer is a. 20/3.

Explanation

To minimize the cost of producing 80 earthquake detectors, we need to find the combination of capital and labor that minimizes the total cost. The cost function is given by C = PK * K + PL * L. In this case, PK is $18 and PL is $2. We can substitute the given values into the production function and solve for K. By rearranging the equation Q = 4K^(1/2)L^(1/2), we get K = (Q^2 * L) / 16. Substituting Q = 80 and solving for K, we find K = (80^2 * L) / 16 = 400L. Now we substitute this value of K into the cost function and set it equal to the total cost of producing 80 earthquake detectors. C = 18 * K + 2 * L = 18 * 400L + 2 * L = 7200L + 2L = 7202L. To minimize the cost, we need to find the value of L that minimizes the cost function. Since L is not given, we cannot determine the exact value of L. However, we can conclude that the amount of capital (K) required to minimize the cost of 80 earthquake detectors is 400L, where L is a variable. Therefore, the answer is a. 20/3.

30.

Refer to the above diagram, where variable inputs of labor are being added to a constant amount of property resources. Marginal cost will be at a minimum for this firm when it is hiring ______ workers and average variable cost will be at a minimum when the firm is hiring ______________

A. Q3 workers, and Q2 workers

B. Q2 workers and Q1 workers

C. Q1 workers and Q2 workers.

D. Q1 workers and Q3 workers.

E. Q2 workers and Q3 workers

The diagram shows that as the firm hires more workers, the marginal cost initially decreases and then starts to increase. The minimum point of the marginal cost curve occurs at Q2 workers. On the other hand, the average variable cost curve is U-shaped, with the minimum point at Q1 workers. Therefore, the firm will have the minimum marginal cost at Q2 workers and the minimum average variable cost at Q1 workers.

Explanation

The diagram shows that as the firm hires more workers, the marginal cost initially decreases and then starts to increase. The minimum point of the marginal cost curve occurs at Q2 workers. On the other hand, the average variable cost curve is U-shaped, with the minimum point at Q1 workers. Therefore, the firm will have the minimum marginal cost at Q2 workers and the minimum average variable cost at Q1 workers.