Production and CostsClass 12 Introductory Microeconomics NCERT Solutions
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Q1Questions
Explain the concept of a production function.
Solution
A production function describes the relationship between the physical inputs used in a production process and the maximum physical output that can be produced. It is a technological relationship that specifies the maximum quantity of output that can be produced with any given combination of inputs.
Key features of a production function are:
- Relationship between Inputs and Output: It shows how inputs like labour (L) and capital (K) are transformed into output (q).
- Technological Efficiency: It assumes that the firm is using its inputs efficiently. This means it is not possible to get any more output from the same level of inputs.
- Given Technology: A production function is defined for a specific state of technology. If technology improves, a new production function is created, allowing more output from the same inputs.
For example, a production function with two inputs, labour (L) and capital (K), can be represented as:
q = f(L, K)
This equation states that the maximum output (q) is a function of the amount of labour and capital used.Q2Questions
What is the total product of an input?
Solution
The Total Product (TP) of an input is the total quantity of output produced by a firm with a given quantity of that input, while keeping all other inputs constant. It describes the relationship between a variable input and the resulting output.
For instance, if we consider labour as the variable input and keep capital fixed, the Total Product of Labour (TP_L) would show the different levels of output obtained by employing different amounts of labour. As the amount of the variable input (labour) increases, the total product typically increases, at least initially.
Q3Questions
What is the average product of an input?
Solution
The Average Product (AP) of an input is defined as the output produced per unit of that variable input. It is calculated by dividing the Total Product (TP) by the quantity of the variable input used.
For example, the Average Product of Labour (AP_L) is calculated as:
AP_L = Total Product of Labour (TP_L) / Quantity of Labour (L)Average product helps in understanding the productivity of the variable input. It typically rises at first, reaches a maximum, and then begins to fall as more of the variable input is employed.
Q4Questions
What is the marginal product of an input?
Solution
The Marginal Product (MP) of an input is the additional output produced by using one more unit of that input, while keeping all other inputs constant. It measures the change in total output resulting from a one-unit change in the variable input.
For example, the Marginal Product of Labour (MP_L) is calculated as the change in Total Product (TP) divided by the change in the quantity of Labour (L):
MP_L = Change in Total Product (ΔTP_L) / Change in Labour (ΔL)Essentially, it is the contribution of the last unit of the variable input to the total production. The MP curve is typically inverse 'U'-shaped.
Q5Questions
Explain the relationship between the marginal products and the total product of an input.
Solution
The relationship between Total Product (TP) and Marginal Product (MP) is fundamental to understanding production in the short run.
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TP as the sum of MP: The Total Product at any level of a variable input is the sum of all the marginal products up to that level. For example, TP of 3 units of labour is MP of the 1st unit + MP of the 2nd unit + MP of the 3rd unit.
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Relationship based on MP's behavior:
- When MP increases: TP increases at an increasing rate. Each additional unit of input adds more to the total output than the previous unit.
- When MP decreases (but is positive): TP increases at a decreasing rate. Each additional unit of input adds less to the total output than the previous unit.
- When MP is zero: TP is at its maximum. Adding one more unit of input does not change the total output.
- When MP is negative: TP starts to decline. Adding more units of the variable input actually reduces the total output.
Q6Questions
Explain the concepts of the short run and the long run.
Solution
In economics, the distinction between the short run and the long run is based on the flexibility of a firm to change its inputs, not on a specific duration of time like months or years.
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The Short Run: The short run is a period in which at least one factor of production is fixed and cannot be changed. To alter the level of output, the firm can only change its variable factors. For example, a firm might be able to hire more workers (variable factor) but cannot build a new factory (fixed factor) in the short run. The costs associated with fixed factors are called fixed costs.
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The Long Run: The long run is a period of time long enough for a firm to vary all its factors of production. In the long run, there are no fixed factors; all inputs, including capital, machinery, and factory size, are variable. This allows the firm to adjust its scale of operations fully to meet changes in demand. Consequently, there are no fixed costs in the long run.
Q7Questions
What is the law of diminishing marginal product?
Solution
The law of diminishing marginal product states that as we increase the quantity of one input (the variable input) while keeping other inputs fixed, the marginal product of the variable input will eventually decline.
This means that after a certain point, each additional unit of the variable input will contribute less to the total output than the previous unit. This occurs because the fixed factor (e.g., land or machinery) becomes overburdened by the variable factor (e.g., labour). Initially, adding more workers might lead to specialization and increased efficiency (increasing marginal product), but eventually, the workplace becomes too crowded, and workers start getting in each other's way, leading to a fall in marginal product.
Q8Questions
What is the law of variable proportions?
Solution
The law of variable proportions is another name for the law of diminishing marginal product. It describes the behavior of output when the quantity of one factor of production is varied, while the quantities of other factors are kept constant. The law states that as we increase the quantity of the variable factor, the marginal product of that factor initially rises, reaches a maximum, and then begins to fall.
The law operates in three phases:
- Phase 1: Increasing Returns: Marginal product increases as the variable factor is increased.
- Phase 2: Diminishing Returns: Marginal product starts to decrease but remains positive.
- Phase 3: Negative Returns: Marginal product becomes negative, causing total product to fall.
Q9Questions
When does a production function satisfy constant returns to scale?
Solution
A production function satisfies Constant Returns to Scale (CRS) when a proportional increase in all inputs results in an increase in output by the same proportion. For example, if a firm doubles all its inputs (labour and capital), its output will also exactly double.
Mathematically, if the production function is
q = f(x₁, x₂) and all inputs are increased by a factor t (where t > 1), the function exhibits CRS if:f(tx₁, tx₂) = t * f(x₁, x₂)Under CRS, the average cost of production remains constant as the scale of production increases.
Q10Questions
When does a production function satisfy increasing returns to scale?
Solution
A production function satisfies Increasing Returns to Scale (IRS) when a proportional increase in all inputs results in an increase in output by a larger proportion. For example, if a firm doubles all its inputs, its output will more than double.
This can happen due to factors like greater specialization, use of more efficient large-scale machinery, and managerial efficiencies.
Mathematically, if the production function is
q = f(x₁, x₂) and all inputs are increased by a factor t (where t > 1), the function exhibits IRS if:f(tx₁, tx₂) > t * f(x₁, x₂)Under IRS, the average cost of production falls as the scale of production increases.
Q11Questions
When does a production function satisfy decreasing returns to scale?
Solution
A production function satisfies Decreasing Returns to Scale (DRS) when a proportional increase in all inputs results in an increase in output by a smaller proportion. For example, if a firm doubles all its inputs, its output will increase, but by less than double.
This often occurs in very large firms due to managerial difficulties, coordination problems, and communication breakdowns.
Mathematically, if the production function is
q = f(x₁, x₂) and all inputs are increased by a factor t (where t > 1), the function exhibits DRS if:f(tx₁, tx₂) < t * f(x₁, x₂)Under DRS, the average cost of production rises as the scale of production increases.
Q12Questions
Briefly explain the concept of the cost function.
Solution
The cost function of a firm describes the minimum cost of producing a certain level of output, given the prices of the factors of production and the available technology. For any desired level of output, a firm can typically use various combinations of inputs. The firm will choose the combination that is least expensive. The cost function mathematically represents this relationship between the level of output and the minimum cost of producing it.
In essence, it answers the question: "What is the lowest possible cost to produce 'q' units of output?"
Q13Questions
What are the total fixed cost, total variable cost and total cost of a firm? How are they related?
Solution
Total Fixed Cost (TFC): This is the cost that a firm incurs on its fixed factors of production. These costs do not change with the level of output. Even if the firm produces zero output, it must still pay its fixed costs (e.g., rent for the factory, salaries of permanent staff). The TFC curve is a horizontal line parallel to the output axis.
Total Variable Cost (TVC): This is the cost that a firm incurs on its variable factors of production. These costs vary directly with the level of output. TVC is zero when output is zero and increases as output increases (e.g., cost of raw materials, wages of temporary workers).
Total Cost (TC): This is the total expenditure incurred by a firm to produce a given level of output. It is the sum of total fixed cost and total variable cost.
Relationship: The relationship between them is straightforward:
TC = TFC + TVCThe TC curve starts from the level of TFC (at zero output) and has the same shape as the TVC curve, but is shifted vertically upwards by the amount of TFC.
Q14Questions
What are the average fixed cost, average variable cost and average cost of a firm? How are they related?
Solution
Average Fixed Cost (AFC): This is the total fixed cost per unit of output. It is calculated by dividing TFC by the quantity of output (q).
AFC = TFC / q
Since TFC is constant, AFC continuously declines as output increases.Average Variable Cost (AVC): This is the total variable cost per unit of output. It is calculated by dividing TVC by the quantity of output (q).
AVC = TVC / q
The AVC curve is typically 'U'-shaped due to the law of variable proportions.Average Cost (AC) or Short Run Average Cost (SAC): This is the total cost per unit of output. It is calculated by dividing TC by the quantity of output (q).
SAC = TC / q
The SAC curve is also 'U'-shaped.Relationship: Average cost is the sum of average fixed cost and average variable cost.
SAC = AFC + AVCThe vertical distance between the SAC and AVC curves is equal to the AFC. Since AFC continuously falls, the gap between the SAC and AVC curves becomes smaller as output increases.
Q15Questions
Can there be some fixed cost in the long run? If not, why?
Solution
No, there cannot be any fixed cost in the long run.
The reason is based on the very definition of the long run. The long run is defined as a period of time sufficient for a firm to vary all its inputs. In the long run, there are no fixed factors of production; all factors, including machinery, buildings, and land, are variable. Since fixed costs are the costs associated with fixed factors, and there are no fixed factors in the long run, there can be no fixed costs. All costs in the long run are variable costs.
Q16Questions
What does the average fixed cost curve look like? Why does it look so?
Solution
The Average Fixed Cost (AFC) curve is a downward-sloping curve that gets progressively closer to the horizontal axis but never touches it. This shape is known as a rectangular hyperbola.
It looks this way because AFC is calculated as Total Fixed Cost (TFC) divided by output (q):
AFC = TFC / q.- TFC is Constant: The numerator (TFC) is a fixed value, as fixed costs do not change with output.
- Output (q) Increases: The denominator (q) increases as production rises.
As you divide a constant number (TFC) by an increasingly larger number (q), the resulting value (AFC) continuously decreases. For example, if TFC is 20, at q=1, AFC=20; at q=2, AFC=10; at q=4, AFC=5, and so on. The curve approaches zero but never reaches it because TFC is never zero. The area of the rectangle formed under the curve at any point (AFC × q) is always equal to the constant TFC.
Q17Questions
What do the short run marginal cost, average variable cost and short run average cost curves look like?
Solution
In the short run, the marginal cost (SMC), average variable cost (AVC), and short run average cost (SAC) curves are all typically 'U'-shaped.
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Short Run Marginal Cost (SMC): The SMC curve first slopes downwards, reaches a minimum, and then slopes upwards. This 'U' shape is a direct result of the law of variable proportions. Initially, increasing marginal returns cause marginal cost to fall. Later, diminishing marginal returns cause marginal cost to rise.
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Average Variable Cost (AVC): The AVC curve is also 'U'-shaped. It lies above the SMC curve when it is falling and below the SMC curve when it is rising. The SMC curve intersects the AVC curve at the minimum point of the AVC.
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Short Run Average Cost (SAC): The SAC curve is also 'U'-shaped and lies above the AVC curve. It is the sum of AVC and AFC. Like the AVC curve, it is cut by the SMC curve at its minimum point. The minimum of the SAC curve occurs to the right of the minimum of the AVC curve because SAC includes the ever-falling AFC.
Q18Questions
Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?
Solution
The Short Run Marginal Cost (SMC) curve cuts the Average Variable Cost (AVC) curve from below at the AVC curve's minimum point. This relationship is mathematical.
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When SMC < AVC: If the cost of producing an additional unit (marginal cost) is less than the average variable cost of all previous units, this new, lower cost will pull the average down. Therefore, as long as SMC is below AVC, the AVC curve must be falling.
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When SMC > AVC: If the cost of producing an additional unit is greater than the current average variable cost, this new, higher cost will pull the average up. Therefore, once the SMC rises above the AVC, the AVC curve must be rising.
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When SMC = AVC: The only point where the AVC is neither falling nor rising is its minimum point. At this specific point, the marginal cost must be equal to the average variable cost. Hence, the SMC curve intersects the AVC curve at its lowest point.
Q19Questions
At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.
Solution
The Short Run Marginal Cost (SMC) curve cuts the Short Run Average Cost (SAC) curve from below at the minimum point of the SAC curve.
Reason: The reasoning is identical to the relationship between SMC and AVC. The SAC is the average of all costs, and the SMC is the cost of the next unit.
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When SMC < SAC: If the marginal cost of the next unit is less than the average cost of all preceding units, it will pull the average cost down. Thus, as long as the SMC curve is below the SAC curve, the SAC curve will be downward sloping.
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When SMC > SAC: If the marginal cost of the next unit is greater than the current average cost, it will pull the average cost up. Thus, when the SMC curve is above the SAC curve, the SAC curve will be upward sloping.
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When SMC = SAC: The SAC is at its minimum point where it is neither falling nor rising. This can only happen when the cost of the additional unit is exactly equal to the average cost. Therefore, the SMC curve must intersect the SAC curve at its minimum point.
Q20Questions
Why is the short run marginal cost curve 'U'-shaped?
Solution
The short run marginal cost (SMC) curve is 'U'-shaped due to the Law of Variable Proportions (or the Law of Diminishing Marginal Product).
Marginal cost is the additional cost of producing one more unit of output. In the short run, this additional cost is mainly the cost of the additional variable input (like labour) required.
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Initially (Downward-sloping part): In the initial stages of production, there are increasing returns to the variable factor. This means the marginal product of the variable input is rising. As each additional worker is more productive than the last, the firm needs progressively less additional labour to produce each extra unit of output. This causes the additional cost per unit, or marginal cost, to fall.
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Eventually (Upward-sloping part): After a certain point, diminishing returns to the variable factor set in. The marginal product of the variable input starts to fall. Now, each additional worker is less productive than the last. The firm needs progressively more additional labour to produce each extra unit of output. This causes the marginal cost to rise.
This pattern of initially falling and then rising marginal cost gives the SMC curve its characteristic 'U' shape.
Q21Questions
What do the long run marginal cost and the average cost curves look like?
Solution
Both the Long Run Average Cost (LRAC) and Long Run Marginal Cost (LRMC) curves are typically 'U'-shaped.
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Long Run Average Cost (LRAC) Curve: The 'U' shape of the LRAC curve reflects the returns to scale.
- Downward-sloping part: Corresponds to Increasing Returns to Scale (IRS). As the firm expands its scale of production, its output increases more than proportionally to the increase in inputs, causing the average cost per unit to fall.
- Minimum point: Corresponds to Constant Returns to Scale (CRS). Here, the firm is operating at its optimal scale, and the average cost is at its lowest.
- Upward-sloping part: Corresponds to Decreasing Returns to Scale (DRS). If the firm expands further, it may face inefficiencies (diseconomies of scale), causing output to increase less than proportionally to inputs, which leads to a rise in average cost.
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Long Run Marginal Cost (LRMC) Curve: The LRMC curve is also 'U'-shaped. It shows the change in long-run total cost from producing one more unit of output. Similar to the short-run relationship, the LRMC curve cuts the LRAC curve from below at the minimum point of the LRAC.
Q22Questions
The following table gives the total product schedule of labour. Find the corresponding average product and marginal product schedules of labour.
L TP_L 0 0 1 15 2 35 3 50 4 40 5 48
Solution
To find the Average Product (AP_L) and Marginal Product (MP_L), we use the following formulas:
AP_L = TP_L / LMP_L = ΔTP_L / ΔL(Change in Total Product / Change in Labour)
The calculated schedules are as follows:
| L (Labour) | TP_L (Total Product) | AP_L (Average Product) | MP_L (Marginal Product) |
|---|---|---|---|
| 0 | 0 | - | - |
| 1 | 15 | 15 / 1 = 15 | (15 - 0) / (1 - 0) = 15 |
| 2 | 35 | 35 / 2 = 17.5 | (35 - 15) / (2 - 1) = 20 |
| 3 | 50 | 50 / 3 = 16.67 | (50 - 35) / (3 - 2) = 15 |
| 4 | 40 | 40 / 4 = 10 | (40 - 50) / (4 - 3) = -10 |
| 5 | 48 | 48 / 5 = 9.6 | (48 - 40) / (5 - 4) = 8 |
Q23Questions
The following table gives the average product schedule of labour. Find the total product and marginal product schedules. It is given that the total product is zero at zero level of labour employment.
L AP_L 1 2 2 3 3 4 4 4.25 5 4 6 3.5
Solution
To find the Total Product (TP_L) and Marginal Product (MP_L), we use the following formulas:
TP_L = AP_L * LMP_L = ΔTP_L / ΔL(Change in Total Product / Change in Labour)
The calculated schedules are as follows:
| L (Labour) | AP_L (Average Product) | TP_L (Total Product) | MP_L (Marginal Product) |
|---|---|---|---|
| 0 | - | 0 | - |
| 1 | 2 | 2 * 1 = 2 | (2 - 0) / (1 - 0) = 2 |
| 2 | 3 | 3 * 2 = 6 | (6 - 2) / (2 - 1) = 4 |
| 3 | 4 | 4 * 3 = 12 | (12 - 6) / (3 - 2) = 6 |
| 4 | 4.25 | 4.25 * 4 = 17 | (17 - 12) / (4 - 3) = 5 |
| 5 | 4 | 4 * 5 = 20 | (20 - 17) / (5 - 4) = 3 |
| 6 | 3.5 | 3.5 * 6 = 21 | (21 - 20) / (6 - 5) = 1 |
Q24Questions
The following table gives the marginal product schedule of labour. It is also given that total product of labour is zero at zero level of employment. Calculate the total and average product schedules of labour.
L MP_L 1 3 2 5 3 7 4 5 5 3 6 1
Solution
To find the Total Product (TP_L) and Average Product (AP_L), we use the following logic and formulas:
- Total Product is the cumulative sum of Marginal Products:
TP_L(n) = TP_L(n-1) + MP_L(n) AP_L = TP_L / L
The calculated schedules are as follows:
| L (Labour) | MP_L (Marginal Product) | TP_L (Total Product) | AP_L (Average Product) |
|---|---|---|---|
| 0 | - | 0 | - |
| 1 | 3 | 0 + 3 = 3 | 3 / 1 = 3 |
| 2 | 5 | 3 + 5 = 8 | 8 / 2 = 4 |
| 3 | 7 | 8 + 7 = 15 | 15 / 3 = 5 |
| 4 | 5 | 15 + 5 = 20 | 20 / 4 = 5 |
| 5 | 3 | 20 + 3 = 23 | 23 / 5 = 4.6 |
| 6 | 1 | 23 + 1 = 24 | 24 / 6 = 4 |
Q25Questions
The following table shows the total cost schedule of a firm. What is the total fixed cost schedule of this firm? Calculate the TVC, AFC, AVC, SAC and SMC schedules of the firm.
Q TC 0 10 1 30 2 45 3 55 4 70 5 90 6 120
Solution
First, we determine the Total Fixed Cost (TFC). TFC is the cost at zero output. From the table, TC at Q=0 is 10. Therefore, TFC = Rs 10.
We can now calculate the other cost schedules using the following formulas:
TVC = TC - TFCAFC = TFC / QAVC = TVC / QSAC = TC / Q(orSAC = AFC + AVC)SMC = ΔTC / ΔQ
The complete cost schedules are as follows:
| Q (Output) | TC (Total Cost) | TFC (Total Fixed Cost) | TVC (Total Variable Cost) | AFC (Average Fixed Cost) | AVC (Average Variable Cost) | SAC (Short-run Average Cost) | SMC (Short-run Marginal Cost) |
|---|---|---|---|---|---|---|---|
| 0 | 10 | 10 | 0 | - | - | - | - |
| 1 | 30 | 10 | 20 | 10.00 | 20.00 | 30.00 | 20 |
| 2 | 45 | 10 | 35 | 5.00 | 17.50 | 22.50 | 15 |
| 3 | 55 | 10 | 45 | 3.33 | 15.00 | 18.33 | 10 |
| 4 | 70 | 10 | 60 | 2.50 | 15.00 | 17.50 | 15 |
| 5 | 90 | 10 | 80 | 2.00 | 16.00 | 18.00 | 20 |
| 6 | 120 | 10 | 110 | 1.67 | 18.33 | 20.00 | 30 |
Q26Questions
The following table gives the total cost schedule of a firm. It is also given that the average fixed cost at 4 units of output is Rs 5. Find the TVC, TFC, AVC, AFC, SAC and SMC schedules of the firm for the corresponding values of output.
Q TC 1 50 2 65 3 75 4 95 5 130 6 185
Solution
First, we find the Total Fixed Cost (TFC). We are given that AFC at 4 units is Rs 5.
AFC = TFC / Q5 = TFC / 4TFC = 5 * 4 = 20So, the Total Fixed Cost is Rs 20.
Now we can calculate the other cost schedules:
TVC = TC - TFCAFC = TFC / QAVC = TVC / QSAC = TC / QSMC = ΔTC / ΔQ(SMC for Q=1 cannot be calculated as TC at Q=0 is not given).
The complete cost schedules are as follows:
| Q (Output) | TC (Total Cost) | TFC (Total Fixed Cost) | TVC (Total Variable Cost) | AFC (Average Fixed Cost) | AVC (Average Variable Cost) | SAC (Short-run Average Cost) | SMC (Short-run Marginal Cost) |
|---|---|---|---|---|---|---|---|
| 1 | 50 | 20 | 30 | 20.00 | 30.00 | 50.00 | - |
| 2 | 65 | 20 | 45 | 10.00 | 22.50 | 32.50 | 15 |
| 3 | 75 | 20 | 55 | 6.67 | 18.33 | 25.00 | 10 |
| 4 | 95 | 20 | 75 | 5.00 | 18.75 | 23.75 | 20 |
| 5 | 130 | 20 | 110 | 4.00 | 22.00 | 26.00 | 35 |
| 6 | 185 | 20 | 165 | 3.33 | 27.50 | 30.83 | 55 |
Q27Questions
A firm's SMC schedule is shown in the following table. The total fixed cost of the firm is Rs 100. Find the TVC, TC, AVC and SAC schedules of the firm.
Q TC 0 - 1 500 2 300 3 200 4 300 5 500 6 800
Solution
There appears to be a typo in the question; the second column is labelled 'TC' but the values represent Short-run Marginal Cost (SMC). Assuming the values are for SMC and TFC = Rs 100.
We can find the schedules using these relations:
- Total Variable Cost (TVC) is the cumulative sum of SMC:
TVC(n) = TVC(n-1) + SMC(n) TC = TFC + TVCAVC = TVC / QSAC = TC / Q
The calculated schedules are:
| Q (Output) | SMC (Short-run Marginal Cost) | TVC (Total Variable Cost) | TFC (Total Fixed Cost) | TC (Total Cost) | AVC (Average Variable Cost) | SAC (Short-run Average Cost) |
|---|---|---|---|---|---|---|
| 0 | - | 0 | 100 | 100 | - | - |
| 1 | 500 | 500 | 100 | 600 | 500.00 | 600.00 |
| 2 | 300 | 500 + 300 = 800 | 100 | 900 | 400.00 | 450.00 |
| 3 | 200 | 800 + 200 = 1000 | 100 | 1100 | 333.33 | 366.67 |
| 4 | 300 | 1000 + 300 = 1300 | 100 | 1400 | 325.00 | 350.00 |
| 5 | 500 | 1300 + 500 = 1800 | 100 | 1900 | 360.00 | 380.00 |
| 6 | 800 | 1800 + 800 = 2600 | 100 | 2700 | 433.33 | 450.00 |
Q28Questions
Let the production function of a firm be Q = 5 L^(1/2) K^(1/2) Find out the maximum possible output that the firm can produce with 100 units of L and 100 units of K.
Solution
Given the production function:
Q = 5 * L^(1/2) * K^(1/2)We need to find the maximum output (Q) when:
- Labour (L) = 100 units
- Capital (K) = 100 units
Substitute the values of L and K into the production function:
Q = 5 * (100)^(1/2) * (100)^(1/2)Since
x^(1/2) is the same as the square root of x (√x):Q = 5 * √100 * √100
Q = 5 * 10 * 10
Q = 500The maximum possible output that the firm can produce is 500 units.
Q29Questions
Let the production function of a firm be Q = 2 L^2 K^2 Find out the maximum possible output that the firm can produce with 5 units of L and 2 units of K. What is the maximum possible output that the firm can produce with zero unit of L and 10 units of K?
Solution
Part 1: With L=5 and K=2
Given the production function:
Q = 2 * L^2 * K^2Substitute L = 5 and K = 2 into the function:
Q = 2 * (5)^2 * (2)^2
Q = 2 * 25 * 4
Q = 200The maximum possible output with 5 units of L and 2 units of K is 200 units.
Part 2: With L=0 and K=10
Substitute L = 0 and K = 10 into the function:
Q = 2 * (0)^2 * (10)^2
Q = 2 * 0 * 100
Q = 0The maximum possible output with zero units of L and 10 units of K is 0 units. This is because in this particular production function, both inputs are necessary for production.
Q30Questions
Find out the maximum possible output for a firm with zero unit of L and 10 units of K when its production function is Q = 5 L + 2 K
Solution
Given the production function:
Q = 5L + 2KWe need to find the maximum output (Q) when:
- Labour (L) = 0 units
- Capital (K) = 10 units
Substitute the values of L and K into the production function:
Q = 5 * (0) + 2 * (10)
Q = 0 + 20
Q = 20The maximum possible output for the firm is 20 units. In this case, the inputs are perfect substitutes, and output can be produced even if one of the inputs is zero.