# Production and Costs

This page contains the NCERT Economics class 12 chapter 3 Production and Costs from Book I Introductory Microeconomics. You can find the solutions for the chapter 3 of NCERT class 12 Economics, for the Short Answer Questions, Long Answer Questions and Projects/Assignments Questions in this page. So is the case if you are looking for NCERT class 12 Economics related topic Production and Costs question and answers.
Exercises
1. Explain the concept of a production function.
A production function serves as a fundamental concept in economics, providing a comprehensive understanding of the relationship between the inputs utilized in production and the resulting output. It is mathematically expressed as:
{Q = f(L, K)}
Here:
{Q} denotes the total quantity of output produced by the firm.
{L} represents the quantity of labor employed in the production process.
{K} signifies the amount of capital invested.
{f} symbolizes the functional relationship that transforms the inputs into output.
The production function is pivotal as it encapsulates the maximum output that can be achieved with various combinations of labor and capital, under the assumption of efficient utilization of resources. It provides a framework for analyzing how changes in the quantity of inputs impact the level of production, aiding firms in making informed decisions regarding resource allocation.
In simpler terms, the production function reflects the technological relationship between inputs and output, showcasing how inputs are converted into goods or services. It is instrumental in identifying the most efficient production techniques and plays a crucial role in cost management and optimization of production processes.
By understanding the production function, firms can strive to achieve optimal productivity, ensuring that they are utilizing their resources in the most effective manner to maximize output and minimize waste.
2. What is the total product of an input?
The total product of an input refers to the total quantity of output produced by a firm as a result of employing a certain amount of that specific input, while keeping other inputs constant. It represents the cumulative output generated from the input and is an important concept in understanding the production function and the efficiency of input utilization.
In simpler terms, the total product shows how much a firm can produce using a specific amount of an input, such as labor or capital, and it helps in analyzing the relationship between input quantities and output levels.
3. What is the average product of an input?
The average product (AP) of an input is defined as the output per unit of the variable input. It is calculated by dividing the total product (TP) by the quantity of the variable input (L). The formula for calculating the average product of labor, when capital is held constant, is:
{AP_L = \dfrac{TP_L}{L}}
For instance, the average product of labor is illustrated with capital fixed at a certain level. The values for the average product are obtained by dividing the total product by the quantity of labor. This gives a numerical example of the average product of labor for a given production function described.
To provide a concrete example, if a firm employs 2 units of labor and produces a total product of 24 units, the average product of labor would be:
{AP_L = \dfrac{24}{2} = 12}
This means that, on average, each unit of labor is producing 12 units of output. The average product is an important measure as it helps in understanding the productivity of the variable input and is used to assess the efficiency of production.
4. What is the marginal product of an input?
The marginal product (MP) of an input is defined as the additional output produced as a result of employing one more unit of that input, while keeping all other inputs constant. The formula for calculating the marginal product of labor, when capital is held constant, is:
{MP_L = \dfrac{ΔTP_L}{ΔL}}

Here, Δ represents the change in the variable. To calculate the marginal product, you take the change in total product {(ΔTP_L)} and divide it by the change in the quantity of the input (ΔL).

For example, if increasing labor from 1 to 2 units leads to an increase in total product from 10 to 24 units, the marginal product of the second unit of labor would be:
{MP_L = \dfrac{24 - 10}{2 - 1} = \dfrac{14}{1} = 14}
This means that the second unit of labor added 14 units to the total output. The concept of marginal product is crucial in economics as it helps to understand the additional output that can be gained by increasing the input by one unit, and it is particularly important when considering how to allocate resources efficiently.
5. Explain the relationship between the marginal products and the total product of an input.
The relationship between the marginal products (MP) and the total product (TP) of an input is foundational in understanding how changes in input levels affect overall production.
Relationship between Marginal Product and Total Product

The marginal product of an input is the additional amount of output that is produced by using one more unit of that input, while other inputs are kept constant. The total product is the total output produced by all units of the input employed.

Here’s how the two are related:
Relationship between TP and MP
1.
Increasing Marginal Returns: Initially, as more units of an input are employed, the marginal product may increase. This is due to factors such as better utilization of fixed inputs or increased specialization and division of labor. During this phase, each additional unit of input contributes more to the total product than the previous unit, leading to an increasing slope in the total product curve.
2.
Constant Marginal Returns: At some point, the marginal product of an input stabilizes, and each additional unit of input adds the same amount to the total product as the previous unit. This results in a linear increase in the total product curve.
3.
Decreasing Marginal Returns: As more and more of the input is employed, the marginal product begins to decline. This happens because the fixed inputs become increasingly overused, and there is less room for the additional input to be as productive as before. The total product continues to increase but at a decreasing rate, and the total product curve starts to flatten.
4.
Negative Marginal Returns: If the input continues to increase beyond a certain point, the marginal product can become negative, meaning that adding more of the input actually reduces the total output. This could be due to severe overcrowding or overuse of the fixed inputs. The total product curve will peak and then start to decline.
In summary, the sum of the marginal products of an input up to a certain level gives us the total product at that level. The total product curve is essentially the graphical representation of the cumulative marginal products. When marginal product is positive, total product is increasing. When marginal product is zero, total product is at its maximum and constant. When marginal product is negative, total product is decreasing.
6. Explain the concepts of the short run and the long run.
The concepts of the short run and the long run are crucial in understanding the production behavior of firms and how they adjust inputs to produce different levels of output.
The concepts of the short run and the long run are also tied to the production function, which is a mathematical representation of the relationship between inputs and the maximum output that can be produced. The production function is typically expressed as:
{q = f(L, K)}
Here, {q} represents the maximum output, {L} is labor, and {K} is capital.
The Short Run
In the short run, at least one factor of production (such as labor or capital) cannot be varied and remains fixed. This means that the firm cannot adjust all inputs freely. The fixed factor is the one that cannot be changed in the short run, while the variable factor is the one that the firm can adjust. For example, if capital is the fixed factor and is set at 4 units, the firm can only vary the amount of labor to change the output level. The short run is characterized by the presence of fixed costs, which do not change with the level of output.
In the short run, the production function may have one fixed input, meaning the firm can only adjust the variable input to change the output. For example, if capital (K) is fixed, the production function with respect to labor (L) might show different levels of output as labor varies while capital remains constant.
The Long Run
In contrast, the long run is a period in which all factors of production can be varied. There are no fixed factors in the long run, allowing the firm to adjust all inputs to produce different levels of output. The long run is a sufficient time period that allows the firm to alter plant size and capacity and to enter or exit an industry. It is defined not by a specific duration in terms of days, months, or years, but by the flexibility of changing all input levels.
In the long run, however, the firm can adjust both labor and capital, and the production function reflects the output levels for any combination of labor and capital. This flexibility allows the firm to reach any desired level of output by varying both inputs, as there are no fixed factors in the long run.
In summary, the key difference between the short run and the long run in economics is the ability to vary factors of production. In the short run, some factors are fixed and cannot be changed, while in the long run, all factors can be adjusted.
7. What is the law of diminishing marginal product?
The Law of Diminishing Marginal Product is a principle in economics that describes a decrease in the incremental output of a production process as the amount of a single factor of production is incrementally increased, while the amounts of all other factors of production stay constant.
Here’s a detailed explanation based on the passage from the document:
The Law of Diminishing Marginal Product and the Law of Variable Proportions
The marginal product (MP) of a factor input is the additional output produced by employing one more unit of that input.
According to the law, the marginal product of a factor input initially rises with its employment level. However, after reaching a certain level of employment, it starts to fall.
This phenomenon can be illustratedwith an example of a farmer who has a fixed amount of land (4 hectares) and can vary the amount of labor employed.
Initially, as more workers are employed, they have more land to work on per person, which increases the marginal product.
As employment continues to increase, the land becomes overcrowded with workers, leading to a decrease in the marginal product for each additional worker. This is when the marginal product begins to fall.
The law reflects the reality that, after a certain point, employing additional units of a variable input (like labor) to a fixed input (like land or capital) will yield progressively smaller increases in output, and can eventually lead to decreases in output if the variable input continues to increase. This is because the fixed input becomes a limiting factor, and the additional variable input cannot be utilized as effectively.
8. What is the law of variable proportions?
The Law of Variable Proportions, also known as the Law of Diminishing Returns, states that if the quantity of one factor of production is increased while the quantities of all other factors of production are held constant, the marginal product of the variable factor will initially increase, but beyond a certain point, it will begin to diminish.
This is further described as below:
The Law of Variable Proportions arises because the ratio in which the two inputs are combined changes as one factor is held constant and the other is increased.
Initially, as the amount of the variable input increases, the factor proportions become more suitable for production, and the marginal product increases.
After reaching a certain level of employment, the production process becomes too crowded with the variable input, leading to a decrease in the marginal product of additional units of input.
Consider the example of a farmer with a fixed amount of land who employs workers. At first, as more workers are hired, they can each cultivate more land efficiently, leading to an increase in the marginal product. However, as more workers are added, the land becomes overcrowded, and each additional worker contributes less to the total output, causing the marginal product to fall.
The Law of Variable Proportions is graphically represented by the shape of the Total Product (TP) and Marginal Product (MP) curves. The MP curve initially rises and then falls after a certain point, forming an inverted ‘U’ shape, which is a graphical representation of the Law of Variable Proportions.
Relationship between TP and MP
9. When does a production function satisfy constant returns to scale?
A production function satisfies constant returns to scale (CRS) when an increase in all inputs by a certain proportion results in an increase in output by the same proportion. In other words, if we double the amount of inputs used in production, the output will also double; if we triple the inputs, the output will also triple, and so on.
For example, let’s consider a simple production function:
{f(L, K)}
where
{L}
is labour and
{K}
is capital.
If this production function satisfies constant returns to scale, then for any positive scalar {n}, we have:
{f(nL, nK) = n × f(L, K)}
To illustrate with numbers, suppose that initially, 10 units of labor and 10 units of capital produce 100 units of output:
{f(10L, 10K) = 100}
If we increase both labor and capital by a factor of 2 (i.e., {n = 2}, then the new output should be 200 units if the production function satisfies CRS:
{f(2 × 10L, 2 × 10K) = 2 × 100 = 200}
This example shows that the production function has constant returns to scale because doubling the inputs has led to a doubling of the output.
10. When does a production function satisfy increasing returns to scale?
A production function satisfies increasing returns to scale (IRS) when an increase in all inputs by a certain proportion results in an increase in output by a larger proportion. This means that if we multiply all inputs by a factor {n}, the output increases by more than {n} times.
For example, let’s consider a production function:
{f(L, K)}
where
{L}
is labor and
{K}
is Capital.
If this production function satisfies increasing returns to scale, then for any positive scalar {n}, we have:
{f(nL, nK) > n × f(L, K)}
To illustrate with numbers, suppose that initially, 10 units of labor and 10 units of capital produce 100 units of output:
{f(10L, 10K) = 100}
If we increase both labor and capital by a factor of 2 (i.e., {n = 2}), then the new output should be more than 200 units if the production function satisfies IRS:
{f(2 × 10L, 2 × 10K) > 2 × 100}
This example demonstrates that the production function has increasing returns to scale because doubling the inputs has led to more than a doubling of the output.
11. When does a production function satisfy decreasing returns to scale?
A production function satisfies decreasing returns to scale (DRS) when an increase in all inputs by a certain proportion results in a less than proportional increase in output. This means that if we multiply all inputs by a factor {n}, the output increases by less than {n} times.
For example, let’s consider a production function:
{f(L, K)}
where
{L}
is labor and
{K}
is capital.
If this production function satisfies decreasing returns to scale, then for any positive scalar {n}, we have:
{f(nL, nK) \lt n × f(L, K)}
To illustrate with numbers, suppose that initially, 10 units of labor and 10 units of capital produce 100 units of output:
{f(10L, 10K) = 100}
If we increase both labor and capital by a factor of 2 (i.e., {n = 2}), then the new output should be less than 200 units if the production function satisfies DRS:
{f(2 × 10L, 2 × 10K) \lt 2 × 100}
This example shows that the production function has decreasing returns to scale because doubling the inputs has led to less than a doubling of the output.
12. Briefly explain the concept of the cost function.
The cost function is an equation that illustrates how the total cost of production {(C)} is related to the quantity of output produced {(Q)}. It reflects how costs accumulate as production scales up, assuming that the technology being used remains unchanged. The function is typically expressed as:
{C = f(Q)}
In this expression, {C} represents the total cost incurred for producing a certain number of goods or services, while {Q} stands for the quantity of output. This relationship is crucial for businesses as it helps in understanding how changes in the level of production affect overall costs, which is vital for pricing and profit optimization strategies.
13. What are the total fixed cost, total variable cost and total cost of a firm? How are they related?
The total fixed cost (TFC), total variable cost (TVC), and total cost (TC) of a firm are three fundamental concepts in the analysis of a firm’s production costs.
Total Fixed Cost (TFC):
TFC are costs that do not change with the level of output produced. They are incurred even if the output is zero and must be paid regardless of the level of production. Examples include rent, salaries of permanent staff, and depreciation of equipment.
Total Variable Cost (TVC):
TVC are costs that change with the level of output. These costs increase as more output is produced and decrease as production is scaled down. Examples include costs of raw materials, energy consumption, and wages of temporary staff.
Total Cost (TC):
TC is the sum of the total fixed and total variable costs. It represents the total economic cost of production and is calculated as follows:
{TC = TFC + TVC}
The relationship between these costs can be illustrated as follows:
When no output is produced, {TC = TFC} because {TVC} is zero.
As output increases, {TC} increases due to the rise in {TVC}.
{TFC} remains constant regardless of the level of output.
The gap between {TC} and {TVC} represents the {TFC}, and this gap remains constant as output changes.
Understanding the relationship between TFC, TVC, and TC is crucial for a firm to make informed decisions about production, pricing, and profitability.
14. What are the average fixed cost, average variable cost and average cost of a firm? How are they related?
The average fixed cost (AFC), average variable cost (AVC), and average cost (AC) of a firm are measures that express the cost of production on a per-unit basis.
Average Fixed Cost (AFC):
AFC is the total fixed cost (TFC) divided by the number of units produced (Q). It shows the fixed cost per unit of output. As output increases, AFC decreases because the fixed costs are spread over more units.
{AFC = \dfrac{TFC}{Q}}
Average Variable Cost (AVC):
AVC is the total variable cost (TVC) divided by the number of units produced (Q). It reflects the variable cost for each unit of output. AVC typically changes with the level of output.
{AVC = \dfrac{TVC}{Q}}
Average Cost (AC) or Average Total Cost (ATC):
AC is the total cost (TC) divided by the number of units produced (Q). It is the sum of AFC and AVC and represents the cost per unit of output.
{AC = \dfrac{TC}{Q} = AFC + AVC}
The relationship between these costs is as follows:
Relationship between AFC, AVC and AC
AC is the sum of AFC and AVC. As Q increases, AFC decreases, but AVC may initially decrease and then increase due to the law of diminishing returns.
The AC curve typically U-shaped because AFC is always declining as output increases, while AVC may initially decline and then increase.
The gap between AC and AVC represents AFC. As output increases, this gap narrows because AFC is spread over more units.
Understanding these average costs is important for a firm in setting prices and determining the level of production that maximizes profit or minimizes losses.
15. Can there be some fixed cost in the long run? If not, why?
No. In the long run, the concept of fixed costs essentially disappears because all costs are variable. The long run is a period of time in which a firm can adjust all of its inputs, including those that are fixed in the short run. This period is long enough for the firm to alter its plant size and capacity, and to enter or exit an industry.
The reason there are no fixed costs in the long run is that all the contracts and commitments that lead to fixed costs in the short run can be renegotiated, terminated, or have expired in the long run. For instance, a lease on a building can be considered a fixed cost in the short run because it cannot be changed immediately. However, in the long run, the firm can choose to renew the lease, move to a different location, or purchase the property, thus making the cost variable.
In essence, the long run provides firms with the flexibility to make changes to all aspects of production, including those that are fixed in the short run, which is why in the long run, all costs are considered variable.
16. What does the average fixed cost curve look like? Why does it look so?
The average fixed cost (AFC) curve is a downward-sloping curve that approaches zero as output increases. As shown in the figure below, it looks this way because fixed costs are spread over an increasing number of units of output.
AFC Curve
Here’s why the AFC curve has this shape:
Fixed Costs are Constant: Since total fixed costs (TFC) do not change with the level of output, the same total amount is spread over more units as output (Q) increases.
Spreading Effect: As more units are produced, the fixed cost per unit (AFC) falls because each unit bears a smaller portion of the fixed costs. This is sometimes referred to as the spreading effect.
Hyperbolic Shape: Mathematically, because AFC is calculated as TFC divided by Q, as Q increases, AFC declines hyperbolically, meaning it decreases at a decreasing rate and never actually reaches zero.
The AFC curve is distinct in that it continually declines, but the rate of decline diminishes as output increases. It will get closer and closer to the horizontal axis but will not touch it or become negative, reflecting the fact that fixed costs can be spread out but not eliminated.
17. What do the short run marginal cost, average variable cost and short run average cost curves look like?
The short run marginal cost (SMC), average variable cost (AVC), and short run average cost (SAC) or short run average total cost (SATC) curves each have distinctive shapes:
Short Run Costs
Marginal Cost (MC):
The MC curve typically has a U-shape in the short run. Initially, it declines as the quantity of output increases due to increasing efficiency and the spreading out of fixed costs over a larger number of units (economies of scale). However, after a certain point, it begins to rise due to the law of diminishing marginal returns, where each additional unit of input contributes less to output than the previous unit.
Average Variable Cost (AVC):
The AVC curve also tends to be U-shaped. It decreases initially due to economies of scale and the spreading of variable costs over a larger number of units. However, it starts to rise after reaching a minimum point due to the law of diminishing marginal returns.
Short Run Average Cost (SAC) or Short Run Average Total Cost (SATC):
The SAC or SATC curve is also U-shaped, reflecting the behavior of both AFC and AVC. Since SAC includes both AFC and AVC (SAC = AFC + AVC), it starts high when output is low because AFC is spread over a few units. As output increases, SAC decreases because AFC is spread over more units, and AVC is also low. However, as output continues to increase, the increasing AVC (due to diminishing returns) will push the SAC back up after reaching a minimum point.
The U-shape of these curves is a fundamental characteristic of cost curves in the short run, reflecting the initial efficiencies and subsequent inefficiencies as output increases. The exact shapes and the points at which the curves turn upward can vary depending on the specific cost conditions and production technologies of a firm.
18. Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?
The short-run marginal cost (SMC) curve cuts the average variable cost (AVC) curve at the minimum point of the AVC curve due to the relationship between marginal and average quantities.
Relationship between SMC and AVC
Here’s the reasoning:
Short Run Marginal Cost (SMC): This is the cost of producing one additional unit of output. It reflects the change in total variable cost (TVC) from producing one more unit.
Average Variable Cost (AVC): This is the TVC divided by the quantity of output (Q). It represents the variable cost per unit of output.
When the SMC is less than the AVC, producing one more unit will decrease the AVC, because adding a unit that costs less than the average will pull the average down. As long as the SMC is below the AVC, the AVC will continue to decline.
At the minimum point of the AVC curve, the SMC must be equal to the AVC. If the SMC were either above or below the AVC at that point, the AVC would either be rising or falling, respectively. Therefore, the only point at which the AVC is at its minimum is when the next unit’s marginal cost is exactly the same as the AVC.
After the minimum point, as output increases, the SMC becomes higher than the AVC because the cost of producing an additional unit is now more than the average, thus pulling the average up. This is why the SMC curve intersects the AVC curve at its lowest point.
19. At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.
The short-run marginal cost (SMC) curve cuts the short-run average cost (SAC) curve at the minimum point of the SAC curve, and the reasoning behind this is similar to the relationship between the SMC and the AVC curves.
Relationship between SMC and SAC
Here’s why this occurs:
Short-Run Marginal Cost (SMC): This represents the additional cost of producing one more unit of output. It is the gradient of the total cost curve.
Short-Run Average Cost (SAC): This is the total cost divided by the quantity of output (Q), which includes both average fixed costs (AFC) and average variable costs (AVC).
As long as the SMC is less than the SAC, producing an additional unit will pull the SAC down, because adding a unit that costs less than the average will decrease the average. Consequently, the SAC curve declines as output increases, up to the point where SMC is equal to SAC.
At the minimum point of the SAC curve, the SMC is exactly equal to the SAC. If the SMC were lower, the SAC would still be decreasing. If the SMC were higher, the SAC would be increasing. Therefore, the point at which the SMC intersects the SAC curve must be at the minimum of the SAC curve, because this is the point where the cost of producing one more unit (the marginal cost) starts to exceed the average cost, causing the average cost to start rising.
After this intersection point, as output increases further, the SMC remains above the SAC, indicating that each additional unit costs more than the previous average, thus pulling the average upwards. This is why the SMC curve intersects the SAC curve at its lowest point.
20. Why is the short run marginal cost curve ‘U’-shaped?
The short-run marginal cost (SMC) curve is ‘U’-shaped due to the law of diminishing marginal returns, which is a fundamental principle in microeconomics that describes the production process in the short run where at least one input is fixed.
Short Run MC Curve
Here’s a step-by-step explanation of why the SMC curve is ‘U’-shaped:
1.
Decreasing Costs at Low Levels of Output:
Initially, as production begins, firms often experience increasing marginal returns due to better utilization of fixed inputs. For example, a factory may have a lot of unused capacity when only a few workers are employed.
As more units of the variable input (like labor) are added, they can make more efficient use of the fixed inputs (like machinery), leading to a decrease in the marginal cost of production.
2.
Minimum Point:
The SMC curve reaches its minimum point at the level of output where marginal returns start to diminish but have not yet turned negative. This is typically where the firm is making the most efficient use of its inputs.
At this point, the cost of producing one more unit is at its lowest.
3.
Increasing Costs at Higher Levels of Output:
Beyond a certain point, as more of the variable input is added, the fixed inputs become increasingly over-utilized, and the additional output generated by each additional unit of input begins to fall. This is the law of diminishing marginal returns in action.
Consequently, each additional unit of output requires more and more of the variable input to produce, leading to an increase in the marginal cost for each additional unit.
4.
Capacity Constraints:
In the short run, firms face capacity constraints due to fixed inputs. As these constraints become binding, the cost of adding additional units of output increases significantly, further steepening the upward slope of the SMC curve.
The ‘U’ shape of the SMC curve reflects these phases of production efficiency and inefficiency. The initial downward slope represents increasing efficiency and the subsequent upward slope represents decreasing efficiency as the firm’s capacity constraints are reached.
21. What do the long run marginal cost and the average cost curves look like?
Shapes of the Long Run Cost Curves:
Shapes of LRMC and LRAC
Long Run Marginal Cost (LRMC): The LRMC curve is ‘U’-shaped. It represents the additional cost of producing one more unit of output in the long run, where all inputs are variable. The LRMC curve intersects the LRAC curve at the minimum point of the LRAC, which signifies the most efficient scale of production for the firm. Initially, for the first unit of output, LRMC and LRAC are the same. As output increases, the LRAC initially falls, and the LRMC is less than the LRAC. When the LRAC starts to rise, the LRMC becomes greater than the LRAC.
Long Run Average Cost (LRAC): The LRAC curve is also typically ‘U’-shaped, reflecting economies and diseconomies of scale. The downward sloping part of the curve corresponds to increasing returns to scale (IRS), where the average cost falls as the firm increases output. The upward rising part corresponds to decreasing returns to scale (DRS), where the average cost rises as the firm increases output. At the minimum point of the LRAC curve, constant returns to scale (CRS) are observed, where the average cost remains constant as output increases.
22. The following table gives the total product schedule of labour. Find the corresponding average product and marginal product schedules of labour.
L
TPL
0
0
1
15
2
35
3
50
4
40
5
48
To find the Average Product (AP) and Marginal Product (MP) schedules from the Total Product (TP) schedule of labor, we use the following formulas:
Average Product (AP) is calculated as:
{AP = \dfrac{TP}{L}}
Marginal Product (MP) is the additional output produced by adding one more unit of labor, calculated as:
{MP = TP_{(L)} - TP_{(L-1)}}
Given the Total Product (TP) schedule, let’s calculate the Average Product (AP) and Marginal Product (MP) for each level of labor (L):
L
{TP_L}
{AP = \dfrac{TP_L}{L}}
{MP = ΔTP_L}
0
0
1
15
\dfrac{15}{1} = 15
15 – 0 = 15
2
35
\dfrac{35}{2} = 17.5
35 – 15 = 20
3
50
\dfrac{50}{3} ≈ 16.67
50 – 35 = 15
4
40
\dfrac{40}{4} = 10
40 – 50 = -10
5
48
\dfrac{48}{5} = 9.6
48 – 40 = 8
Please note that for L = 0, the AP and MP are undefined because you cannot divide by zero or have a change in labor from a non-existent amount. Also, the MP for L = 4 is negative, which indicates that adding the fourth unit of labor actually decreased the total output, suggesting a possible misallocation of resources or inefficiency at that level of labor input.
23. 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
{\text{AP}_\text{L}}
1
2
2
3
3
4
4
4.25
5
4
6
3.5
To find the Total Product (TP) and Marginal Product (MP) schedules from the Average Product (AP) schedule of labor, we will use the following relationships:
Total Product (TP) is calculated as:
{TP = AP × L}
Marginal Product (MP) is the change in total product when one more unit of labor is employed, calculated as:
{MP = TP_{(L)} - TP_{(L-1)}}
Given that the total product is zero at zero level of labor employment, we can calculate the TP for each level of labor (L) using the AP provided:
L
{AP_L}
{TP = AP_L × L}
MP = ΔTP
1
2
2 × 1 = 2
2
3
3 × 2 = 6
6 – 2 = 4
3
4
4 × 3 = 12
12 – 6 = 6
4
4.25
4.25 × 4 = 17
17 – 12 = 5
5
4
4 × 5 = 20
20 – 17 = 3
6
3.5
3.5 × 6 = 21
21 – 20 = 1
For the first unit of labor (L = 1), the MP is not calculated because there is no previous TP value to compare it to. However, if we consider the given that TP is zero at zero level of labor employment, then the MP for L=1 would be the TP itself, which is 2.
The MP is the difference in TP as one more unit of labor is added. From the table above, we can see the MP decreases as more labor is added, which is consistent with the law of diminishing marginal returns.
24. 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
{\text{MP}_\text{L}}
1
3
2
5
3
7
4
5
5
3
6
1
To calculate the Total Product (TP) and Average Product (AP) schedules from the Marginal Product (MP) schedule of labor, we use the following relationships:
Total Product (TP) is the cumulative sum of the marginal products up to that point.
Average Product (AP) is calculated as:
{AP = \dfrac{TP}{L}}
Given that the total product of labor is zero at zero level of employment, we can calculate the TP for each level of labor (L) by adding the MP of each level of labor to the previous total. Then we can calculate the AP.
Let’s calculate the TP and AP schedules:
L
{MP_L}
{TP = \text{Cumulative }MP_L}
{AP = \dfrac{TP}{L}}
1
3
3
{\dfrac{3}{1} = 3}
2
5
3 + 5 = 8
{\dfrac{8}{2} = 4}
3
7
8 + 7 = 15
{\dfrac{15}{3} = 5}
4
5
15 + 5 = 20
{\dfrac{20}{4} = 5}
5
3
20 + 3 = 23
{\dfrac{23}{5} = 4.6}
6
1
23 + 1 = 24
{\dfrac{24}{6} = 4}
So, the TP is the cumulative sum of the MP as labor increases, and the AP is the TP divided by the number of labor units. The AP peaks when the addition of labor units starts adding less to the TP than the previous units, which is a reflection of the law of diminishing returns.
25. 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
To calculate the Total Variable Cost (TVC), Average Fixed Cost (AFC), Average Variable Cost (AVC), Short-Run Average Cost (SAC), and Short-Run Marginal Cost (SMC) schedules from the Total Cost (TC) schedule, we first need to identify the Total Fixed Cost (TFC). The TFC can be found from the cost at zero output, since at zero output, the total cost is entirely fixed.
Given that the TC at zero output (Q = 0) is 10, this is the TFC for all levels of output.
Now, let’s calculate each schedule:
Total Variable Cost (TVC): TVC is calculated by subtracting TFC from TC.
{TVC = TC - TFC}
Average Fixed Cost (AFC): AFC is calculated by dividing TFC by the quantity of output (Q).
{AFC = \dfrac{TFC}{Q}}
Average Variable Cost (AVC): AVC is calculated by dividing TVC by Q.
{AVC = \dfrac{TVC}{Q}}
Short-Run Average Cost (SAC): SAC is calculated by dividing TC by Q.
{SAC = \dfrac{TC}{Q}}
Short-Run Marginal Cost (SMC): SMC is the change in TC when one additional unit of output is produced.
{SMC = TC_{(L)} - TC_{(L-1)}}
Let’s calculate these for each level of output:
Q
TC
TFC
TVC = TC – TFC
{AFC = \dfrac{TFC}{Q}}
{AVC = \dfrac{TVC}{Q}}
{SAC = \dfrac{TC}{Q}}
SMC = ΔTC
0
10
10
0
1
30
10
20
{\dfrac{10}{1} = 10}
{\dfrac{20}{1} = 20}
{\dfrac{30}{1} = 30}
30 – 10 = 20
2
45
10
35
{\dfrac{10}{2} = 5}
{\dfrac{35}{2} = 17.5}
{\dfrac{45}{2} = 22.5}
45 – 30 = 15
3
55
10
45
{\dfrac{10}{3} ≈ 3.33}
{\dfrac{45}{3} = 15}
{\dfrac{55}{3} ≈ 18.33}
55 – 45 = 10
4
70
10
60
{\dfrac{10}{4} = 2.5}
{\dfrac{60}{4} = 15}
{\dfrac{70}{4} = 17.5}
70 – 55 = 15
5
90
10
80
{\dfrac{10}{5} = 2}
{\dfrac{80}{5} = 16}
{\dfrac{90}{5} = 18}
90 – 70 = 20
6
120
10
110
{\dfrac{10}{6} ≈ 1.67}
{\dfrac{110}{6} ≈ 18.33}
{\dfrac{120}{6} = 20}
120 – 90 = 30
Please note that AFC is undefined at Q=0 because we cannot divide by zero. Similarly, SAC and AVC are undefined at Q=0 for the same reason. The SMC for Q=1 is calculated by the change in TC from Q=0 to Q=1, and so on for subsequent quantities.
26. 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 ₹ 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
Given that the Average Fixed Cost (AFC) at 4 units of output is ₹ 5, we can calculate the Total Fixed Cost (TFC) because AFC is the TFC divided by the quantity (Q).
So, for 4 units of output:
{AFC = \dfrac{TFC}{Q}}
{5 = \dfrac{TFC}{4}}
{TFC = 5 × 4}
{TFC = ₹~20}
Now that we have the TFC, we can calculate the Total Variable Cost (TVC), Average Variable Cost (AVC), AFC, Short-Run Average Cost (SAC), and Short-Run Marginal Cost (SMC) for each level of output.
TVC: TVC is TC minus TFC.
{TVC = TC - TFC}
AVC: AVC is TVC divided by Q.
{AVC = \dfrac{TVC}{Q}}
AFC: AFC is TFC divided by Q.
{AFC = \dfrac{TFC}{Q}}
SAC: SAC is TC divided by Q.
{SAC = \dfrac{TC}{Q}}
SMC: SMC is the change in TC for an additional unit of output.
{SMC = TC_{(L)} - TC_{(L-1)}}
Let’s calculate these for each level of output:
Q
TC
TFC
TVC = TC-TFC
{AVC = \dfrac{TVC}{Q}}
{AFC = \dfrac{TFC}{Q}}
{SAC = \dfrac{TC}{Q}}
SMC = ΔTC
1
50
20
30
{\dfrac{30}{1} = 30}
{\dfrac{20}{1} = 20}
{\dfrac{50}{1} = 50}
2
65
20
45
{\dfrac{45}{2} = 22.5}
{\dfrac{20}{2} = 10}
{\dfrac{65}{2} = 32.5}
65 – 50 = 15
3
75
20
55
{\dfrac{55}{3} ≈ 18.33}
{\dfrac{20}{3} ≈ 6.67}
{\dfrac{75}{3} = 25}
75 – 65 = 10
4
95
20
75
{\dfrac{75}{4} = 18.75}
{\dfrac{20}{4} = 5}
{\dfrac{95}{4} = 23.75}
95 – 75 = 20
5
130
20
110
{\dfrac{110}{5} = 22}
{\dfrac{20}{5} = 4}
{\dfrac{130}{5} = 26}
130 – 95 = 35
6
185
20
165
{\dfrac{165}{6} ≈ 27.5}
{\dfrac{20}{6} ≈ 3.33}
{\dfrac{185}{6} ≈ 30.83}
185 – 130 = 55
The SMC for Q = 1 is not calculated because we do not have the TC for Q = 0.
The SMC for each subsequent level of output is the difference in TC from the previous level of output.
The AFC, AVC, and SAC are calculated for each level of output using the formulas provided above.
27. A firm’s SMC schedule is shown in the following table. The total fixed cost of the firm is ₹ 100. Find the TVC, TC, AVC and SAC schedules of the firm.
Q
TC SMC
0
1
500
2
300
3
200
4
300
5
500
6
800
Given the Short-Run Marginal Cost (SMC) schedule and the Total Fixed Cost (TFC) of ₹ 100, we can calculate the Total Variable Cost (TVC), Total Cost (TC), Average Variable Cost (AVC), and Short-Run Average Cost (SAC) for the firm.
The TVC at each level of output (Q) is the sum of the marginal costs up to that point. The TC is the sum of TVC and TFC. The AVC is the TVC divided by Q, and the SAC is the TC divided by Q.
Let’s calculate these schedules:
1.
2.
TC: TVC + TFC.
3.
AVC: {\dfrac{TVC}{Q}}.
4.
SAC: {\dfrac{TC}{Q}}.
Here are the calculations:
Q
SMC
TFC
TVC = Cumulative SMC
TC = TVC + TFC
{AVC = \dfrac{TVC}{Q}}
{SAC = \dfrac{TC}{Q}}
0
100
0
100
1
500
100
500
600
{\dfrac{500}{1} = 500}
{\dfrac{600}{1} = 600}
2
300
100
500 + 300 = 800
900
{\dfrac{800}{2} = 400}
{\dfrac{900}{2} = 450}
3
200
100
800 + 200 = 1000
1100
{\dfrac{1000}{3} ≈ 333.33}
{\dfrac{1100}{3} ≈ 366.67}
4
300
100
1000 + 300 = 1300
1400
{\dfrac{1300}{4} = 325}
{\dfrac{1400}{4} = 350}
5
500
100
1300 + 500 = 1800
1900
{\dfrac{1800}{5} = 360}
{\dfrac{1900}{5} = 380}
6
800
100
1800 + 800 = 2600
2700
{\dfrac{2600}{6} ≈ 433.33}
{\dfrac{2700}{6} = 450}
Note:
The TVC at Q = 0 is zero because there is no production and hence no variable cost.
The TC at Q = 0 is equal to the TFC, which is ₹ 100.
The AVC and SAC cannot be calculated for Q=0 because we cannot divide by zero.
The SMC for Q=1 is the additional cost to produce the first unit, which also equals the TVC for Q=1 since the initial TVC is zero.
28. Let the production function of a firm be
{Q = 5L^\frac{1}{2}K^\frac{1}{2}}
Find out the maximum possible output that the firm can produce with 100 units of L and 100 units of K.
The production function given is:
{Q = 5L^{1/2}K^{1/2}}
To find the maximum possible output with 100 units of labor (L) and 100 units of capital (K), we substitute these values into the production function:
Q
{5 × (100)^{1/2} × (100)^{1/2}}
= 5 × 10 × 10
= 500
Therefore, the maximum possible output that the firm can produce with 100 units of labor and 100 units of capital is 500 units of output.
29. Let the production function of a firm be
{Q = 2L^2K^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?
Given the production function:
{Q = 2L^2K^2}
To find the maximum possible output with 5 units of labor (L) and 2 units of capital (K):
Q
{= 2 × 5^2 × 2^2}
= 2 × 25 × 4
= 200
So, the maximum possible output with 5 units of L and 2 units of K is 200 units of output.
To find the maximum possible output with zero units of labor (L) and 10 units of capital (K):
Q
{= 2 × 0^2 × 10^2}
= 2 × 0 x 100
= 0
So, the maximum possible output with zero units of L and 10 units of K is 0 units of output. This is because labor (L) is a factor in the production function, and without it (i.e., L = 0), the total product (Q) will be zero.
30. 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 = 5L + 2K}
Given the production function:
{Q = 5L + 2K}
To find the maximum possible output with zero units of labor (L) and 10 units of capital (K), we substitute these values into the production function:
Q
= 5 × 0 + 2 × 10
= 0 + 20
= 20
Therefore, the maximum possible output for the firm with zero units of L and 10 units of K is 20 units of output.