CBSE Class 12 Economics Chapter 6: Cost NCERT Solutions

Solution: The cost function establishes a direct relationship between the level of output produced and the total cost incurred by a firm. It indicates the minimum expenditure required to produce a given quantity of output, assuming the prices of inputs are constant. Mathematically, it is represented as:

$$C\; =\; f(X)$$

where $C$ represents the total cost of production and $X$ represents the quantity of output. This function is derived under the assumption that other factors influencing cost (like input prices) remain unchanged (ceteris paribus).

Solution:

The costs incurred by a firm can be broadly classified into Total Fixed Cost (TFC) and Total Variable Cost (TVC). Their sum constitutes the Total Cost (TC).

1. Total Fixed Cost (TFC): These are costs that do not change with the level of output in the short run. They are incurred even when production is zero. Examples include rent of the factory, salaries of permanent staff, etc. The TFC curve is a horizontal line parallel to the x-axis, indicating that it remains constant regardless of the output level.
2. Total Variable Cost (TVC): These costs vary directly with the level of output. They are zero when production is zero and increase as more output is produced. Examples include costs of raw materials, wages of daily laborers, etc. The TVC curve typically starts from the origin and is inverse S-shaped due to the law of variable proportions.
3. Total Cost (TC): This is the sum of Total Fixed Cost and Total Variable Cost. It represents the total expenditure incurred by the firm for producing a certain level of output. The relationship is expressed as: $$TC\; =\; TFC\; +\; TVC$$ The TC curve starts from the level of TFC (when output is zero) and is also inverse S-shaped, reflecting the behavior of TVC.

Diagrammatic Representation:

In a single diagram, the TFC curve is a horizontal line. The TVC curve starts from the origin and rises. The TC curve starts from the TFC level on the vertical axis and rises parallel to the TVC curve after a certain output level. The vertical distance between the TC and TVC curves at any output level represents the TFC.

Note: The provided source did not contain an actual diagram, so a placeholder description is used.

Solution:

These are per-unit cost measures derived from total costs:

1. Average Fixed Cost (AFC): This is the fixed cost per unit of output. It is calculated by dividing the Total Fixed Cost (TFC) by the quantity of output (Q).

   $$AFC\; =\; \backslash frac\{TFC\}\{Q\}$$

   As output increases, AFC continuously falls because the constant TFC is spread over a larger quantity.
2. Average Variable Cost (AVC): This is the variable cost per unit of output. It is calculated by dividing the Total Variable Cost (TVC) by the quantity of output (Q).

   $$AVC\; =\; \backslash frac\{TVC\}\{Q\}$$

   AVC initially decreases due to increasing returns to variable factors but eventually starts increasing due to diminishing returns. Thus, the AVC curve is U-shaped.
3. Average Cost (AC): This is the total cost per unit of output. It is calculated by dividing the Total Cost (TC) by the quantity of output (Q).

   $$AC\; =\; \backslash frac\{TC\}\{Q\}$$

   Like AVC, the AC curve is also U-shaped because it is influenced by both falling AFC and eventually rising AVC.

Relationship between AC, AFC, and AVC:

The Average Cost (AC) is the sum of Average Fixed Cost (AFC) and Average Variable Cost (AVC). This relationship can be expressed as:

$$AC\; =\; AFC\; +\; AVC$$

This means that the AC curve lies above the AVC curve, and the vertical distance between them is equal to the AFC, which decreases as output rises.

Solution: No, there are no fixed costs in the long run. In the long run, a firm has enough time to adjust all its factors of production, including those that are fixed in the short run (like capital, land, and plant size). All factors become variable, and therefore, all costs associated with them also become variable. Fixed costs are a characteristic exclusively of the short-run production period.

Solution:

The Average Fixed Cost (AFC) curve has the shape of a downward-sloping rectangular hyperbola.

Reason for its shape:

AFC is calculated by dividing the Total Fixed Cost (TFC) by the quantity of output (Q): $AFC\; =\; \backslash frac\{TFC\}\{Q\}$. In the short run, TFC remains constant regardless of the output level. As the firm increases its output (Q), this constant TFC is spread over an increasingly larger number of units. Consequently, the AFC per unit falls continuously. The curve approaches the x-axis but never touches it, as output cannot be infinite, and AFC cannot be zero (since TFC is positive). This characteristic shape is known as a rectangular hyperbola because the area under the curve at any point (representing TFC) remains constant.

Solution: The Short-Run Marginal Cost (SMC) curve, the Average Variable Cost (AVC) curve, and the Short-Run Average Cost (SAC) curve all typically exhibit a U-shape. This U-shape is a consequence of the law of variable proportions, which describes how the returns to a variable factor change as more of it is added to a fixed factor.

Solution: The Short-Run Marginal Cost (SMC) curve intersects the Average Variable Cost (AVC) curve at the latter's minimum point due to the way marginal and average concepts are related:

1. When AVC is falling: If the cost of producing one additional unit (SMC) is less than the current average variable cost (AVC), then producing that additional unit will pull the average down. Therefore, when AVC is falling, SMC < AVC.
2. When AVC is rising: If the cost of producing one additional unit (SMC) is greater than the current average variable cost (AVC), then producing that additional unit will pull the average up. Therefore, when AVC is rising, SMC > AVC.
3. At the minimum point of AVC: For the AVC to stop falling and start rising, there must be a point where it is neither falling nor rising. At this specific minimum point, the cost of the additional unit (SMC) must be exactly equal to the average variable cost (AVC).

Thus, the SMC curve must cut the AVC curve precisely at the minimum point of the AVC curve. The same logic applies to the intersection of SMC and SAC.

Solution: The Short-Run Marginal Cost (SMC) curve cuts the Short-Run Average Cost (SAC) curve at the minimum point of the SAC curve.

Reason: The relationship between marginal and average concepts dictates this intersection:

1. When SAC is falling: If the cost of producing an additional unit (SMC) is less than the current average cost (SAC), then producing this extra unit will reduce the average cost. Hence, when SAC is falling, SMC < SAC.
2. When SAC is rising: If the cost of producing an additional unit (SMC) is greater than the current average cost (SAC), then producing this extra unit will increase the average cost. Hence, when SAC is rising, SMC > SAC.
3. At the minimum point of SAC: For the SAC to reach its lowest point before starting to rise, the cost of the marginal unit produced must be exactly equal to the average cost at that output level. Therefore, at the minimum point of SAC, SMC = SAC.

This explains why the SMC curve intersects the SAC curve at its lowest point.

Solution: The Short-Run Marginal Cost (SMC) curve is U-shaped primarily due to the **Law of Variable Proportions**. This law states that as more units of a variable factor are added to a fixed factor, the total product initially increases at an increasing rate, then at a decreasing rate, and eventually may decrease.

Here's how this impacts SMC:

1. Increasing Returns Phase: Initially, as variable inputs are added, productivity is high. Each additional unit of input contributes significantly to output, and the cost of producing an extra unit (marginal cost) tends to fall.
2. Diminishing Returns Phase: As more variable inputs are added to the fixed factor, the efficiency of the variable inputs starts to decline (diseconomies of variable proportions set in). Producing each additional unit of output requires more and more of the variable input, thus increasing the marginal cost.
3. Negative Returns Phase (possible): If excessive variable inputs are added, total product may even fall, leading to a sharp increase in marginal cost.

Therefore, the SMC curve first falls, reaches a minimum, and then rises, forming the characteristic U-shape.