Updated NCERT Solutions for Class 11 Micro Economics Chapter 3: Production and Costs

A production function explains the technical relationship between the physical inputs used in the production process and the maximum physical output that can be produced. It specifies the maximum output that can be produced with any given combination of inputs.

In simple terms, it's like a recipe: it tells you how much output (e.g., cakes) you can make with a certain amount of inputs (e.g., flour, sugar, labour).

The production function is typically written as:

Q = f(L, K)

Where:

• Q = Maximum output produced
• f = Functional relationship
• L = Labour (a variable input)
• K = Capital (a fixed input in the short run)

It's important to remember that the production function assumes that the inputs are used efficiently and the technology is constant.

Total Product (TP) refers to the total quantity of output produced by a firm with a given amount of variable input, while keeping all other inputs fixed. It is the sum total of output produced by all units of the variable input.

For example, if 5 workers (variable input) produce 50 chairs in a factory, the Total Product is 50 chairs.

Average Product (AP) is defined as the output produced per unit of the variable input. It is calculated by dividing the Total Product by the number of units of the variable input.

• Formula: AP = Total Product (TP) / Units of Variable Input (L)

For example, if 5 workers produce 50 chairs, the Average Product of labour would be 50 / 5 = 10 chairs per worker.

Marginal Product (MP) is the additional output produced by using one more unit of the variable input, while other inputs are held constant. It is the change in Total Product resulting from a one-unit change in the variable input.

• Formula: MPn = TPn - TPn-1 (where 'n' is the number of units of the variable input)
• Alternatively: MP = Change in Total Product (ΔTP) / Change in Variable Input (ΔL)

For example, if 5 workers produce 50 chairs and adding a 6th worker increases the total production to 58 chairs, the Marginal Product of the 6th worker is 58 - 50 = 8 chairs.

The relationship between Marginal Product (MP) and Total Product (TP) is fundamental to understanding production. It can be explained in three phases:

1. When MP is positive and increasing, TP increases at an increasing rate. This is the initial phase where each additional worker adds more to the total output than the previous worker.
2. When MP is positive but decreasing, TP increases at a decreasing rate. After a certain point, while the output is still increasing, the contribution of each additional worker starts to diminish. TP reaches its maximum when MP becomes zero.
3. When MP is negative, TP starts to fall. This happens when there are too many variable inputs (e.g., workers) for the fixed input (e.g., machinery), leading to overcrowding and inefficiency.

Key Relationship:

• As long as MP is positive, TP increases.
• When MP = 0, TP is at its maximum.
• When MP becomes negative, TP starts to decline.

The distinction between the short run and the long run in economics is based on the flexibility of inputs, not on a specific calendar duration.

• Short Run: The short run is a period in which a firm cannot change all its inputs. At least one factor of production is fixed (e.g., plant, machinery, factory building), while others are variable (e.g., labour, raw materials). In the short run, a firm can change its level of output only by changing its variable inputs.
• Long Run: The long run is a period in which a firm can change all its inputs. There are no fixed factors; all factors of production are variable. In the long run, a firm can change its entire scale of operation, including the size of its plant and machinery.

The Law of Diminishing Marginal Product (also known as the Law of Variable Proportions) states that as we add more units of a variable input (like labour) to a fixed amount of other inputs (like capital), the marginal product of the variable input will eventually decline.

Explanation: Initially, adding more workers might lead to specialization and increased efficiency, causing MP to rise. However, beyond a certain point, the fixed input (e.g., machinery) becomes overburdened. This leads to overcrowding and reduced efficiency, causing the additional output from each new worker (MP) to decrease.

The Law of Variable Proportions explains the behaviour of output when only one variable input is increased, keeping other inputs fixed. It states that as we increase the quantity of a variable factor, the Total Product (TP) passes through three distinct stages:

• Stage 1: Increasing Returns to a Factor: TP increases at an increasing rate. MP increases and reaches its maximum. This is due to better utilization of fixed factors and specialization of labour.
• Stage 2: Diminishing Returns to a Factor: TP increases at a decreasing rate and reaches its maximum. MP starts to fall but remains positive. This stage ends when MP is zero and TP is maximum. A rational producer always operates in this stage.
• Stage 3: Negative Returns to a Factor: TP starts to decline. MP becomes negative. This is due to overcrowding and poor coordination between fixed and variable factors.

A production function satisfies Constant Returns to Scale (CRS) when a proportional increase in all inputs results in an equally proportional increase in output.

For example, if a firm doubles all its inputs (labour and capital), and its output also doubles, it is experiencing constant returns to scale.

Condition: If f(λL, λK) = λ * f(L, K), where λ is the factor of increase.
(Increasing inputs by factor λ increases output by the same factor λ).

A production function satisfies Increasing Returns to Scale (IRS) when a proportional increase in all inputs results in a more than proportional increase in output.

For example, if a firm doubles all its inputs, and its output more than doubles (e.g., triples), it is experiencing increasing returns to scale. This is often due to economies of scale, such as specialization and improved technology.

Condition: If f(λL, λK) > λ * f(L, K).
(Increasing inputs by factor λ increases output by more than factor λ).

A production function satisfies Decreasing Returns to Scale (DRS) when a proportional increase in all inputs results in a less than proportional increase in output.

For example, if a firm doubles all its inputs, and its output increases by less than double (e.g., by 50%), it is experiencing decreasing returns to scale. This is often due to diseconomies of scale, such as management difficulties and coordination problems in a very large firm.

Condition: If f(λL, λK) < λ * f(L, K).
(Increasing inputs by factor λ increases output by less than factor λ).

The cost function shows the functional relationship between the quantity of output produced and the minimum cost of producing that output. It tells us the least possible cost to produce a given level of output, given the technology and prices of inputs.

The cost function is expressed as:

C = f(Q, Pi, T)

Where:

• C = Total Cost
• Q = Quantity of output
• Pi = Prices of inputs
• T = Technology

In a simpler form, for a given set of input prices and technology, it's shown as C = f(Q). It is the financial counterpart of the production function.

• Total Fixed Cost (TFC): These are the costs incurred on fixed factors of production. They do not change with the level of output. Even at zero output, TFC is positive. Examples include rent for the factory, salaries of permanent staff, and insurance premiums. The TFC curve is a horizontal line parallel to the X-axis.
• Total Variable Cost (TVC): These are the costs incurred on variable factors of production. They change directly with the level of output. TVC is zero when output is zero and increases as output increases. Examples include the cost of raw materials, wages of temporary workers, and electricity bills. The TVC curve is upward sloping.
• Total Cost (TC): This is the sum of Total Fixed Cost and Total Variable Cost. It represents the total expenditure incurred to produce a certain level of output.

Relationship:
The relationship is simple and direct:
TC = TFC + TVC

Since TFC is constant, the change in TC is entirely determined by the change in TVC. The TC curve has the same shape as the TVC curve but starts from the TFC level on the Y-axis, not from the origin.

• Average Fixed Cost (AFC): This is the fixed cost per unit of output. It is calculated by dividing TFC by the quantity of output (Q).
  Formula: AFC = TFC / Q
  AFC continuously falls as output increases because the constant TFC is spread over more units.
• Average Variable Cost (AVC): This is the variable cost per unit of output. It is calculated by dividing TVC by the quantity of output (Q).
  Formula: AVC = TVC / Q
  The AVC curve is typically U-shaped due to the Law of Variable Proportions.
• Average Cost (AC) / Average Total Cost (ATC): This is the total cost per unit of output. It is calculated by dividing TC by the quantity of output (Q).
  Formula: AC = TC / Q

Relationship:
Since TC = TFC + TVC, if we divide the entire equation by Q, we get:
(TC/Q) = (TFC/Q) + (TVC/Q)
Therefore, the primary relationship is:
AC = AFC + AVC

The AC curve is also U-shaped. It lies above the AFC and AVC curves. The vertical distance between the AC and AVC curves is the AFC, which continuously decreases.

No, there cannot be any fixed cost in the long run.

The definition of the long run is a time period long enough for a firm to change all its factors of production. In the long run, there are no fixed inputs; all inputs are variable. Since fixed costs are costs associated with fixed inputs, the absence of fixed inputs means there can be no fixed costs. The firm can change its plant size, build new factories, or shut down old ones, making all costs variable.

The Average Fixed Cost (AFC) curve is a downward-sloping curve that is a rectangular hyperbola.

Why it looks so:

1. Downward Sloping: AFC is calculated as AFC = TFC / Q. Since Total Fixed Cost (TFC) is constant, as output (Q) increases, the AFC must decrease. The constant cost gets spread over a larger number of units.
2. Rectangular Hyperbola: The AFC curve has this specific shape because the area under the curve at any point (AFC × Q) is always equal to the constant TFC.
3. Never Touches Axes: The AFC curve never touches the X-axis because TFC is always positive, so AFC can never be zero. It also never touches the Y-axis because production cannot be infinite at zero cost.

In the short run, the Marginal Cost (MC), Average Variable Cost (AVC), and Average Cost (AC) curves are all U-shaped.

• Short-run Marginal Cost (SMC) Curve: It is U-shaped. It initially falls due to increasing returns, reaches a minimum, and then rises steeply due to diminishing returns.
• Average Variable Cost (AVC) Curve: It is also U-shaped. It falls initially, reaches a minimum, and then rises. Its shape reflects the Law of Variable Proportions.
• Short-run Average Cost (SAC) Curve: This is also U-shaped. It is the sum of AFC and AVC. It falls initially faster than AVC (as both AFC and AVC are falling), reaches a minimum, and then rises. The U-shape is due to both the Law of Variable Proportions and the continuously falling AFC.

The relationship between a marginal and an average value explains this.

• When SMC < AVC, the average cost of production is pulled down. Thus, the AVC curve is falling.
• When SMC > AVC, the cost of producing an additional unit is higher than the average, which pulls the average up. Thus, the AVC curve is rising.
• Therefore, the SMC curve must intersect the AVC curve at the exact point where AVC is at its minimum. At this point, SMC = AVC. Before this point AVC was falling, and after this point, it starts rising.

Think of it like cricket scores: If a batsman's next score (marginal) is less than his average, his average will fall. If his next score is more than his average, his average will rise. The average stops falling and starts rising at the point where the marginal score equals the average.

The logic is identical to the relationship between SMC and AVC.

• When SMC < SAC, it means the cost of the next unit is less than the average of all previous units. This pulls the average down, so the SAC curve falls.
• When SMC > SAC, the cost of the next unit is higher than the average, which pulls the average cost up. So, the SAC curve rises.
• Logically, the SMC curve must intersect the SAC curve when the SAC has stopped falling and is about to rise. This happens precisely at the minimum point of the SAC curve, where SMC = SAC.

The short-run marginal cost (SMC) curve is U-shaped primarily due to the Law of Variable Proportions.

1. Initial Falling Phase: In the beginning (Stage 1 of production), when more variable inputs are added to fixed inputs, there are increasing returns to a factor. Efficiency increases, and the marginal product (MP) of the variable factor rises. Since each additional unit of input produces more output, the additional cost (MC) per unit of output falls.
2. Minimum Point: MC reaches its minimum when MP is at its maximum.
3. Rising Phase: After a certain point (Stage 2 of production), diminishing returns to a factor set in. The marginal product (MP) starts to decline due to factors like overcrowding and strain on fixed assets. Since each additional unit of input now produces less output, the additional cost (MC) per unit of output starts to rise.

This behaviour of initially falling and then rising marginal cost gives the SMC curve its characteristic 'U' shape.

The relationship between AP and MP is as follows:

• When MP > AP, AP rises.
• When MP < AP, AP falls.
• When MP = AP, AP is at its maximum.

The MP curve cuts the AP curve from above at the AP curve's highest point.

The LAC curve is flatter than the SAC curve because of the greater flexibility a firm has in the long run. In the long run, a firm can choose the most efficient (least cost) plant size for any given level of output. It can adjust all inputs. In the short run, the firm is stuck with a fixed plant size, making it less flexible and leading to steeper cost increases beyond the optimal capacity. The LAC is an envelope curve that tangentially encloses a series of SAC curves.

The Law of Variable Proportions states that as we increase the quantity of one variable input, keeping other inputs fixed, the Total Product first increases at an increasing rate, then at a decreasing rate, and finally starts to fall.

Schedule:

Explanation of Stages:

• Stage 1 (Up to 3 units of Labour): TP increases at an increasing rate (10, 14, 18). MP is rising.
• Stage 2 (From 4 to 7 units of Labour): TP increases at a diminishing rate. MP is falling but remains positive. TP is maximum (70) when MP is zero. This is the rational stage of production.
• Stage 3 (8th unit of Labour): TP starts to fall. MP becomes negative (-2).

Explanation:

• TFC is constant at 100.
• TC = TFC + TVC.
• AFC = TFC / Q.
• AVC = TVC / Q.
• AC = TC / Q or AC = AFC + AVC.
• MC = ΔTC / ΔQ (e.g., for Q=1, MC = 150-100 = 50).

MP is the change in TP from adding one more baker.

TP with 4 bakers = 60
TP with 5 bakers = 70

MP of 5th baker = 70 - 60 = 10 cakes.

When the 7th baker is hired, the bakery enters Stage 3: Negative Returns to a Factor.

Reason: The Total Product (TP) falls from 70 to 65 cakes. The Marginal Product (MP) of the 7th baker is 65 - 70 = -5, which is negative. This indicates that adding the 7th baker created overcrowding or inefficiency, leading to a decrease in total output.

TC = AC × Q
TC = ₹50 × 10 = ₹500.

TFC = AFC × Q
TFC = ₹20 × 10 = ₹200.

We know TC = TFC + TVC.
Therefore, TVC = TC - TFC
TVC = ₹500 - ₹200 = ₹300.

Alternatively, AC = AFC + AVC -> 50 = 20 + AVC -> AVC = 30. Then TVC = AVC x Q = 30 x 10 = 300.