The following table shows the total cost schedule of a firm. What is the total fixed cost schedule of this fir

Exercises · Q25

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.

$Q$	$TC$ (Rs)
0	10
1	30
2	45
3	55
4	70
5	90
6	120

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Concept understanding — Cost Concepts

Cost Concepts: From Everyday Intuition to Economic Precision

Think about the last time you bought something — say, a plate of chole bhature from a roadside stall. The stall owner paid for flour, oil, spices, gas, and the helper's wages. That's the obvious cost. But what about the rent of the cart? The interest on the loan he took to buy the stove? And what about the fact that he could have worked as a driver instead — the income he gave up? That last one is a cost too, though no money changed hands.

That's where economics begins to separate itself from simple accounting. Costs are not just what you pay; they are what you sacrifice.

The Core Idea: Opportunity Cost

The single most important cost concept in economics is opportunity cost. The NCERT Class-12 textbook defines it clearly: opportunity cost is the cost of the next best alternative foregone.

Important

Opportunity cost = value of the next best alternative that you give up when you make a choice.

Why does this matter? Because resources — time, money, land, labour — are scarce. Every choice has a hidden cost: the thing you didn't choose. When the stall owner chooses to run his stall, he gives up the salary he could have earned as a driver. That foregone salary is a real cost, even if it never appears in his cash register.

Explicit vs Implicit Costs

From opportunity cost, we get two categories:

Explicit costs — actual money payments made to others (wages, rent, raw materials, electricity bills). These are recorded in the books.
Implicit costs — the value of self-owned resources used in production, for which no explicit payment is made. The owner's own labour, his own capital, his own land — these have opportunity costs that are not paid to anyone else.

Note

In accounting, only explicit costs are counted. In economics, both explicit and implicit costs matter, because economics is about the full sacrifice.

Total, Average, and Marginal Costs

Once we move to production, costs are studied in relation to output. The NCERT textbook introduces these three measures:

Total Cost (TC)

The sum of all costs — explicit and implicit — incurred to produce a given level of output.

Average Cost (AC)

Cost per unit of output.

AC = \frac{TC}{Q}

where $Q$ is the quantity of output.

Marginal Cost (MC)

The additional cost incurred to produce one more unit of output.

MC = \frac{\Delta TC}{\Delta Q}

where $\Delta$ means "change in".

Tip

MC is the cost of the last unit produced. AC is the cost of all units averaged. They behave differently as output changes.

Short-Run vs Long-Run Costs

This distinction is crucial. In the short run, at least one factor of production is fixed (typically capital — factory size, machinery). In the long run, all factors are variable.

Short-Run Cost Categories

Cost	Symbol	Definition
Total Fixed Cost	TFC	Cost that does not change with output (rent, insurance, interest on loans)
Total Variable Cost	TVC	Cost that changes with output (raw materials, wages of daily workers, electricity)
Total Cost	TC	$TC = TFC + TVC$

From these, we derive:

Average Fixed Cost (AFC) = $\frac{TFC}{Q}$ — falls continuously as output rises.
Average Variable Cost (AVC) = $\frac{TVC}{Q}$ — typically U-shaped.
Average Cost (AC) = $\frac{TC}{Q} = AFC + AVC$

Watch out

A common mistake: thinking that AC and AVC are the same. They are not. AC includes AFC, so AC always lies above AVC. The gap between them is AFC, which shrinks as output increases.

The Shape of the Curves

Imagine a graph with output on the horizontal axis and cost on the vertical axis.

TFC is a horizontal straight line — it never changes. …

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The total fixed cost (TFC) is the cost incurred when the output level is zero. From the given table, when $Q=0$ , the total cost ( $TC$ ) is Rs 10. Therefore, the total fixed cost for this firm is Rs 10, and it remains constant at all levels of output.

The various cost schedules are calculated using the following formulas:

TFC = TC \text{ at } Q=0

Using these formulas, we can calculate the required schedules:

$Q$	$TC$ (Rs)	$TFC$ (Rs)	$TVC$ (Rs)	$AFC$ (Rs)	$AVC$ (Rs)	$SAC$ (Rs)	$SMC$ (Rs)
0	10	10	0	-	-	-	-
1	30	10	$30-10=20$	$10/1=10.00$	$20/1=20.00$	$30/1=30.00$	$30-10=20$
2	45	10	$45-10=35$	$10/2=5.00$	$35/2=17.50$	$45/2=22.50$	$45-30=15$
3	55	10	$55-10=45$	$10/3=3.33$	$45/3=15.00$	$55/3=18.33$	$55-45=10$

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This problem requires understanding and applying various short-run cost concepts to a given total cost schedule. The key is to first identify total fixed cost (TFC) at zero output, then derive total variable cost (TVC), and subsequently calculate average fixed cost (AFC), average variable cost (AVC), short-run average cost (SAC), and short-run marginal cost (SMC) using their respective formulas.

In the short run, a firm's total costs are divided into two main categories: fixed costs and variable costs. Understanding these distinctions is crucial for analyzing a firm's production decisions and profitability. Fixed costs are those expenses that do not change with the level of output in the short run, such as rent for factory space or salaries of permanent administrative staff. These costs are incurred even if the firm produces zero output. Variable costs, on the other hand, are expenses that vary directly with the level of output, such as raw material costs or wages for production workers. As output increases, variable costs increase, and as output decreases, they fall.

The total cost (TC) at any level of output is simply the sum of total fixed cost (TFC) and total variable cost (TVC). From these total cost figures, we can derive various per-unit costs, which provide insights into the efficiency of production. Average fixed cost (AFC) tells us the fixed cost per unit of output, average variable cost (AVC) tells us the variable cost per unit, and short-run average cost (SAC) gives the total cost per unit. Finally, short-run marginal cost (SMC) measures the change in total cost (or total variable cost) resulting from producing one additional unit of output.

Let's calculate each of these schedules step-by-step using the provided total cost data.

1. Total Fixed Cost (TFC) Schedule

Total Fixed Cost (TFC) is the cost incurred by the firm even when no output is produced. Looking at the given table, when the quantity ( $Q$ ) is 0, the Total Cost ( $TC$ ) is Rs 10. This Rs 10 represents the fixed cost of the firm, as it must be paid regardless of production. Since fixed costs do not change with output in the short run, the TFC will remain constant at Rs 10 for all levels of output.

TFC = TC \text{ when } Q = 0

Therefore, the TFC schedule is:

$Q$	$TFC$ (Rs)
0	10
1	10
2	10
3	10
4	10
5	10
6	10

2. Total Variable Cost (TVC) Schedule

Total Variable Cost (TVC) is the portion of total cost that changes with the level of output. It can be calculated by subtracting the Total Fixed Cost (TFC) from the Total Cost (TC) at each level of output.

TVC = TC - TFC

Let's calculate TVC for each output level:

For $Q=0$ : $TVC = 10 - 10 = 0$
For $Q=1$ : $TVC = 30 - 10 = 20$
For $Q=2$ : $TVC = 45 - 10 = 35$
For $Q=3$ : $TVC = 55 - 10 = 45$
For $Q=4$ : $TVC = 70 - 10 = 60$
For $Q=5$ : $TVC = 90 - 10 = 80$
For $Q=6$ : $TVC = 120 - 10 = 110$

3. Average Fixed Cost (AFC) Schedule

Average Fixed Cost (AFC) is the fixed cost per unit of output. It is calculated by dividing Total Fixed Cost (TFC) by the quantity of output ( $Q$ ). As output increases, the fixed cost is spread over more units, so AFC continuously declines.

AFC = \frac{TFC}{Q}

Watch out

AFC is undefined at $Q=0$ because division by zero is not possible.

Let's calculate AFC for each output level:

For $Q=0$ : $AFC$ is undefined.
For $Q=1$ : $AFC = \frac{10}{1} = 10$
For $Q=2$ : $AFC = \frac{10}{2} = 5$
For $Q=3$ : $AFC = \frac{10}{3} \approx 3.33$
For $Q=4$ : $AFC = \frac{10}{4} = 2.5$
For $Q=5$ : $AFC = \frac{10}{5} = 2$
For $Q=6$ : $AFC = \frac{10}{6} \approx 1.67$

4. Average Variable Cost (AVC) Schedule

Average Variable Cost (AVC) is the variable cost per unit of output. It is calculated by dividing Total Variable Cost (TVC) by the quantity of output ( $Q$ ).

AVC = \frac{TVC}{Q}

Watch out

AVC is undefined at $Q=0$ .

Let's calculate AVC for each output level:

For $Q=0$ : $AVC$ is undefined.
For $Q=1$ : $AVC = \frac{20}{1} = 20$
For $Q=2$ : $AVC = \frac{35}{2} = 17.5$
For $Q=3$ : $AVC = \frac{45}{3} = 15$
For $Q=4$ : $AVC = \frac{60}{4} = 15$
For $Q=5$ : $AVC = \frac{80}{5} = 16$
For $Q=6$ : $AVC = \frac{110}{6} \approx 18.33$

5. Short-run Average Cost (SAC) Schedule

Short-run Average Cost (SAC), also known as Average Total Cost (ATC), is the total cost per unit of output. It can be calculated by dividing Total Cost (TC) by the quantity of output ( $Q$ ), or by summing Average Fixed Cost (AFC) and Average Variable Cost (AVC).

SAC = \frac{TC}{Q} \quad \text{or} \quad SAC = AFC + AVC

Watch out

SAC is undefined at $Q=0$ .

Let's calculate SAC for each output level:

For $Q=0$ : $SAC$ is undefined.
For $Q=1$ : $SAC = \frac{30}{1} = 30$ (or $10 + 20 = 30$ )
For $Q=2$ : $SAC = \frac{45}{2} = 22.5$ (or $5 + 17.5 = 22.5$ )
For $Q=3$ : $SAC = \frac{55}{3} \approx 18.33$ (or $3.33 + 15 = 18.33$ )
For $Q=4$ : $SAC = \frac{70}{4} = 17.5$ (or $2.5 + 15 = 17.5$ )
For $Q=5$ : $SAC = \frac{90}{5} = 18$ (or $2 + 16 = 18$ ) …

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1. Total Fixed Cost (TFC) Schedule

2. Total Variable Cost (TVC) Schedule

3. Average Fixed Cost (AFC) Schedule

4. Average Variable Cost (AVC) Schedule

5. Short-run Average Cost (SAC) Schedule

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