Chapter 6 Cost 11th Commerce

Concept

INTRODUCTION

In the previous chapter, we studied the various concepts and laws related to the behaviour of product. A firm uses various inputs to produce goods and services. Firm has to make payments for such inputs as they do not come free. The expenditure incurred on these inputs is known as the cost of production.

Since production costs are important in determining a firm's output, we will understand several aspects about a firm's costs in this chapter. This comprehensive study will lay the foundation for understanding the supply decisions of business firms.

Concept

MEANING OF COST

Cost is the total expenditure incurred in producing a commodity. In Economics, Cost is the sum total of:

Explicit Cost It is the actual money expenditure on inputs or payment made to outsiders their factor services. For example, wages paid to the employees, rent paid for hired premises, payment for raw materials, etc.

Implicit Cost: It is the estimated value of the inputs supplied by the owners including normal profit. For example, interest on own capital, rent of own land, salary for the services of entrepreneur, etc. Such costs are the costs of self supplied factors.

So, Cost in economics includes actual expenditure on inputs (i.e. explicit cost) and the imputed value of the inputs supplied by the owners (i.e. implicit cost).

Economic cost of production includes not only the accounting cost (i.e. the explicit costs) but also the implicit cost. The sum of Explicit cost and Implicit cost is the total cost of production of a commodity

Concept

How to Measure Implicit Cost?

Implicit cost is measured by determining the value of self supplied factors in terms of their market price. For example, if a doctor has opened a clinic at his home, then imputed value of salary for his services will be included Value of salary will be calculated on the basis of salary that he would receive if he is employed by someone else.

Implicit cost is calculated because if such factors were not owned and used by the entrepreneur in his firm, then he would have hired them from outsiders. So imputed value of factors, Le implicit cost is included in the total cost of production.

Concept

Explicit Cost Vs Implicit Cost

Concept

Cost Function

The relation between cost and output is known as ‘Cost function’. Cost function refers to the functional relationship between cost and output.

It is expressed as: C = f (q)

{Where C = Cost of production; q = Quantity of output; f = Functional relationship}

Concept

Opportunity Cost

Opportunity cost is cost of the next best alternative foregone.

The concept of opportunity cost is very important as it forms the basis of the concept of cost. When a firm decides to produce a particular commodity, then it always considers the value of the alternative commodity, which is not produced. The value of the alternative commodity is the opportunity cost of the good that the firm is now producing.

For example, suppose, a farmer can produce either 50 quintals of rice or 40 quintals of wheat on his land with the given resources. If he chooses to produce rice, then he will have to forego the opportunity of producing 40 quintals of wheat.

Cost can be of different types:

Money Cost;
Real Cost;
Private Cost; and
Social Cost.

Refer ‘Power Booster’ for their brief discussion.

Concept

6.3 SHORT RUN COSTS

We know, in the short nun, there are some factors which are fixed, while others are Similarly, short run costs are also divided into two kinds of costs:

Fixed Cost
Variable Costs

The sum total of fixed cost and variable cost is equal to total cost.

Let us discuss the short run costs in detail.

Concept

Total Fixed Cost (TFC) or Fixed Cost (FC)

Fixed Costs refer to those costs which do not vary directly with the level of output. For example, rent of premises, interest on loan, salary of permanent staff, insurance premium, etc.

Fixed Cast is also known as:

Supplementary Cost; or
Overhead Cost or
Indirect Cost; or
General Cost; or
Unavoidable Cost.

Fixed cost is incurred on fixed factors like machinery, land, building, etc., which cannot be changed in the short run. The payment to these factors remains fixed irrespective of the level of output, i.e. fixed cost remains the same, whether output is large, small or even zero.

Example Fixed Cost

Suppose, you start a furniture business of making wooden chairs. You hire a shop at a monthly rent of rs. 4,000 and take a loan of rs. 1,00,000 from ICICI Bank @ 1% interest per month. Now, your monthly total fixed cost will be rs. 5,000 {rs. 4,000 as rent and rs. 1,000 as monthly interest on loan (1% of 1,00,000)}. You will have to pay 5,000 per month irrespective of the number of chairs produced.

The concept of fixed cost can be better explained through following schedule and diagram:

Table 6.1: Total Fixed Cost Schedule

Fixed costs are diagrammatically shown in Fig. 6.1 Units of output are measured along the X-axis and fixed costs along the Y-axis. TFC is the fixed cost curve obtained by plotting the points shown in Table 6.1. The curve makes intercept on the Y-axis, which is equal to the fixed Cost of Rs. 12 TFC curve in a horizontal straight line parallel to the X-axis because TTC remains same at all levels of output even if the output is zero.

Why does Fixed Cost no vary with output?

Fixed costs like salary of a permanent manager, rent of telephone, etc. are paid irrespective of the level of output. Buch costs are indivisible even if the fins a producing zero or small output means a fem cannot have half a manager or half a telephone just because is operating at a low eve of output.

Concept

Total Variable Cost (TVC) or Variable Cost (VC)

Variable costs refer to those costs which very directly with the level of output. For example, payment for raw material, power, fuel, wages of casual labour, etc. Variable costs are incurred on variable factors like raw material, direct labour, power, etc. which changes with change in level of output. It means, variable costs rise with increase in the output and fall with decrease in the output. Such costs are incurred till there is production and became at zero level of output.

Variable cost is also known as ‘Prime Cost’, ‘Direct Cost’ or ‘Avoidable Cost’.

Let us discuss the concept of variable cost with the help of the following schedule and diagram:

Table 6.2: Total Variable Cost Schedule

TVC curve is inversely S-shaped as it initially increases at decreasing rate and later it increases at increasing rate. TVC is zero at 0 level of output

In Fig. 6.2. units of output are measured along the X-axis and vantable cost along the axis TVC is the variable coal curve obtained by plating the points shown in Table 6.2. As seen in the diagram, TVC curve starts from the origin indicating that is zero, variable cost is also zero TVC is an inversely S-shaped curve due to the Law of Variable when output Proportions

Concept

Differences Between Total Variable Cost and Total Fixed Cost

Concept

Total Cost (TC)

Total Cost (TC) is the total expenditure incurred by a firm on the factors of production required for the production of a commodity.

TC is the sum of total fixed cost (TFC) and total variable cost (TVC) at various levels of output.

TC=TFC+TVC

Since TFC remains same at all levels of output, the change in TC is entirely due to TVC The concept of total cost can be better understood through Table 63 and Fig. 6.3.

Table 6.3: Total Cost Schedule

In Table 6.3, TC = TFC = ₹12 at zero level of output because TVC is zero. At 1 unit of output, TFC remains same at ₹12, but TVC increases to ₹6. As a result, TC becomes 12 + 6 = ₹18. Similarly, other values of TC have been calculated.

In Fig. 6.3, TC curve is obtained by summation of TVC and TFC curve. The change in TC curve is entirely due to TVC as TFC remains constant. By adding TFC to TVC curve, we get the TC curve. The vertical distance between TC and TVC always remains the same due to constant TFC Like TVC curve, TC curve is also inversely S-shaped, due to the Law of Variable Proportions.

The change in TC is entirely due to TVC as TFC is constant at all levels of output, TC = TFC at zero output as variable cost is zero. With increase in output, TC also increases by the extent of increase in TVC.

Concept

Relationship between TC, TFC and TVC

The various points of relationship between TC, TFC and TVC can be better explained with the help of Table 6.3 and Fig. 6.3.

TFC curve is a horizontal straight fine parallel to X-axis as it remains constant at all levels of output.
TC and TVC curves are inversely S-shaped because they rise initially at a decreasing rate them at a constant rate and finally, at an increasing rate. The reason behind their shape is the Law of Variable Proportions.
At zero output, TC is equal to TFC because there is no variable cost at zero level of output. So, TC and TFC curves start from the same point, which is above the origin.
The vertical distance between TFC curve and TC curve is equal to TVC. As TVC rises with increase in the output, the distance between TFC and TC curves also goes on increasing
TC and TVC curves are parallel to each other and the vertical distance between them remains the same at all levels of output because the gap between them represents TFC, which remains constant at all levels of output.

Concept

AVERAGE COSTS

The per unit costs explain the relationship between cost and output in a more realistic manner. From total fixed cost (TFC), total variable cost (TVC) and total cost (TC), we can obtain per unit costs. The 3 kinds of per unit costs are:

Average Fixed Cost (AFC)
Average Variable Cost (AVC)
Average Total Cost (ATC) or Average Cost (AC)

Concept

Average Fixed Cost (AFC)

Average fixed cost refers to the per unit fixed cost of production. It is calculated by dividing TFC by total output.

AFC = TFC Q

{Where: AFC = Average fixed cost; TFC = Total fixed cost; Q = Quantity of output}

AFC falls with increase in output as TFC remain same at all levels of output.

Table 6.4: Average Fixed Cost

As seen in Table 6.4, AFC falls with rise in output because constant TFC is divided by increasing output AFC curve in Fig. 6.4 is obtained by plotting the points shown in Table 6.4. AFC curve is a rectangular hyperbola, i.e. area under AFC curve remains same at different point.

AFC does not touch any of the axes

As AFC is a rectangular hyperbola, it approaches both the axes. It gets nearer and nearer the axes, but never touches them.

AFC can never touch the X-axis as TFC can never be zero.
AFC curve can never touch the Y-axis because at zero level of output. TFC is a positive value and any positive value divided by zero will be an infinite value.

Concept

Average Variable Cost (AVC)

Average variable cost refers to the per unit variable cost of production. It is calculated by dividing TVC by total output.

AVC = TVC Q

{Where: AVC = Average variable cost; TVC = Total Variable cost; Q = Quantity of output}

AVC initially falls with increase in output. Once the output rises till optimum level, AVC starts Rising. It can be better understood with the help of Table 6.5 and Fig. 6.5.

Table 6.5: Average Variable Cost

Concept

Average Total Cost (ATC) or Average Cost (AC)

Average cost refers to the per unit total cost of production. It is calculated by dividing TC by total output.

AC = TC Q

{Where: AC = Average cost; TC = Total cost; Q = Quantity of output}

Average cost is also defined as the sum of average fixed cost (AFC) and average variable cost (AVC), i.e. AC = AFC + AVC

Like AVC, average cost also initially falls with increase in output. Once the output rises till optimum level, AC starts rising. It can be better understood with the help of Table 6.6 and Fig. 6.6.

Table 6.6: Average Cost

As seen in Table 6.6, AC is calculated by adding AFC and AVC. As seen in Fig. 6.6, AC curve is a U-shaped curve. It means AC initially falls (1^st phase), and after reaching its minimum point (2^nd phase), it starts rising (3^rd phase).

Let so understand the three phases of AC:

1^st Phase: When both APC and AVC fall till the level of 2 units

of output, AC also falls Le till point A.

2^nd Phase: From 2 units to 3 units, AFC continues to fall, but

AVC remains constant. So, AC falls (due to falling

AFC) till it reaches its minimum point 'B' From 3

units to 4 units, fall in AFC (by? 1) is equal to rise in

AVC (by 1), 50, AC remains constant.

3^rd Phase: After 4 units of output, rise in AVC (by1) is more than

fall in AFC (by 0.60) and, therefore, AC starts rising.

Concept

Important Observations: AC, AVC and AFC

AC curve will always lie above the AVC curve (See Fig. 67) because AC, at all levels of output includes both AVC and AFC.
AVC reaches its minimum point (point 'B') at a level of output lower than that of AC (point 'A') because when AVC is at its minimum point, AC is still falling because of falling AFC.
As the output increases, the gap between AC and AVC curves decreases, but, they never intersect each other. It happens because the vertical distance between them is AFC, which can never be zero.

Concept

MARGINAL COST

Marginal cost refers to addition to total cost when one more unit of output is produced. For example, If TC of producing 2 units is 200 and TC of producing 3 units is 240, then

MC = 240 – 200 - ₹40.

MC_n= TC_n- TC_{n - 1}

Where:

n = Number of units produced

MC_n = Marginal cost of the n unit

TC_n = Total cost of n units

TC_n-1 = Total cost of (n-1) units.

One More way to Calculate MC

We know, MC is the change in TC when one more unit of output is produced. However, when change in units produced is more than one, then MC can also be calculated as:

If TC of producing 2 units is ₹200 and TC of producing 5 units is ₹350, then MC will be:

MC is not affected by Fixed Costs

We know, MC is addition to TC when one more unit of output is produced. We also know, TC = TFC + TVC. As TFC does not change with change in output. MC is independent of TFC and is affected only by change in TVC.

This can be explained with the help of a simple mathematical derivation:

We know:

MC_n = TC_n – TC_n-1 …. (1)

MC_n = TC_n – TC_n-1 …. (2)

Putting the value of (2) in (1), we get

MC_n = (TFC_n + TVC_n) – (TFC_n-1 + TVC_n-1)

= TFC_n + TVC_n – TFC_n-1 – TVC_n-1

= TFC_n – TFC_n-1 + TVC_n – TVC_n-1

Now, TFC is same at all levels of output, so TFC_n = TFC_n-1

It means, TFC_n – TFC_n-1 = 0

So, MC_n = TVC_n- TVC_n-1

Let us now understand the concept of MC with the help of a schedule and diagram:

Table 6.7: Marginal Cost

As seen in Table 6.7, MC can be calculated from both TC and TVC. MC curve in Fig. 6.8 is obtained by plotting the points shown in Table 6.7. MC is a U-shaped curve, i.e. MC initially falls till it reaches its minimum point and thereafter, its starts rising. The reason behind its U-shape is the Law of Variable Proportions.

Concept

RELATIONSHIP BETWEEN SHORT RUN COST CURVES

As discussed earlier, there exists a close relationship between the various types of costs. Let us understand the relationship between the following costs:

1. Average Cost (AC) and Marginal Cost (MC)

2. Average Variable Cost (AVC) and Marginal Cost (MC)

3. Average Cost (AC) and Average Variable Cost (AVC) and Marginal Cost (MC)

4. Average Cost (AC) and Average Variable Cost (AVC)

5. Total Cost (TC) and Marginal Cost (MC) 6. Total Variable Cost (TVC) and Marginal Cost (MC)

Concept

Relationship between AC and MC

There exists a close relationship between AC and MC.

Both AC and MC are derived from total cost (TC). AC refers to TC per unit of output and MC refers to addition to TC when one more unit of output is produced.
Both AC and MC curves are U-shaped due to the Law of Variable Proportions.

The relationship between them can be better illustrated through following schedule and diagram.

Table 6.8: Relationship between AC and MC

With the help of Table 6.8 and Fig. 6.9, the relationship can be summarized as under:

When MC is less than AC, AC falls with increase in the output, i.e. till 3 units of output.
When MC is equal to AC, i.e. when MC and AC curves intersect each other at point A, AC is constant and at its minimum point.
When MC is more than AC, AC rises with increase in output, i.e. from 5 units of output.
Thereafter, both AC and MC rise, but MC increases at a faster rate as compared to AC. As a result, MC curve is steeper as compared to AC curve.

AC depends on the nature of MC

When MC curve lies below the AC curve, it pulls the latter downward
When MC curve lies above AC curve, it pulls the latter upwards
Consequently, MC and AC are equal where MC intersects AC curve

Can AC Fall, when MC is rising?

Yes AC can fall when MC is rising. How ever it is only possible when MC is less then AC. It means that as long as MC curve is below the AC curve , AC will fall even if MC is rising. As per table 6.8, when we move from 2 units to 3 units, MC Rises and AC Falls. It happens because during this range, MC is less than AC.

Can AC rise, when MC is falling?

No AC cannot se, when MC is falling because when MC falls, AC will also fall

Concept

Relationship between AVC and MC

The relationship between AVC and MC curves is similar to that of AC and MC. Both AVC and MC are derived from total variable cost (TVC). AVC refers to TVC per unit of output and MC is the addition to TVC, when one more unit of output is produced.

Both AVC and MC curves are U-shaped due to the Law of Variable Proportions. The relationship between AVC and MC can be better illustrated with the help of following schedule and diagram.

Table 6.9: Relationship between AVC and MC

When MC is less than AVC, AVC falls with increase in the output, i.e. till 2 units of output.
When MC is equal to AVC, i.e. when MC and AVC curves intersect each other at point B, AVC is constant and at its minimum point (at 3rd unit of output).
When MC is more than AVC, AVC rises with increase in output, i.e. from 4 units of output.
Thereafter, both AVC and MC rise, but MC increases at a faster rate as compared to AVC. As a result, MC curve is steeper as compared to AVC curve.

Concept

Relationship between AC, AVC and MC

The relationship between AC, AVC and MC can be better illustrated with the help of following schedule and diagram.

Table 6.10: Relationship between AC, AVC and MC

When MC is less than AC and AVC, both of them fall with increase in the output.
When MC becomes equal to AC and AVC, they become constant. MC curve cuts AC curve (at 'A') and AVC curve (at 'B') at their minimum points.
When MC is more than AC and AVC, both rise with increase in output.

Concept

Relationship between AC and AVC

The relationship between AC and AVC can be discussed with the help of Fig. 6.11. 1. AC is greater than AVC by the amount of AFC.

The vertical distance between AC and AVC curves continues to fall with increase in output because the gap between them is AFC, which continues to decline with rise in output.
AC and AVC curves never intersect each other as AFC can never be zero.

Both AC and AVC curves are U-shaped due to the Law of Variable Proportions.
MC curve cuts AVC and AC curves at their minimum points.
The minimum point of AC curve (point A) lie always to the right of the minimum point of AVC curve (point B).

Concept

Relationship between TC and MC

The main points of relationship between TC and MC are:

Marginal cost is the addition to total cost, when one more unit of output is produced. MC is calculated as: MC_n = TC_n - TC_n-1
_{When TC rises at a diminishing rate, MC declines.}
When the rate of increase in TC stops diminishing, MC is at its minimum point, i.e. point E in Fig. 6.1
When the rate of increase in total cost starts rising, the marginal cost is increasing.

Concept

Relationship between TVC and MC

We know, MC is addition to TVC when one more unit of output is produced. So, TVC can be obtained as summation of MC's of all the units produced. If output is assumed to be perfectly divisible, then total area under the MC curve will be equal to TVC.

As seen in the diagram, at OQ level of output, TVC is equal to the shaded area OPLQ in the diagram.

Solved Practical’s

Example 1. Calculate Total Fixed Cost (TFC) and Total Variable Cost (TVC).

Note : TFC = TC at 0 level of output.

Example 2. The total cost curve makes an intercept of ₹50 on the Y-axis. Calculate total fixed cost and total variable cost.

Note : The intercept of ₹50 on the Y-axis indicates that total cost (TC) is equal to ₹50 at zero output. It means, TFC = ₹50 as TC = TFC at zero output.

Example 3. The details about total variable cost (TVC) of a firm is given. It is also given that the vertical distance between TVC curve and total cost (TC) curve is fixed at ₹60 at all levels of output. On the basis of this data, calculate TC.