Cost of production

Meaning of cost

Cost means whatever is sacrificed to obtain or produce something. In economics cost may be in monetary form like

salaries to employees as well as in non-monetary form like real costs. Therefore, in economics the term cost is used in a

wider sense while in financial accounting it is used in a narrower sense.

Opportunity costs / Economic costs / Alternative costs

Opportunity cost means the value of the next best opportunity missed or given up to adopt another opportunity. For

example: Rick has ` 10,000 to invest either in fixed deposit of a bank yielding 10% interest or in debentures of a company

yielding 12% interest. He decides to invest in the debentures, then the opportunity cost of this investment is the interest on

the fixed deposit forgone i.e. 10% of ` 10,000 = ` 1000.

Explicit costs

These are the monetary payments made to outsiders for supplying raw materials, labour services, electricity,

transportation facility etc. Salaries to employees, electricity bills, telephone bills, material purchase etc. are examples of

explicit costs.

Implicit costs

These are the monetary payments that self-owned could have earned if its alternative use was exercised. In fact they are

opportunity costs.

Social costs

These are the costs which are borne by a society as a whole. In fact, social costs are negative side effects arisen due to

production of a good. For example: Factories emit smoke in the environment causing Air pollution, discharge their waste

materials into rivers causing water pollution. Air pollution, water pollution affects the health of people negatively and

therefore they are social costs.

Real costs

Real costs mean the pain and the discomforts felt, the sacrifices made by labour or entrepreneur while doing production or

business. These costs are subjective costs i.e. they cannot be measured in money terms.

Fixed costs

These are those costs which remain fixed irrespective the output level. In other words, those costs which do not change

with the output level, then they are known as fixed costs. Rent of factory, insurance premium etc. are some examples

fixed costs because they are fixed and whether output is zero or more, nevertheless they have to be paid. The fixed cost

curve is a straight line parallel to the X-axis as shown in the figure.

0 Output

FC

0 Output

FC

VC

Variable costs

These are those costs which change as the output level changes. If output is zero, then there is no variable cost. Raw

material cost, labour cost, motive power etc. are variable costs because they increase as the output increases. In economics

there is a special pattern of variable costs i.e. initially they are assumed to be increasing at decreasing rate then at

moderate rate and finally at increasing rate. This pattern makes variable costs curve like inverted S.

Total cost

Total cost means the addition of total fixed costs (TFC) and total variable costs (TVC). Therefore, total cost can be

defined as follows:

TC=FC+VC

In economics there is a special pattern of total cost i.e. initially this is assumed to be increasing at decreasing rate then at

moderate rate and finally at increasing rate. This pattern makes the total cost curve like inverted English letter S. One

point must be noted here that the TC curve starts from where the FC curve starts.

VC

0 Output

FC

TC = TFC +TVC

0 Output

MC

TC/TVC/FC

Marginal Cost (MC)

When output is increased from one level to another level, then the total cost changes and this change in the total cost is

termed as marginal cost. Mathematically, marginal cost is defined as the ratio of change in total cost ant change in output.

MC=∆ TC∆Q

Using calculus we can define the marginal cost as follows:

Suppose that C = f (Q) is a total cost function, then

MC= ddQ

(TC ) ……………….(1)

Since

TC=TVC+TFC

Therefore

MC= ddQ

(TVC +TFC )= ddQ

(TVC ) ……………….(2)

Equation (1) states that the marginal cost is the derivative of the cost function with respect to the output and equation (2)

states that the marginal cost is the derivative of the total variable cost function with respect to the output. Thus, the

marginal cost can be calculated using either the total cost or the total variable cost. Apart, since the derivative of a

function gives its slope, therefore marginal cost can also be defined as the slope of the TC curve or the TVC curve.

In economics the MC curve looks like English letter “U” as shown in the figure.

TVC

MC

MPL MCFirst stageFirst stage

Second stageSecond stage

Labour Output

0 Output

AFC

Reason of the U-shaped: The MC curve is U shaped because of the law of variable proportion. In fact marginal cost is

also defined as the ratio of labour wage rate “w” and the marginal production of labour MPL. Therefore,

MC= wMPL

Now we know that the law of variable proportion states that the MPL increases in the first stage and decreases in the

second stage. Therefore, mathematically in the first stage when the MPL increases, then the above ratio of w and MPL i.e.

MC must decrease and in the second stage when the MPL decreases, then the above ratio must increase. In this way, in the

first stage the MC curve falls and in the second stage the MC curve increases causing it U shaped. This is all shown in the

following diagram.

Average Fixed Cost (AFC)

AFC is defined as the ratio of total fixed cost and total output. Therefore,

AFC= FCQ

AFC curve is downward sloping and never touches the X-axis because fixed cost is not zero. In this way the AFC curve is

a rectangular hyperbola.

Average Variable Cost (AVC)

AVC is defined as the ratio of total variable cost (TVC) and total output (Q). Therefore,

AFC

0 Output

AC

APL

APL

AVCFirst stageFirst stage

Second stageSecond stage

Labour Output

AVC

AVC=VCQ

Reason of the U-shaped: The AVC curve is U shaped because of the law of variable proportion. In fact AVC is also

defined as the ratio of labour wage rate “w” and the average production of labour APL. Therefore,

AVC= wAP L

Now we know that the law of variable proportion states that the APL increases in the first stage and decreases in the

second stage. Therefore, mathematically in the first stage when the APL increases, then the above ratio of w and APL i.e.

AVC must decrease and in the second stage when the APL decreases, then the above ratio must increase. In this way, in

the first stage the AC curve falls and in the second stage the AVC curve increases causing it U-shaped. This is all shown

in the following diagram.

Average cost

Average cost is defined as the ratio of total cost and total output. Symbolically,

AC=TCQ

Average cost is also defined as the sum total of average fixed costs and average variable costs. Therefore,

AC=AFC+ AVC

In economics the AC curve looks like English letter “U” as shown in the figure.

AC

E

ACMC

AC/MC

0 Output

Reason of the U-shaped: The AC curve is U shaped because of the law of variable proportion. In fact AC is also defined

as the ratio of labour wage rate “w” and the average production of labour APL plus AFC. Therefore,

AC=AFC+ wAP L

Now we know that the law of variable proportion states that the APL increases in the first stage and decreases in the

second stage. Therefore, mathematically in the first stage when the APL increases, then the ratio of w and APL i.e. AVC

must decrease and in the second stage when the APL decreases, then the ratio must increase. In this way AVC gets U-

shaped. Further we also know that AFC curve is downward sloping and reaches to zero and therefore adding AFC to AVC

creates the same shape as that of AVC. In this way, in the first stage the AC curve falls and in the second stage the AVC

curve increases causing it U-shaped. This is all shown in the following diagram.

Relationship between MC and AC

There are three relationships between MC and AC

1. When MC < AC, then AC falls.

2. When MC = AC, then AC is minimum is at point E.

3. When MC > AC, then AC rises.

Logic / Rationale / Reason / Cause of the above relationships

Suppose that you have three subjects Mathematics, Economics and Accountancy in which your grades are 10, 15 and 20

respectively, then the average grade should be

10+15+203

=453

=15

Now suppose that your are given the fourth subject Statistics in which your grade is 7, then the new average should be

10+15+20+74

=524

=13

Now if your grade in the fourth subject were 18, then the new average should be

10+15+20+254

=704

=17.5

It is obvious that, when the grade in the fourth subject i.e. 7 is less than the initial average grade i.e.15, then the new

average is falls to 13 and when the grade in the fourth subject i.e.18, is greater than the initial average grade i.e.15, then

the new average increases to 17.5. This is the mathematics of average and additional (or marginal) grades which is

exactly the same as the mathematics of average cost and marginal cost. Thus when the marginal cost remains less than

the old average cost, then the new average cost falls and when the marginal cost remains more than the old average cost,

then the new average cost increases.

For the lovers of Mathematics (OPTIONAL)

Mathematical Proof of the above relationships

Suppose that TC = f (Q) is a cost function in which TC is the total cost and Q is the output. We know that the average cost

is defined as:

AC=TCQ

Differentiating AC with respect to Q we get

ddx

( AC )= ddx (TC

Q )Applying the quotient rule in the right hand side of the equation

ddx

( AC )= 1

Q2 (Qd

dQTC−TC

ddQ

Q)We know that

Marginal cost=MC= ddx

TC

Therefore

ddx

( AC )= 1

Q2(Q × MC−TC )

ddx

( AC )= Q

Q2 (MC−TCQ )

ddx

( AC )= 1Q

( MC−AC )

Now we are able to derive the following conclusions from the last equation:

1. When MC <AC, then the slope of the AC is negative i.e. the AC curve must be decreasing.

2. When MC = AC, then the slope of the AC is zero.

3. When MC >AC, then the slope of the AC is positive i.e. the AC curve must be increasing

E

AVCMC

AC/MC

0 Output

Relationship between MC and AVC

There are three relationships between MC and AVC

1. When MC < AVC, then AVC falls.

2. When MC = AVC, then AVC is minimum at point E.

3. When MC > AVC, then AVC rises.

Logic / Rationale / Reason / Cause of the above relationships

Suppose that you have three subjects Mathematics, Economics and Accountancy in which your grades are 10, 15 and 20

respectively, then the average grade should be

10+15+203

=453

=15

Now suppose that your are given the fourth subject Statistics in which your grade is 7, then the new average should be

10+15+20+74

=524

=13

Now if your grade in the fourth subject were 18, then the new average should be

10+15+20+254

=704

=17.5

It is obvious that, when the grade in the fourth subject i.e. 7 is less than the initial average grade i.e.15, then the new

average is falls to 13 and when the grade in the fourth subject i.e.18, is greater than the initial average grade i.e.15, then

the new average increases to 17.5. This is the mathematics of average and additional (or marginal) grades which is

exactly the same as the mathematics of average variable cost and marginal cost. Thus when the marginal cost remains

less than the old average variable cost, then the new average variable cost falls and when the marginal cost remains more

than the old average variable cost, then the new average cost increases.

For the lovers of Mathematics (OPTIONAL)

Mathematical Proof of the above relationships

Suppose that TVC = f (Q) is a variable cost function in which TVC is the total variable cost and q is the output. We know

that the average variable cost is defined as:

AVCMC

AC/MC

0 Output

AC

AVC=TVCQ

Differentiating AVC with respect to Q we get

ddx

( AVC )= ddx (TVC

Q )Applying the quotient rule in the right hand side of the equation

ddx

( AVC )= 1

Q2 (Qd

dQTVC−TVC

ddQ

Q)We know that

Marginal cost=MC= ddx

TVC

Therefore

ddx

( AVC )= 1

Q2(Q × MC−TVC )

ddx

( AVC )= 1Q (MC−TVC

Q )

ddx

( AVC )= 1Q

( MC−AVC )

Now we are able to derive the following conclusions from the last equation:

1. When MC <AVC, then the slope of the AVC is negative i.e. the AVC curve must be decreasing.

2. When MC = AVC, then the slope of the AVC is zero.

3. When MC >AVC, then the slope of the AVC is positive i.e. the AVC curve must be increasing

AC, AVC and MC together

Long run cost

Long run average cost (LAC): Its derivation

Or

Relationship between the long run cost and the short run cost.

Suppose there are three plants x, y and z with the short run average cost curves SACx, SACy and SACZ respectively such

that x is a small plant, y is a medium plant and z is a large plant. Now if the producer wants to produce the output Q1, then

he has two options i.e. either produce at plant x or plant y. If plant y is selected, then the average cost is ACA

corresponding to point A on SACx and if plant y is selected, then the average cost is ACB corresponding to point B on

SACy. From the figure, this is obvious that ACA < ACB, therefore he should produce at plant x. In this way, he has point A

at which he minimizes his average cost. Similarly, if he wants to produce the output Q2, then plant y is better because the

average cost at plant x (i.e. ACD corresponding to point D on SACx) is greater than the average cost of plant y (i.e. ACC

corresponding to point C on SACY). In this way, he has point C at which he minimizes his average cost. Now, if the

producer wants to produce the output Q3, then plant z is better because the average cost of this plant (i.e. ACF

corresponding to point F on SACy) is greater than the average cost of plant z (i.e. ACE corresponding to point E on SACz).

In this way we can find others cost minimizing points on these plants. By joining these points we get a curve known as the

long run average cost curve. In the diagram, the crosshatched parts of the short run average cost curves constitute the

long run average cost curve. However, if there were “n” number of plants instead of just three, then the long run average

cost curve would have been the dark curve labeled as LAC. Since the long run average cost curve LAC envelops the

short run average cost curves, therefore the curve (LAC) is also known as the “envelope curve”. This curve is also

known as the “planning curve” because the producer is able to plan the plant to be used for a given amount of

production.

LACAC D

AC C

AC E

AC F F

E

D

C

B

A

AC B

AC A

0 Q1 Q2 Q3 Output

Average cost

SACz

SACy

SACx

Why is LAC downward sloping? Or

Explanation of the downward portion of LAC

LAC is downward sloping up to a certain point of output because of the economies of scale. Economies of scale of mean

the benefits or reduction in cost due to operating at large scale. Economies of scale are classified into two categories.

These categories are:

1. Internal Economies :

These are those economies which accrue to the firm increasing the scale i.e. such economies are enjoyed by that

firm only which has increased its scale not by the industry as whole. Internal economies may include:

a. Managerial economies

In a large firm, the managers can concentrate on the important decisions i.e. strategic decisions etc. Routine

jobs or tasks can be allocated or delegated to the other persons who are qualified in their respective fields.

Thus, large scale production means better use of and greater specialization in management. But in a small

organization, a specialist may have to divide his or her time between several executive functions like

marketing, accounts, human resource etc. A larger scale of production means the sales expert can supervise

sales related work full time, while appropriate specialists perform other managerial functions. It results in

greater efficiency and lower per unit cost.

b. Specialization and division of labour

When the scale of production expands, then there is division of labour i.e. the entire work is divided into

various tasks among the specialists. As a result, a worker does only that task in which he or she is specialized.

It results in the productivity of labour and reduces time.

c. Technical economies

Large firms are able to afford the latest, sophisticated, automatic machines and technology of production

which small firms can not afford. Although the fixed costs in such machines and technology increase, yet

average cost lowers because the total cost is allocated over a large amount of output.

d. Marketing economies

When the production of a firm expands, then it needs raw material in more quantity than before. As a result,

big orders of raw materials are placed with the suppliers who are ready to give quantity discounts. These

quantity discounts reduce the cost of material. Apart, big quantity of raw materials cause the transport cost to

decline because the carriers operators are generally ready to facilitate the transport at lower rates. Reducing

costs make the firm able to reduce its selling price

e. Credit economies / Finance economies

Large firms need huge money for their fixed capital requirement and working capital requirement. Such firms

can issue debentures at large scale, therefore can secure finance from banks at lower interest rates which is

very difficult in case of small firms. It reduces the cost of finance.

f. Inventory economies

A large firm is able to maintain safety stock in large quantity and therefore when there is a shortage in the

supply of raw material and the raw material is sold by the suppliers at very high prices, nevertheless the

production does not stop. The firm is able to produce at lower cost than the small producers who are not able

to maintain safety stock in a large quantity.

2. External Economies

According to Cairn Cross, “External economies are those which are shared in by a number of firms or industries

when the scale of production in any industry of group of industries increases.” The main types of external

economies are as follows:

a. Economies of concentration of an industry

When various firms belonging to a particular industry club at a particular place, then this is known as the

localization of industry or concentration of an industry. Such localization of an industry may be due to the

easiness in availability of the raw materials or other inputs, better government laws or facilities, transport

system etc. For example: Bollywood in Mumbai, tea industry in Assam, jute industry in Bengal etc.

Localization of an industry results in certain advantages accruing to the firms externally.

b. Economies of information

When an industry expands, then the availability of necessary, useful and qualitative information is available

easily. Firms may agree to spend money on research and development on collective basis. Scientific journals,

trade journals, Universities researches etc. make the industry available qualitative and useful information and

such information may be relating to better production processes or methods, disadvantages of existing

methods, new laws, marketing etc. causing the fall in the cost or increase in the output.

c. Economies of disintegration or comparative advantage

When an industry expands, then the firms belonging to it may follow the concept of comparative advantage.

A firm is said to have comparative advantage over the other firm if its opportunity cost of doing something is

less than the opportunity cost of doing the same by the other firm. The firms in an industry may agree to avail

the benefit of specialization in a particular product relating to the industry.

Why is LAC upward sloping? Or

Explanation of the upward portion of LAC

Diseconomies of scale are responsible for the upward portion of the long run average cost curve. Diseconomies of scale

mean the disadvantages of large scale. Diseconomies are of two types:

Internal Diseconomies

External Diseconomies