COST ANALYSIS
o OBJECTIVES
o INTRODUCTION
o MEANING
o DEFINITIONS
o TYPES OF COSTS
 MONETARY COSTS
 REAL COSTS
 OPPORTUNITY COSTS
 ECONOMIC COSTS
 ACCOUNTING COSTS
 INCREMENTAL COSTS
 SUNK COSTS
 FUTURE COSTS
 PRIVATE, EXTERNAL AND SOCIAL COSTS
 FIXED / SUPPLEMENTARY / OVERHEAD COSTS
 VARIABLE / PRIME COSTS
 REPLACEMENT COSTS
 PRODUCTION COSTS
 SELLING COSTS
 CONTROLLABLE COSTS
 DIRECT COSTS
 INDIRECT COSTS
o SHORT RUN COSTS CURVES
o LONG RUN COSTS CURVES
OBJECTIVES
o To understand the meaning of cost.
o To discuss different types of costs.
o To describe in detail the short run and long run costs.
o To understand the importance of cost in managerial
decision-making.
INTRODUCTION
To decide about the quality and quantity of a product depends upon the cost of the cost of
the product. In producing a product / service a firm has in incur various costs in form of
wages, interest and price of raw – material etc. Hence, from a firm point of view, to
estimate correct cost is important for decision-making. An incorrect estimation or a
misunderstanding of the costs may have a negative effect on the profit and growth of an
organization.
MEANING OF COST
In simple words the payments rent, wage, interest and profit which are made to factors of
production (land, labour, capital and entrepreneur) for their services. It means cost
includes the value of the factors of production employed. The term costs mean sacrifice
(interms of money or comforts) which are made to produce goods and services.
Cost function depends on various factors such as output, technology and price of input,
productivity of inputs.
C
=
f (Q, T, PI, ProI, S)
C = Cost, O = Output, PI = Price of Input, S = Size of Plant, T = Technology, Pro I =
Productivity of Input
The most important determinant of cost is output. Generally cost of production increases
with the increase in Output. Technology also has effect on the cost of production. If
technology is modern, then cost of production will low and vice-versa. Due to rise in the
price of input, the cost of production will also rise productivity of input also determines
the cost. If productivity of input is high then cost of production will low and vice-versa.
Size of plant – As the size of plant increases, costs of production decreases and viceversa.
DEFINITION
TYPES OF COSTS
1.
Money Cost : Money cost is that cost, in which cost is incurred in terms of
money. In simple words, money cost refers to the amount of money which is
incurred to produce a good or services. For example – to produce 10 shirts, a
producer has to pay Rs.1,000. Hence the money cost is Rs.1000 to produce 10
shirts. Rent, wages, interest, depreciation, packing charges, transport cost,
normal profits cost of raw material, selling costs are included in money costs.
J. L. Hanson, “The money cost of producing a certain output of a commodity
is the sum of all the payments to the factors of production engaged in the
production of that commodity.”
Money cost is of two types –
a) Explicit Costs : Explicit costs are those costs, which are paid to the others
for their services and goods. According to Leftwitch, Explicit costs are
those cash payments which firms make to outsiders for their services and
goods.” These costs are also known as out of packets costs or accounting
costs. Explicit costs includes, following items of a firm’s expenditure i. Cost of raw material
ii. Transportation cost
iii. Packing cost
iv. Power changes
v. Taxes
vi. Rent
vii. Wages
viii. Interest
b) Implicit Costs : Implicit costs are those costs, which are paid by an
entrepreneur to his own resources or factors of production (own land, own
labour, own capital and own building etc.). Implicit costs are costs of self
– owned and self-employed resources.” Implicit cost does not involve a
physical cash payment, because it uses the factors which a firm does not
buy or hire but already owns. Implicitly money costs are as follows : i.
Wages of his own labour
ii.
Rent of his own land
iii.
Interest on his own capital
iv.
Profits for his own entrepreneurial functions.
Total Money Cost = Explicit Costs + Implicit Costs
2.
Real Costs : Real Costs are non quantifiable in money terms. These costs are
psychological in nature.
Real costs refers to the payments which are paid to factors of production for
their efforts, rain, discomforts, execution and sacrifice, in producing the
different products. According to Marshall, “The production of a commodity
generally requires many different kinds of labour and the use of capital in
many forms. The exertions of all the different kinds of labour that are directly
or indirectly involves in making it together with the abstinences or rather the
waiting required for saving the capital used in making it – all these efforts and
sacrifices together will be called the real cost of production of commodity.”
Real costs involves –

Compensation package given to employees for the troubles in producing a
product.

3.
Compensation for sound effects of pollution caused by factory smoke.
Opportunity Costs : Opportunity cost is also known as alternative cost. The
concept of opportunity cost was introduced by D.I. Green in 1894, but Prof.
Knight made it popular. Factors of production or resources, in an economy are
limited and have alternative uses. To produce a particular good the resources
has to be withdrawn / sacrificed from the production of other goods. The cost
of sacrifice or foregone for the next best use of resource is known as
opportunity cost. Ferguson, “The opportunity cost of producing one unit of
‘X’-commodity is the amount of ‘Y’-commodity that must be sacrificed.”
Leftwitch -, “Opportunity Cost of a particular product is the value of foregone
alternative products that resources used in its production, could have
produced.”
For example, in an economy two goods X and Y are produced. The quantity
of X good is OX and Y
good is OY. If the quantity
Y
Figure -
increase from OY to YY’,
then the quantity of X
commodity has increased
Y-Commodity
of Y commodity has to
Y1
Y
from OX to OX’.
O
1
4.
Economic
Costs:
X
X
X
X-Commodity
Economic costs includes the payments such as rent, wages, interest and profit,
which are paid to factors of production – land, labour, capital and entrepreneur
for their services. Hence, economic costs include normal profits which are
paid to an entrepreneur for his managerial and entrepreneurial skills. It means
economic costs refer to the payment costs which are paid to factors of
production. (outside resources) for their services as well as payments for
owned factors. In simple words, economic costs include explicit and implicit
costs.
Economic Costs =
Explicit Costs + Implicit Costs
Or
Economic Costs =
Accounting Costs + Implicit Costs
5.
Accounting Costs: - An accountant’s view is differed from an economists
view on cost. Accounting costs refer to only cash payments which are made to
factors of production for their services. Hence, an accountant will include only
explicit costs. It means accounting costs include rent, wage and interest but
not the profits.
Accounting Costs = Explicit Costs
Or
Accounting Costs = Rent + Wage + Interest
6.
Incremental Costs: - Incremental costs refer to the additional cost that a firm
has to incur as a result of implementing a major managerial decision.
Examples of incremental costs are purchasing new company, hiring new staff.
7.
Sunk Costs: - Sunck costs are the historical costs which are made in past.
These costs are irrelevant while making decisions.
8.
Future Costs: Future costs are also known as planned or budgeted costs.
These costs are incurred in the future for making financial, managerial,
business decisions.
9.
Private, External and Social Costs: - Private costs are the costs which are
incurred by a firm for the production of a commodity. Whereas social costs
are the costs which are incurred by the society as a whole. The cost which is
incurred by others in society is known as external cost.
Social Cost = Private Cost + External Cost
10.
Fixed Cost / Supplementary / Overhead Costs:– Fixed / Supplementary/
Overhead costs are those costs which do not change with the change in level
of output. It means if the output of firm is zero, even than a producer has to
pay it and this cost remain fixed with the increase in the level of output.
Examples payments of rent for a building, insurance premium, interest on
capita etc.
11.
Output
Fixed Cost
0
10
1
10
2
10
3
10
4
10
5
10
Variable / Prime Costs: - Variable / Prime costs are the costs which change
with the change in level of output when output is zero, the variable cost also
zero. It will increase with the increase in level of output. Examples are
expenses on raw material, electricity changes, telephone charges.
Output
Fixed Cost
0
0
1
5
12.
2
12
3
14
4
15
5
20
Replacement Costs: - Replacement cost is also known as depreciation cost.
With the continue utilization of fixed assets such as tools, equipments and
machinery, they depreciated. Hence, there is need to replace these assets. The
cost at which these assets are replaced is known as replacement cost.
13.
Production Costs: - Production costs are the costs which are incurred to
increase the level of output of a firm. The payments which are made to factors
of production are known as product costs.
14.
Selling Costs: - Selling costs are incurred t increase the sale of available
products. Examples are commission paid to salesman, advertisement of
different products.
15.
Controllable Costs: - Controllable Costs are controlled by the management
of a firm. For example cost of quality control, fringes benefits to employees.
16.
Uncontrollable Costs: - These types of costs are beyond the control of the
management of a firm. For example – price of raw material.
17.
Direct Costs: - Direct costs refers to those costs which can be attributed to
any particular activity.
18.
Indirect Costs: - These types of costs can not be attributed to a particular
activity.
Figure 10.1
Costs According to Time Period
Short Run Cost Curve
Total Cost
(TC)
Total
Fixed
Costs
(TFC)
Total
Variable
Costs
(TVC)
Average
Cost
(AC)
Average
Fixed
Costs
(AFC)
Long Run Cost Curve
Marginal
Cost
(MC)
Average
Variable
Costs
(AVC)
Long Run
Total Costs
(LTC)
[TC =TFC+TVC]
Long Run
Average
Costs (LAC)
Long Run
Marginal
Costs (LMC)
[AC = AFC+AVC]
MC = TCn – TCn-1
Or
MC = ΔTC
ΔQ
According to ‘Time Period’ Cost is of two types : a)
Short Run Cost
b)
Long Run Cost
a) Short Run Cost : In short run, some factors remain fixed and other are variable. In
short run, costs are of three types: i) Total Costs
ii) Average Costs
iii) Marginal Costs
i)
Total Costs : - Total cost is the aggregate of money, which is spend by a firm
in the production of a commodity. For example, if a firm is spending Rs.1000
on the production of 500 units. Then total cost is Rs.1000. In other words total
cost is the sum of the fixed and variable cost.
TC
=
TFC + TVC
Or
TC
=
FC + VC
TC
=
Total Costs
TFC
=
Total Fixed Costs
TVC
=
Total Variable Costs
FC
=
Fixed Costs
VC
=
Variable Costs
Dooley, “Total cost of production is the sum of all production is the sum of all
expenditure incurred in producing a given volume of output.
Total costs are of two types: a)
Total Fixed or Supplementary Costs : - Total Fixed Cost is the cost of
fixed factors which are used to produce goods in short time period. Firm
spends on plant, fittings, equipments etc. even starting the production. It
means fixed costs do not change with the change in output.
If the production is zero, even than a firm has to pay fixed cost. As the
quantity of output increases, the fixed costs do not change. Fixed Costs are
also known as, supplementary cost, indirect costs overall costs or plant
costs.
1. Anatol Murod, “Fixed costs are cost which do not change with
changes in the quantity of output.”
2. Benham, “The fixed costs are those costs that do not vary with the size
of its output.
Rent, depreciation, normal profit, license fee, insurance premium are the
expenses included in fixed costs.
indicates
2
fixed
costs
remain
fixed
whatever
the
level of output.
Fixed cost is
parallel to OX
1210-
6-
that fixed cost
4-
remain
2-
same
either output is
zero or 10. It
costs
F
C
8-
axis. It reveals
means
Figure -2
Fixed Costs
Y
that
Fixed Costs (Rs.)
Figure
O
|
1
|
2
|
3
|
4
fixed
|
5
|
6
|
7
|
8
|
9
|
10
X
Output
remain
same irrespective of the volume of output.
b)
Total Variable or Prime or Special Costs : - Total variable or prime or
special costs refer to those costs which change with the change in volume
of level of production.
Dooley, “Variable costs is one which varies as the level of output varies.”
If output increases, variable costs also increase and as the output
decreases, Costs also decrease. When output zero, these costs are also
zero. The short run variable costs are – Prices of raw material, wages of
temporary labour, excise duties and sales tax, wear and tear expenses,
transport costs etc.
Table 2, shows that costs increase with the increase in level of output, When
output is zero, total variable costs are also zero. When Output is 1 unit, cost is
Rs.12 and when it reaches 10 units the variable costs are Rs.74.
Table 10.2
Total Variable Costs
Figure
3,
Output
Total Variable
0
0
1
12
2
20
3
26
4
30
5
32
6
32
7
40
8
48
9
58
10
70
shows
that the shape of
Y
100-
total variable costs
cost
is
determined by the
Law of Returns.
Initially
factors
employed
variable
when
80-
Total Variable Costs
variable
70D.R.
6050-
C.R.
4030-
are
20-
then
10O
factor
VC
90-
is inverse S shape.
The shape of total
Figure -3
Total Variable Costs
I.R.
|
|
|
|
|
|
|
|
|
|
1
2
3
4
5
6
7
8
9
10
Output
X
brings in more than proportionate returns, hence cost increases at diminishing
rate. At the point of optimum capacity, the returns of variable factors remain
constant, hence cost is also constant. At last, after optimum point every additional
unit of variable factor yields only less than proportionate return, hence cost
increase. Variable cost curve is sloping upwards at diminishing, constant and
increasing rate.
IR
=
Increasing Returns
CR
=
Constant Returns
DR
=
Decreasing Returns
Relationship between Total, Fixed and Variable Cost
In short time period, total costs is the aggregate of total fixed costs and total variable
costs.
1)
TC
=
TFC + TVC
OR
TC
=
FC + VC
2)
VC
=
TC – FC
3)
FC
=
TC – VC
TC
=
Total Costs
VC
=
Variable Costs
FC
=
Fixed Costs
TFC
=
Total Fixed Costs
TVC
=
Total Variable Costs
Table 10.3
Total Costs
Output
Fixed Costs
Variable Costs
Total Costs
(Rs.)
(Rs.)
(Rs.)
0
10
0
10
1
10
12
22
2
10
20
30
3
10
26
36
4
10
30
40
5
10
32
42
6
10
34
44
7
10
40
50
8
10
48
58
9
10
58
68
10
10
72
82
Table 3, shows that when output is zero, fixed cost is rs.10 and variable cost is Rs.
Zero, while total cost is [FC(10+VC(0) = Rs. 10]. It reveals that total costs are the
sum of fixed and variable costs. When output increases to 8 units total costs go up
Rs. 58 (Rs.10+Rs.48).
Figure 4 shows the relationship between total costs, fixed costs and variable costs.
Total costs are the
sum total of fixed
and variable costs.
6050-
hence total costs is
40-
also
Total
30-
Cost and variable
20-
cost
10O
Rs.10.
parallel
other.
2)
Rs.10,
70-
Costs
cost
curves
to
are
each
VC
80-
zero and variable
fixed
TC
90-
At point O, output is
cost is also zero but
Figure - 4
Total Costs
Y
100-
FC
|
|
|
|
|
|
|
|
|
|
1
2
3
4
5
6
7
8
9
10
Output
Average Costs : - Average cost is the per unit cost of a commodity.
Dolley, “The average cost of production is the total cost per unit of output.”
Ferguson -, “Average cost is total cost divided by output.”
X
Hence AC can be calculated as following
AC
=
AC
=
TC
Q
Average Cost
TC
=
Total Cost
Q
=
Quantity
The other method to calculate average cost is
AC
=
AFC + AVC
AC
=
Average Cost
AFC
=
Average Fixed Cost
AVC =
Average Variable Cost
AFC
=
AC – AVC
AVC =
AC – AFC
Table 10.4
Average Cost
Output
Total Cost
Average Cost
(Rs.)
(Rs.)
0
10
∞
1
22
22
2
30
15
3
36
12
4
40
10
5
42
8.4
6
44
7.3
7
50
7.1
8
58
7.2
9
68
7.5
10
82
8.2
Table 10.4 depicts that average cost can be calculated by dividing total costs with
output. In the beginning average cost is high and then it diminishing. At unit 7,
AC is minimum, after this point as the level of output increases, AC also
increasing.
Figure 5, shows the
90-
shape of AC is ‘u’
In
beginning,
level
of
80-
the
as
the
output
70-
Costs
shaped.
Figure - 5
Average Cost
Y
100-
60-
AC
50-
increases,
AC
40-
diminishes
and
30-
reach at ‘M’ point
20-
which
10O
shows
minimum cost. After
M
|
|
|
|
|
|
|
|
|
|
1
2
3
4
5
6
7
8
9
10
point ‘M’ average
X
Output
cost again rises.
a) Average Fixed Cost : - Average Fixed Cost, can be calculated by dividing total
fixed cost with the level of output. As the level of output increases, the average
fixed cost decreases.
AFC =
AFC
=
TFC
Q
Average Fixed Cost
TFC
=
Total Fixed Cost
Q
=
Quantity
Table 10.5
Average Fixed Costs
Output
Total Fixed Cost
Average Fixed Cost
(Rs.)
(Rs.)
0
10
∞
1
10
10
2
10
5
3
10
3.3
4
10
2.5
5
10
2
6
10
1.7
7
10
1.4
8
10
1.2
9
10
1.1
10
10
1
Table 5 conveys that as level of output is increasing the Average Fixed Cost
diminishing.
Figure 6, shows that
the slope of average
fixed cost is downward
90-
sloping, it means as the
80-
level
output
70-
increases the average
60-
fixed costs diminish.
50-
Average
Cost
40-
curve is a rectangular
30-
of
Fixed
hyperbola, because the
total area under the
curve
at
different
Figure - 6
Average Fixed Costs
Y
100-
2010O
AFC
|
|
|
|
|
|
|
|
|
|
1
2
3
4
5
6
7
8
9
10
points will be the same.
X
Quantity
b) Average Variable Costs : - Average Variable Cost is the per unit cost of the
variable factors of production. It can be calculated dividing total variable cost by
output.
AVC =
AVC =
TVC
Q
Average Variable Cost
TVC
=
Total Variable Cost
Q
=
Output
Table 10.6
Average Variable Costs
Output
Total Fixed Cost
Average Fixed Cost
(Rs.)
(Rs.)
0
0
0
1
12
12
2
20
10
3
26
8.6
4
30
7.5
5
32
6.4
6
34
5.6
7
40
5.7
8
48
6
9
58
6.4
10
72
7.2
Table 6, conveys that if
output is zero, total
variable cost is also
zero,
hence
average
8070-
Upto 6 units of output,
60-
average variable cost is
50-
falling, but it begins to
40-
increase
the
30-
seventh units. This is
20-
happened because of
10O
implication of law of
variable proportion.
AVC
90-
variable cost is also.
from
Figure - 7
Average Variable Costs
Y
100-
|
|
|
|
|
|
|
|
|
|
1
2
3
4
5
6
7
8
9
10
Quantity
X
In Figure 7, Output is shown on OX-axis and costs is shown on OY axis. The
shape of AVC is ‘U’ shaped.
It shows that upto 6 units of output, AVC is falling because as the output is
increasing, AVC is diminishing. From 7 units onward, AVC begins to increase,
which implies that AVC is increasing with increase in output.
Relation between AC, AFC and AVC : AC is the aggregate of AFC and AVC.
AC
=
AFC + AVC
AC
=
TC/Q
AFC
=
TFC/Q
AVC
=
TVC/Q
AFC
=
AC – AVC
AVC
=
AC - AFC
Table 10.7
Relation between AC, AFC & AVC
Output
AFC (Rs.)
AVC (Rs.)
AC = AFC+AVC
(Rs.)
0
∞
0
∞
1
10
12
22
2
5
10
15
3
3.3
8.6
12
4
2.5
7.5
10
5
2
6.4
8.4
6
1.7
5.6
7.3
7
1.4
5.7
7.1
8
1.2
6
7.2
9
1.1
6.4
7.5
10
1
7.2
8.2
Table 7 shows that at zero output AFC is ∞ and AVC is zero, hence AC is equal
to ∞. Then at 7 units AFC is Rs.1.4 and AVC is Rs.5.7, hence AC is Rs.7.1, here
AC is at minimum. After 7 units AC is increasing.
Figure 8 reveals
that

Y
AC
Figure - 8
Relation b/w AC, AFC & AVC
is
AC
obtained
AC
by adding
of
Costs
and
AVC.

A
AFC
B
AC curve
tends
F
to
AC
come
close
to
O
AVC but
it
Q
Q1
Quantity
never
touches the latter.

On point ‘A’ AC is falling. Hence a firms AC is minimum because it
making full use of its available resources and output is maximum, i.e.
OQ1. After A point there is only rise is cost but not in production. AVC
minimum point is ‘B’, when level of output is less i.e. OQ as compare to
OQ1.

The combination of AFC and AVC at point F gives U shape and exactly
above this point AC curve is showing in U shape. It reveals that AC is ‘U’
shaped but also is the combination of AFC and AVC.
Causes of AC is ‘U’ shaped.
AC is ‘U’ shaped like English alphabet ‘U’. It shows that initially average cost
falls with the rise in production, after then it reaches at its minimize point due to
X
maximum production and after this it begins to rise upward due to fall in
production.
There are following causes of ‘U’ shape of AC : i)
Basis of Internal Economies : - In short run when a firm increase its level
of production then due to indivisibles of fixed factors firm gets its internal
economies such as market economies, managerial economies, technical
economies etc. Hence with the increase in production level its cost per unit
fall.
ii)
Basis of Diseconomies : - In short run due to various diseconomies such
as poor division of labour, inefficient management, poor or updated
technology, unskilled labour with the rise level of production, cost per unit
increases.
iii)
Basis of Law of Variable Proportions : - Law of variable proportion is
applicable in short run in which only one factor i.e. labour is variable ad
all factors are fixed. Here are three stages of law of variable proportion –
(a) Law of Increasing Returns to Factors : – When this law is applicable
with the rise in level of production, the cost decreases.
(b) Law of Constant Returns to Factors : – It means at this point the
production is maximum due to optimum utilization of factors, hence cost
is minimum.
(c) Law of Decreasing Returns to Factors : - According to this law as
the number of variable factor increases, the production beings to diminish,
which means cost per unit of production increase. Hence these are the
causes of AC is ‘U’ shaped.
3) Marginal Cost :- Marginal Cost is an addition made to total cost by the
production of one more unit of output. In other words marginal cost is the change
in total cost with the one unit change in output. It measure the increase in total
cost as increase in one unit. It is also known as extra unit cost or incremental cost.
MC
=
∆TC
∆Q
MC
=
Marginal Cost
∆TC
=
Change in Total Cost
∆Q
=
Change in Output
OR
MC
=
TCn – TCn-1
MC
=
Marginal Cost
TCn
=
Total Cost of ‘n’ units
TCn-1 =
Total Cost of ‘n-1’ units
If the total cost of production of 7 units of a commodity is Rs.100. When 8 units
are produced, change in total cost is Rs.120. Thus the marginal cost is
i)
MC
=
TCn – TCn-1
MC
=
120 – 100
MC
=
Rs.20/-
Samuelson, “Marginal Cost at any output level is the extra cost producing
one extra unit more or less.”
ii)
Ferguson, “Marginal Cost is the addition to total cost due to the addition
of one unit of output.”
Table 10.8
Marginal Cost
Output
TC (Rs.)
MC (Rs.)
0
10
-
1
22
12
2
30
8
3
36
6
4
40
4
5
42
2
6
44
2
7
50
6
8
58
8
9
68
10
10
82
4
It is clear from table 8, that marginal cost initially falls with the rise in the level of
output. After then constant and ultimately rises with the rise in level of output.
Figure 9, reveals
that the shape of
is
‘U’
shaped.
In
starting
MC
falls
with
the
rise in level of
16-
12108-
‘M’
is
6-
and
4-
after ‘M’ point
2-
minimum
MC rises with
MC
14-
output. At point
MC
Figure -9
Marginal Cost
18-
Costs
MC
Y
20-
O
M
|
|
|
|
|
|
|
|
|
|
1
2
3
4
5
6
7
8
9
10
the rise in the
X
Output
level of output.
Relationship between Average Cost and Marginal Cost :i)
Both AC & MC are calculated from TC.
Both AC and MC are calculated from TC.
i)
Formula to calculate AC.
ii)
AC = TC
Q
Formula to calculate MC
MC = TCn – TCn-1
ii)
When AC falls MC also falls. Figure 10, shows that when AC falls MC
also fall more than AC. It means MC curve is below than AC.
iii)
When AC rises,
Y
MC also rises –
Figure 10
Relation between AC and MC
Figure 10 shows
that
after
M
AC
MC
Costs
point when AC
runs, MC also
rises more than
M
AC.
iv)
M
MC cuts AC at
its
1
minimum
point M from
O
Q1
below.
v)
X
Q
Quantity
Attraction
between AC and
MC – Figure 11
Y
Figure 11
Attraction between AC and MC
shows that
MC
When MC>AC
:- It pulls AC
upwards.

Costs

AC
MC
When MC =
AC :- Then Ac
MC
is constant.

When
MC
<
O
Output
AC:- Then MC
pushes AC downward.
Estimation of Cost Function
Cost function expresses the relationship between cost and output.
TC
=
f (Q)
TC
=
Total Cost
Q
=
Output
X
Costs function is of three types
i)
Linear Cost Function : - A linear cost function in short run is as
under:TC
=
a + bQ
a
=
is intercept (represent Total Fixed Cost)
bQ
=
slope coefficient (represent Total Variable Cost)

AFC
=

AVC =

ATC
=

MC
=
TFC
Q
TVC
Q
=
=
TC = a + bQ
Q
Q
∆TC = b
∆Q
a
b
bQ
Q
= b
= a+b
Q
Figure 12 shows linear relationship TC, AC & MC.
Figure 12
Linear Cost Function
Costs
Y
AC=MC
O
ii)
TC
Output
X
Quadratic Cost Function :- Quadratic Cost function is as
following : -
TC  a  BQ  CQ 2
a
AC   b  CQ
Q
MC  b  2CQ
Quadratic Cost function shows law of diminishing returns only.
Figure
13
Figure 13
Quadratic Cost Function
conveys that
Y
MC and AC
are
MC
AC
rising
but MC is
than
Costs
rising more
AC,
hence law of
diminishing
returns
is
applying.
X
Output
Cubic Cost Function : - Cubic Cost function is as following :TC  a  BQ  CQ 2  dQ 3
AC 
a
 b  CQ  dQ 2
Q
MC  b  2CQ  3dQ 2
Figure 14
Y
shows
Figure 14
Cubic Cost Function
Cubic
relations
MC
AC
hip
between
AC
&
Costs
iii)
O
M
MC. MC
cuts AC
from
below at
O
its
minimum points ‘M’.
Output
Q
X
Long Run Cost Curves : In short run except few factors of production, all factors of production consumed to be
constant. Whereas in long run all factors of production are changeable. In long run a firm
can increase its capacity, equipment, machinery, land, employee, etc. in order increase
output. Hence, there is no difference between fixed and variable costs. All costs are
variable costs.
Koutsoyiannis, “The long run is the period in which all factors are variable.
Figure 15
Long Run Costs Curve
Long Run
Total Cost
Long Run
Marginal
Costs
Long – Run Total Cost :- Long run total cost is always equal or less than to
short run total cost, but it is never more than long run total cost (LTC) i.e.
LTC≤ STC. In long run
when output is zero and
all costs being variable
Y
Figure 16 (A)
Long Run Total Costs
LTC
costs, hence, total cost
is also equal to zero.
Hence, it starts from
origin. Long run total
costs, is of three types:-
Costs
i)
Long Run
Average Cost
Figure 16(A), shows
that
LTC
Curve
is
based on an assumption
O
Output
X
that as output is increased cost in starting rises at diminishing rate and later at
increasing rate.
Figure 16(B) shows that increase in output, followed by increase in cost at
constant rate.
Y
Figure 16 (B)
Long Run Total Costs
Costs
LTC
O
X
Output
Figure 16(C) shows that as output is increased, cost rises at diminishing rate.
The Final Shape of
LRTC is

Y
Figure 16 (C)
Long Run Total Cost
OQ point shows
that when returns
scale
are
increasing
at
increasing
rate,
total cost increases
Costs
to
LTC
at diminishing rate.

OQ1 point shows
that returns to scale
are constant hence
total cost is also
constant.
O
Output
X

Beyond Q1 point in figure 17 shows that returns to scale are decreasing,
hence total cost
is increasing at
Figure -17
Long Run Total Cost
Y
faster rate.
LRTC
Costs
D.R.
C.R
.
I.R
.
O
ii)
Q
Q1
X
Long Run Average Cost : - Long run average cost is also known as
‘Envelope Curve’ or ‘Planning Curve’. Long Run average cost refers to the
minimum cost of producing different quantities.
Definition :a) J. S. Bain, “The long run average cost curve shows for each possible output,
the lower cost of producing that output in the long run.”
b) Robert Awh, “The LAC shows the lowest AC of producing output when all
inputs can be varied freely.”
Long run average cost involves various short run average cost plan. It helps a
producer to choose.
In long run each firm has various plants and each plant has its short run
average cost (SAC), which helps to estimate about LAC. Plants help a
producer to choose that plant whose average cost is minimum.
Let a firm has three types of plants – Small plant operates with cost SAC1, the
medium plant operates with the cost SAC2 and large plant operates with the
cost SAC3. If firm wants to produces OQ1 quantity of output, then it will
select the small plant. If it wants to produce OQ3 quantity of output it will go
for large plant. Figure 18, reveals that small plant produces at minimum cost
upto OU quantity of output. After this point cost will begin to rise. If demand
is likely to exceed OB in future then firm will start medium sized plant
because its quantity is more and cost is less as compare to small size plant i.e.
OQ2 and OC2. If firm excepts that the demand for its product will exceed OC
units, then it will install large size plant. LAC is also known as envelope curve
because it is the envelope of a group of SAC. LAC Curve is like a planning
device, because it helps a producer to choose optimum scale of plant.
SAC1
Figure 18
Long Run Average Cost
SAC2
Y
SAC3
C1
C2
Cost
C3
O
u
Q1
Q2
v
Quantity
Q3
w3
X
Figure 19 shows LAC is the tangent to each short average cost curves. The
figure shows that optimum scale of plant for a producer is at M point. At this
point long run average cost and short run average cost are equal to each other
(LAC = SAC).
Figure 19
Envelope Or Planning Curve
Y
SAC1
SAC5
SAC2
SAC4
LAC
Cost
SAC3
M
O
X
Quantity
Economies of Scale and the LAC
The shape of LAC Curve is less U-shaped or rather dish or source shaped. The
LAC Curve is the mirror image of the returns to the scale in the long run. The
returns to scale
are based on
Y
Figure 20
Economies and Diseconomies
and LAC
economies and
diseconomies
of scale.
LAC
In figure 20,
Costs
A
(IRTS )
Economies
the point from
increasing
B
returns to scale
which
firm
means
is
(DRTS)
Diseconomies
(CRTS)
A to B shows
O
Economies
=
Diseconomies
Quantity
D
C
X
enjoying various economies the points B and shows constant returns to scale
which indicates that economies and diseconomies are equal to each other.
After C point there is decreasing returns to scale which means diseconomies
are arising.
Long Run Marginal Cost : - Long run marginal cost is the change in long
run total cost due to the production of one more unit.
LMC 
LTC
Q
The shape of LMC
curve has a flatter
Y
U-shape.
Figure - 21
Long Run Marginal Cost
Figure 21, depicts
that
Long
LMC
Run
SMC
Marginal Cost is of
flatter
shape
indicating that due
to increasing scale
of
initially
Marginal Cost
iii)
production,
output
expands but after
certain
point
tends to decrease.
it
O
Quantity
X
Case of Economies of Scale and Cost Minimization
A well known, car manufacturing firm in India that is Maruti Udyog Limited,
has revealed the importance of economies of scale in business decision
making. Due to these economies the firm could achieved three fold rise in its
net profit earnings in the year 2003-04. The firm has reduced its average fixed
cost by increasing its output and sales volume by 30 percent.
Source : MUL Gains from Cost-Saving Measures, Sify India, 18 May,
2004.
Modern approach of cost curves: The concept of modern approach of cost curve was propounded by Sargent,
Andrews, Stigler, Florence and Friedmen etc. According to traditional theory of
costs, Cost curves are of ‘U’ shape. But according to modern theory cost curves
are of ‘L’ shaped. Like traditional theory, modern theory is based on two time
periods i.e. (i) Short Run and (ii) Long Run.
Average Fixed Cost, Average Variable Cost, Average Cost and Marginal Cost
Curves are explained in Short Run time period is as following –
Short Run Average Fixed Cost: - Average Fixed cost includes cost such
as depreciation of machinery, salaries of permanent staff members,
salaries and other expenses of administrative staff etc. In short run a firm
has limited capacity to increase the level of output but in long run it has
largest capacity units, which is indicated in figure 22, by boundary line N.
The
firm
has
also
Y
limited
Figure - 22
Short-Run Average Fixed Cost
as per Modern Theory
L
boundary
N
line L which
is shown in
figure.
In
case of N
boundary
Cost
(i)
c
line a firm
d
a
can expand
b AFC
its short run
output upto
N by paying
O
Quantity
X
overtime to labour for longer working hours. In this case AFC is ab line. A
firm can also increase it output by purchasing additional machinery. In this
case, the AFC shifts upwards and starts falling again, as shown by the
dotted line cd.
Average Variable Cost: - As per modern theory, the shape of short run
average variable costs curve is saucer – shaped, that is it has a flat stretch
over a range of output. Flat stretch represents the built in reserve capacity
of the plant. There are various reasons to have some reserve capacity for a
firm – (a) to meet seasonal and cyclical fluctuations in demand, (b) it gives
a freedom to an entrepreneur to increase output upto to desire level, (c)
due to change in technology etc.
Figure
23,
shows that the
Figure 23
Short Run Average Variable Cost
Y
falling portion
(AB)
of
SAVC shows
reduction
in
cost whereas
the
SAVC
D
A
Costs
(ii)
rising
portion (CD)
B
of the SAVC
shows
increase
C
the
in
cost. The BC
O
Quantity
portion shows that SAVC is equal to the marginal cost.
X
(iii)
Short Run Average Cost Curve: - According to modern theory AC
curve
is
continuously
falling
Figure - 24
Shirt Run Average Cost
Y
upto
a
given level of
output.
Thereafter
AC
SAC
upward.
Cost
Curve is rising
It
means AC will
rise if output is
increased
beyond reserved
O
capacity (figure
X
Quantity
24).
Short – Run
Figure - 25
Short Run Marginal Cost
Y
Marginal
Cost Curve:
- Figure 25
shows that in
MC
AVC
initial MC is
below
to
AVC.
From
AVC
Cost
(iv)
MC
M
N
point M to N
marginal cost
is horizontal
which mean
O
AVC=MC.
After point N, MC rises above to AVC.
Quantity
X
Long Run Cost Curves
According to Modern theory long run average cost curve and long run marginal
cost curve are not ‘U’ shaped but ‘L’ – shaped.
i)
Long Run Average Cost Curve:- There are two main causes of L –
shape of LAC – (a) Technological Progress and (b) Learning by doing.
According to
modern
Figure - 26
L-Shape of Long Run Average Cost
Y
theory, a firm
normally
makes use of
2/3
of
its
Cost
plant’s
production
capacity.
On
the basis of
short
run
average
cost
relating
to
LAC
O
Quantity
X
2/3rd utilization of plant capacity the shape of LAC is L-shaped, which is
shown in figure-26.
Long Run marginal
Cost
Curve:-
shape
of
depends
MC
upon
relation
Figure – 27 (A)
Shape of LMC
The
is
the
between
LAC and LMC Curve
Cost
ii)
Y
is shown in figure
10.27(A)
and
LAC
10.27(B)
LMC
respectively.
O
Quantity
X
Figure 10.27(A) shows that when L-shaped LAC curve is falling then
LMC Curve will also be falling. LMC falling portion will be below the
falling portion of LAC Curve.
Figure
10.27(B)
shows
that
when
LAC
is
inverted
shaped
of
LAC
Jthen
Cost
Curve
Figure – 27(B)
Shape of LMC
Y
LMC is below
than
LAC
Curve.
When
LAC
is
constant, LMC
also
LAC = LMC
LM
C
O
Quantity
X
become
constant.
Case Study 10.1: Estimate of Short-Run and Long-Run Cost Functions:
The results of 16 empirical studies on short run and long run cost
functions, as well as on the method of estimation, reported by A.A.
Walters in 1963. The questionnaire’s method is based on managers’
answers to questions asked by the researcher on the firm’s production
costs. Most studies found that in the short run. MC is constant in the
observed range of outputs. Most studies also indicate the presence of
economies of scale at all observed levels of output. Firms, however, seen
to avoid expanding into the range of decreasing returns to scale in the long
run.
Another empirical study on the extent of economies of scale in specific
U.S. industries over the 1967-1970 periods by William G. Shepherd found
economies of scale to be slight in steel, fabric, weaving, shoes, paints,
cement, automobile, batteries and petroleum refining, slight to moderate in
beer and refrigerators. Another study of 29 industries in India by V. K.
Gupta in 1968 found that 18 industries had L-shaped LAC Curves, 6
industries had horizontal or nearly horizontal LAC curves and the
remaining 5 industries had U-shaped LAC Curves.
Source : Marginal Economies: Principles and Worldwide Applications by
Salvatore, Dominick.
Case Study 10.2:Cost Analysis of Bajaj Auto Limited –
In India Bajaj Auto Limited has been the most dominant two wheeler
manufacturer. The goal of the company is to provide the best value for his
money to its customer. Till 1996, Bajaj Auto India had an overall 49
percent share in the market. Bajaj Scooter, Bajaj Moped and Bajaj three
Wheeler had 69 percent, 12 percent and 90 percent share in the market.
The company claims to be the lowest cost producer of scooters in the
world and its nearest competitor that LML charges a price 50percent
higher.
In spite of having the most illustrious market profile, the company’s
overall performance has taken a beating. Its profit margin has fallen from
20.24 percent in 1995-96 to 19 percent in 1996-97. It competitors such as
TVS Suzuki, Kinetic Honda etc have slowly been eating into its 44
percent share in two wheelers, bringing it down to 41.6 percent in 1996-97
alone. The scooter has dipped to a 6.6 percent share in the market, the
moped share down by 2 percent to 10 percent and three wheeler share
down by 5 percent to 85 percent share of the market.
The present plant near Pune and Indore are running to their full capacity
manufacturing one million scooters per year making Bajaj the only
company to the have achieved the feet outside Japan. The new plant
coming at Chakan near Pune and the expansion of capacity at 1999.
Bajaj Auto is a legendary story of optimizing cost to maximize value for
the customer. In its quest to minimize costs it has shown tremendous
amount of professionalism in beating competition not only through cutting
down heavily on manufacturing costs, but also on other indirect farm a
part of overheads results which show that Bajaj being an Indian company
has successfully prevented foreign giants to invade the Indian markets and
capture large market shares.
Source : Managerial Economics by Atmanand
OBJECTIVE QUESTIONS:Q1.
Define Cost?
Q2.
What is Monetary Cost?
Q3.
Describe Opportunity Cost?
Q4.
Write down the difference between economic and accounting costs?
Q5.
Distinguish between production and selling cost?
Q6.
Write down the different names of Fixed Costs?
Q7.
Distinguish between Sunk and Future Costs?
Q8.
Distinguish between controllable and uncontrollable costs?
Q9.
What is the shape of AFC?
Q10.
Write down the formula to calculate Marginal Cost?
Q11.
What is Variable Cost?
Q12.
Distinguish between Explicit and Implicit Costs?
Q13.
What is the shape of AVC?
Q14.
What is the shape of AVC in the long run as per modern theory?
Q15.
Draw the different shapes of LRTC?
Q16.
Which curve is known as Envelope Curve?
Q17.
Write down Quadratic Cost Function?
Q18.
What is the shape of LMC as per modern theory?
Q19.
Explain the relationship between AC and MC?
DESCRIPTIVE QUESTIONS: Q1.
Define Cost? Explain in detail different types of costs in general?
Q2.
Explain the traditional theory of cost with tables and diagrams?
Q3.
Can cost function be derived graphically from production functions?
Q4.
Explain AC, AFC and AVC in detail. Also draw schedules and diagrams?
Q5.
Why AVC Curve ‘U’ shaped?
Q6.
Describe why AVC curve is known as planning curve?
Q7.
Discuss the relationship between TC, Ac and MC?
Q8.
Explain modern theory of costs in detail?
Q9.
Explain the relationship between LAC and LMC according to modern theory of
cost curves?
Q10.
Calculate – TFC, TVC, AC, AFC AVC and MC from the following table:
Output
0
1
2
3
4
5
6
Total Cost
40
100
120
130
150
190
210
ASSIGNMENTS: 1. Collect the data regarding Total Fixed Cost, Total Variable Cost, Average Fixed
Cost, then from this data calculate: a)
Total Cost
b)
Average variable Cost
c)
Average Cost
d)
Marginal Cost
Also draw diagrams of all these costs.
2. Collect the Long Run Average Cost of different firms and study the shape the
LRAC either it is ‘U’ shaped or L-shaped?
SUGGESTED READINGS:1. Raj Kumar and Kuldip Gupta (2007), “Business Economics”, UDH Publishers
and Distributors (P) Ltd, New Delhi, pp.338-362.
2. Mithani, D.M.(2010), Marginal Economics: Theory and Applications, Himalaya
Publishing House, New Delhi, Mumbai, pp.271-302.
3. Geetika, Piyali, Ghosh and Purba Roy Choudhary, (2008), “Managerial
Economics, “Tata McGraw Hill, pp.215-230.
4. Jain, T.R.(1996), Micro Economics, V.K. Publishing House, Delhi, pp.188-218.
5. Atmanand (2005), “Managerial Economics, Published by Anurag Jain, New
Delhi, pp.125-166.