Theory of costs

Cost concepts, Types of
costs, derivation of costs,
theory of costs
Tilak Raj Chaulagai

Opportunity cost and actual cost
• Opportunity cost
 Refers to the loss of earnings due to opportunities foregone
because of the scarcity of resources.
 If resources are unlimited – there would be no opportunity
cost
 The opportunity cost may be defined as the expected
returns from the second best use of the resources foregone
due to the scarcity of resources.
 Economic rent or economic profit – excess of the earning
from current business over the income from other alternative
foregone
 Implication – investing in the current business is preferable
so long as its economic rent is greater than zero.

Opportunity cost and actual cost
• Actual cost
 Those costs which are actually incurred by the firm in
payment for labour, material, plant, building, machinery,
equipment, travelling and transport, advertisement, etc.
 The total money expenses, recorded in the books of
accounts are, for all practical purposes, the actual costs.
Actual cost comes under the accounting concept.

Business Costs and Full Costs:
• Business cost
 Business costs include all the expenses which are incurred
to carry out business.
 The concept of business costs is similar to the actual or real
costs.
 Business costs “include all the payments and contractual
obligations made by the firm together with the book cost of
depreciation on plant and equipment”.
 These cost concepts are used for calculating business
profits and losses and for filling returns for income-tax and
also for other legal purposes.

Business Costs and Full Costs:
• Full costs
 Full costs, on the contrary, include business costs,
opportunity cost and normal profit.
 The opportunity cost includes the expected earnings from
the second best use of the resources, or the market rate of
interest on the total money capital, and also the value of
entrepreneur’s own services which are not charged for in the
current business.
 Normal profit is a necessary minimum earning in addition to
the opportunity cost, which a firm must get to remain in its
present occupation.

Explicit and Implicit or Imputed Costs:
• Explicit costs
 Explicit costs refer to those which fall under actual
or business costs entered in the books of accounts.
 The payments for wages and salaries, materials,
license fee, insurance premium, depreciation
charges are the examples of explicit costs.
 These costs involve cash payments and are
recorded in normal accounting practices.

Explicit and Implicit or Imputed Costs:
• Implicit costs
 costs which do not take the form of cash outlays,
nor do they appear in the accounting system.
 Implicit costs may be defined as the earning
expected from the second best alternative use of
resources.
 Implicit costs are not taken into account while
calculating the loss or gains of the business, but
they form an important consideration in whether or
not a factor would remain in its present occupation.
 The explicit and implicit costs together make the
economic cost.

Out-of-Pocket and Book Costs:
Out-of-pocket costs means costs that
involve current cash payments to
outsiders while book costs such as
depreciation do not require current cash
payments.
Book costs can be converted into out-
of-pocket costs by selling the assets
and having them on hire. Rent would
then replace depreciation and interest.

Short-Run and Long-Run Costs:
• Short-run costs are the costs which vary with the
variation in output, the size of the firm remaining the
same. In other words, short-run costs are the same as
variable costs.
• Long-run costs, on the other hand, are the costs which
are incurred on the fixed assets like plant, building,
machinery, etc. Such costs have long-run implication in
the sense that these are not used up in the single batch
of production.
• ‘the short-run costs are those associated with variables
in the utilization of fixed plant or other facilities whereas
long-run costs are associated with the changes in the
size and kind of plant.’

Incremental Costs and Sunk Costs
• Incremental Costs
 Incremental costs are closely related to the concept of
marginal cost but with a relatively wider connotation. While
marginal cost refers to the cost of the marginal unit of
output, incremental cost refers to the total additional cost
associated with the marginal batch of output.
 The concept of incremental cost is based on the fact that in
the real world, it is not practicable for lack of perfect
divisibility of inputs to employ factors for each unit of output
separately.
 Besides, in the long run, firms expand their production; hire
more men, materials, machinery and equipment.
 The expenditures of this nature are incremental costs and
not the marginal cost

Incremental Costs and Sunk Costs
• Sunk Costs
 The Sunk costs are those which cannot be altered,
increased or decreased, by varying the rate of
output.
 For example, once it is decided to make
incremental investment expenditure and the funds
are allocated and spent, all the preceding costs are
considered to be the sunk costs since they accord
to the prior commitment and cannot be revised or
reversed or recovered when there is change in
market conditions or change in business decisions.

Historical and Replacement Costs:
• Historical costs are those costs of an asset acquired
in the past whereas replacement cost refers to the
outlay which has to be made for replacing an old
asset.
• Stable prices over time, other things given, keep
historical and replacement costs on par with each
other. Instability in asset prices makes the two costs
differ from each other.
• Historical cost of assets is used for accounting
purposes, in the assessment of net worth of the firm.
The replacement cost figures in the business
decision regarding the renovation of the firm.

Private and Social Costs:
• Private costs are those which are actually incurred or
provided for by an individual or a firm on the
purchase of goods and services from the market.
• For a firm, all the actual costs both explicit and
implicit are private costs. Private costs are
internalized costs that are incorporated in the firm’s
total cost of production.
• Social costs on the other hand, refer to the total cost
to the society on account of production of a
commodity.

Urgent and Postponable Cost:
• Urgent costs are those costs which must be incurred
in order to continue operations of the firm. For
example, the costs of materials and labour which
must be incurred if production is to take place.
• Postponable costs refer to those costs which can be
postponed at least for some time e.g., maintenance
relating to building and machinery.

Theory of Cost
 Traditional Theory of Cost
 Modern Theory of Cost

Traditional Theory of Cost
 Short run
 Short run is the period during which some
factor(s) is fixed;
 usually capital equipment and entrepreneurship
are considered as fixed in the short run.
 Long run
 The long run is the period over which all factors
become variable.

• Costs of a firm is incurred to establish the
production unit and to purchase different
factors of production.
• Cost of a firm (TC) is classified into two
broad categories - Fixed cost (TFC) and
Variable cost (TVC).
i.e. TC = TFC + TVC
• However, nothing is fixed in the long run.

Fixed costs
Fixed costs are expenses that does not
change in proportion to the activity of a
business.
Fixed costs include overheads (rent,
insurance-premium, interests), and also
direct costs such as payroll (particularly
salaries).

Fixed cost does not change with the
volume of production.
TFC
Q
costs
100
O

Variable costs
Variable costs change in direct
proportion to the activity of a business
such as sales or production volume. In
retail, the cost of goods is almost entirely
variable. In manufacturing, direct material
costs, wages, fuel costs are examples of
variable costs.

For example, a manufacturing firm pays for
raw materials. When activity is decreased,
less raw material is used, and so the
spending for raw materials falls. When
activity is increased, more raw material is
used and spending therefore rises.
Although tax usually varies with profit, which
in turn varies with sales volume, it is not
normally considered a variable cost.

fig
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
TFC
Output
(Q)
0
1
2
3
4
5
6
7
TFC
(£)
12
12
12
12
12
12
12
12
Total costs for firm X

fig
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
TFC
Output
(Q)
0
1
2
3
4
5
6
7
TFC
(£)
12
12
12
12
12
12
12
12
TVC
(£)
0
10
16
21
28
40
60
91

fig
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
TVC
Output
(Q)
0
1
2
3
4
5
6
7
TFC
(£)
12
12
12
12
12
12
12
12
TVC
(£)
0
10
16
21
28
40
60
91
TFC

fig
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
TVC
TFC
Diminishing marginal
returns set in here

fig
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
TVC
TFC
Output
(Q)
0
1
2
3
4
5
6
7
TFC
(£)
12
12
12
12
12
12
12
12
TVC
(£)
0
10
16
21
28
40
60
91
TC
(£)
12
22
28
33
40
52
72
103

fig
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
TC
Output
(Q)
0
1
2
3
4
5
6
7
TFC
(£)
12
12
12
12
12
12
12
12
TVC
(£)
0
10
16
21
28
40
60
91
TC
(£)
12
22
28
33
40
52
72
103
TVC
TFC

fig
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8
TC
TVC
TFC
returns set in here

Average fixed cost
Average fixed cost (AFC) = TFC/Q
where TFC = fixed cost, Q = total number of
units produced.
Unit fixed costs decline along with volume,
following a rectangular hyperbola. As a
result, the total unit cost of a product will
decline as volume increases.

Average Fixed costs
Q
Costs
AFC
O

Average variable cost
Average variable cost (AVC) is the TVC of a firm
divided by the total units of output (Q).
AVC = TVC/Q
Q
costs
Y
AVC
O

Average cost
Average cost (AC) is the TC of a firm divided by
the total units of output (Q).
AC = TC/Q = AFC + AVC
Q
costs
Z
AC
O

Marginal Cost
The additional cost incurred to produce one
additional unit of output is called the
Marginal Cost (MC).
MC = dC/dQ

MC
The marginal cost curve is U-shaped.
Marginal cost is relatively high at small
quantities of output - then as production
increases, it declines - then reaches a
minimum value - then rises.
This shape of the marginal cost curve is
directly attributable to increasing, then
decreasing marginal returns (the law of
diminishing marginal returns).

fig
Output (Q)
Costs(£)
MC
x
returns set in here
Marginal costsMarginal costs

Numerical Example
Q TFC TVC TC AFC AVC AC MC
0 100 0 100
1 100 20 120 100
20 120 20
2 100 37 137 50
18.5 68.5 17
3 100 52 152 33.33
17.33 50.67 15
4 100 80 180 25
20 45 28
5 100 120 220 20
24 44 40
6 100 165 265 16.67 27.5 44.17 45

fig
Output (Q)
Costs(£)
AFC
AVC
MC
x
AC
z
y
Average and marginal costs

Relationship between MC and AC

Production Rules for the Short-Run
1. If expected selling price < minimum AVC
(which implies TR<TVC)
 A loss cannot be avoided
 Minimize loss by not producing
 The loss will be equal to TFC
2. If expected selling price < minimum ATC but
> minimum AVC (TR > TVC but < TC)
 A loss can not be avoided
 Minimize loss by producing where MR = MC
 The loss will be between 0 and TFC

Production Rules for the Short-Run
3. If expected selling price > minimum ATC
(which implies TR>TC)
 A profit can be made
 Maximize profit by producing where MR=MC

LONG RUN COSTS
The Envelope Curve

Long run cost curves
The Long run average cost (LRAC or LAC)
curve illustrates - for a given quantity of
production - the average cost per unit
which a firm faces in the long run (i.e.
when no factors of production is fixed).

LRAC
LRAC curve is derived from a series of short run
average cost curves.
It is also called the ‘Envelope curve' since it
envelops all the short run average cost curve.
The curve is created as an envelope of an
infinite number of short-run average total cost
curves.
The LAC is derived from short-run cost curves.
Each point of on the LAC corresponds to a
point on a short-run cost curve, which is
tangent to the LAC at that point.

LAC
The LRAC curve is U-shaped, reflecting
economies of scale when it is negatively-
sloped and diseconomies of scale when it
is positively sloped.
In perfect competition, the LRAC curve is
flat at the point of equilibrium – in this
stage the firm is enjoying constant returns
to scale.

LAC
In some industries, the LRAC is L-shaped,
and economies of scale increase
indefinitely. This means that the largest
firm tends to have a cost advantage, and
the industry tends naturally to become a
monopoly, and hence is called a natural
monopoly. Natural monopolies tend to
exist in industries with high capital costs in
relation to variable costs, such as water
supply and electricity supply.

fig
Long-run average cost curves
OutputO
Costs
LRAC
Economies of Scale

fig
OutputO
Costs
LRAC
Diseconomies of Scale
long-run average cost curves

fig
OutputO
Costs
LRAC
Constant costs
long-run average cost curves

Long-run Costs
• Long-run average costs
– assumptions behind the curve
• factor prices are given
• state of technology and factor quality are given
• firms choose least-cost combination of factors

fig
A typical long-run average cost curve
OutputO
Costs
LRAC

fig
OutputO
Costs
LRACEconomies
of scale
Constant
costs
Diseconomies
of scale
A typical long-run average cost curve

fig
Long-run average and marginal costs
OutputO
Costs
LRAC
LRMC
Economies of Scale

fig
OutputO
Costs
LRAC
LRMC
Diseconomies of Scale
Due to managerial
inefficiencies

fig
OutputO
Costs
LRAC = LRMC
Constant costs

fig
OutputO
Costs
LRMC
LRAC
Initial economies of scale,
then diseconomies of scale

Envelope Curve
The envelope curve is based on the point of
each short-run ATC curve that provides the
lowest possible average cost for each quantity
of output.
It is a planning curve because on the basis of
this curve the firm decides what plant to set up
in order to produce optimally the expected
level of output.
The LAC envelops the SAC curves because of
the assumption that each plant size is
designed to produce optimally a single level of
output

Deriving long-run average cost curves: plants of fixed size
SRAC3
Costs
Output
O
SRAC4
SRAC5SRAC1 SRAC2

fig
SRAC1
SRAC3
SRAC2
SRAC4
SRAC5
LRAC
Costs
Output
O
Deriving long-run average cost curves: factories of fixed size

fig
Deriving a long-run average cost curve: choice of factory size
Costs
Output
O
Examples of short-run
average cost curves

fig
LRAC
Costs
Output
O
Deriving a long-run average cost curve: choice of factory size

Envelope Curve
Each point on the LAC represents the least unit
cost for producing the corresponding level of
output. Any point above the LAC is inefficient
in that it shows a higher cost for producing the
corresponding level of output.
Any point below the LAC is economically
desirable because it implies a lower unit cost,
but it is not attainable in the current state of
technology and with the prevailing market
prices of factors of production.

LMC
The LMC is derived is derived from the SMC
curves but does not envelope them.
The LMC is formed from points of intersection of
the SRMC curves with vertical lines drawn
from the points of tangency of the
corresponding SAC curves and the LRA cost
curves.
The LMC must be equal to the SMC for the
output at which the corresponding SAC is
tangent to the LAC.

Overall
The TC curve is roughly S-shaped
ATC, AVC and MC are all U shaped
MC curve intersects the other two curves at their
minimum points

• The short-run average variable cost has a flat
stretch over a range of output which reflects the
fact that firms build plants with some flexibility in
their productive capacity
Because
• The businessman will want to be able to seasonal
and cyclical fluctuations in his demand
• It gives the businessman greater flexibility for
repairs of broken down machinery without disrupting
the smooth flow of the production process
• The entrepreneur will want to have more freedom to
increase his output if demand increases because
he/she does not like to let all new demand go to his
rivals

• It also gives him/her some flexibility for minor alterations of
his product, in view of changing tastes of customers.
• Technology usually makes it necessary to build into the plant
some reserve capacity
• It is always allowed in case of land and building because
operations may be seriously limited if new land or new
buildings have to be acquired
• There will be some reserve capacity on the organizational
and administrative level.
In summary,
The businessman will not necessarily choose the plant which
will give him today the lowest cost, but rather that equipment
which will allow him the greatest possible flexibility, for minor
alterations of his product or his technique.

• Average Variable Costs
• Average Fixed Costs
Short Run Costs

• The salaries and other expenses of administrative
staffs
• The salaries of staff involved directly in the
production, but paid on a fixed-term basis
• The wear and tear of machinery
• The expenses for maintenance of buildings
• The expenses for the maintenance of land on which
the plant is installed and operates.
Short Run Average Fixed Costs

SAFC
C
O
A B
XA XB
a
b
X
Largest capacity units of
machinery as absolute limit in
the short run
Small unit machinery – sets
a limit to expansion
By paying
overtime to
direct labor
By buying
additional
small unit
types of
machinery

• Direct labor which varies with output
• Raw materials
• Running expenses of machinery
Short Run Average Variable Costs

SAVC
C
O
X
Better utilization of the fixed
factor and the consequent
increase in skills and
productivity of variable factor,
reduced wastage of raw
materials
SAVC = MC
MC SAV
C
MC
SAV
C
• Reduction in labor
productivity due to
longer hours of work;
• increase cost of labor
due to overtime
payment;
• wastage of materials;
• frequent breakdown of
machinery

• Due to the reserve capacity, which is further
planned in order to give maximum flexibility in the
operation of the firm
• Reserve capacity is completely different from
excess capacity
Why SAVC flat shaped over a range

Excess capacity vs reserve capacity
C
0 X
SAVC
X XM
Excess
capacity
C
0 XX1 X2
SAVC
Reserve
capacity

SATC
C
O
X
SAVC = MC
MC
SAV
C
MC
SAV
C
XA

• Production Costs
• Managerial Costs
Long-Run Costs

• Production costs falls steeply to begin with and then
gradually as the scale of production increases
• The L-shape of production cost curve is due to the technical
economies of large scale production
• Initially these economies are substantial
• But after a certain level of output is reached all or most of
these economies are attained and the firm is said to have
reached the minimum optimal scale, given the technology of
the industry.
• If new techniques are invented for larger scales of output,
they must be cheaper to operate.
Production costs

• Each management technique is applicable to
a range of output.
• Organizational techniques may be small
scale as well as large scale
• The cost of different techniques of
management first fall up to a certain plant
size.
• At very large scales of output managerial
costs may rise, but very slowly
Managerial Costs

• Production costs fall smoothly at very large
scales, while managerial costs may rise only
slowly at very large scales.
• The fall in production costs more than offsets
the probable rise of managerial costs, so that
the LRAC curve falls smoothly or remains
constant at very large scales of output.
LRC curves

Derivation of LRAC Curve
• Load factor: Ratio of average actual rate of use to the capacity
• In business practice it is customary to consider that a plant is used
‘normally’ when it operates at a level between two-thirds and three-
quarters of capacity.
• Here the typical load factor of each plant is taken as 2/3
SAC1
X
2/3
C
2/3
2/3
2/3
LAC
0
SAC2
SAC3
SAC4
LMC
• LAC does not turn up at very
large scales of output
• It is not the envelope of the
SATC curves, but rather
intersects them

LAC
C
O
X
LAC = LMC
LMC
LAC
XA
Minimum
optimal scale

Theory of costs

Theory of costs

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