COST analysis and BEP notes

1. Cost Analysis
Cost refers to the amount of expenditure
incurred in acquiring some thing. In business
firm it refers to the expenditure incurred to
produce an output or provide service. Thus the
cost incurred in connection with raw material,
labour, other heads constitute the overall cost of
production.
A managerial economist must have a clear
understanding of the different cost concepts for
clear business thinking and proper application.
Output is an important factor which influences
the cost.
The cost-output relationship plays an important
role in determining the optimum level of
production. The knowledge of the cost output
relation helps the manager in cost control,
profit, production, pricing, promotion etc. the
relation between cost and its determinants
explained through the following function
∫= ),,,( TPOSC
Where
C= Cost
S= Size of Plant / Scale of operation
O= Output level
P= Prices of inputs
T= Technology
As per the formula, as the size of the plant
increases, the economies of scale start following
and hence the cost per unit will come down.
Similarly, an increase in output results in
increase in cost and vice versa.
Apart from output, prices of inputs represent a
positive relationship with cost of production. As
we know, a sophisticated technology may
reduce cost compared to outdated technology
lastly, managerial efficiency also has a bearing
on cost of production.
Cost Concepts
The various relevant concepts of costs used in
business decisions are discussed below.
 Opportunity Costs and Outlay Cost
 Explicit and Implicit/ Imputed Cost
 Historical Cost and Replacement Cost
 Short Run and Long run Costs
 Out of Pocket and Book Costs
 Fixed Cost and Variable Costs
 Past and Future Costs
 Traceable Cost and Common Costs
 Avoidable Costs and Unavoidable Costs
 Controllable Cost and Uncontrollable
Cost
 Incremental Cost and Suck Costs
 Total, Average and Marginal Costs
 Accounting and Economic Costs
They are
 Opportunity Costs and Outlay Cost:
Out lay costs, also known as actual costs or
absolute costs. These are the payments made for
labour, material, plant, transportation etc. All
these are appearing in the books of accounts.
Opportunity cost implies the earning foregone
on the next best alternative has the present
option been undertaken. This cost is often
measured by assessing the alternative which has
to be sacrificed if the particular line is followed.
Ex. A business man is able to borrow certain
amount at 10% to buy a machine. Instead of
buying the machine he can reinvest the
borrowed fund at say 12%. In this situation, the
opportunity cost is said to be 12% and outlay
cost 10%.
 Explicit and Implicit/ Imputed Cost
Explicit costs are those expenses that involve
cash payments. These are the actual or business

2. Me Notes
costs that appear in the books of accounts.
Explicit cost is the payment made by the
employer for those factors of production hired
by him from outside.
E.g. Wages, Salaries paid, payments for raw
materials, interest on borrowed capital funds
Implicit costs are the costs of the factor units
that are owned by the employer himself. It does
not involve cash payment and hence does not
appear in the books of accounts. These costs are
not actually incurred but would have been
incurred in the absence of employment of self-
owned factors.
 Historical Cost and Replacement Cost
Historical cost is the original cost of an asset.
Historical cost valuation shows the cost of an
asset paid originally when the asset was
acquired in the past. Historical valuation is the
basis for financial accounts. Replacement cost is
the price that would have to be paid currently to
replace the same asset.
E.g The price of a machine at the time of
purchase was Rs. 17,000 and the present price
of the machine is Rs. 20,000 is the replacement
cost.
 Short Run and Long run Costs:
Time is another variable for cost distinction.
Short-run is a period during which the physical
capacity of the firm remains fixed. Any increase
in output during this period is possible only by
using the existing physical capacity more
intensively.
But in the long run it is possible to change the
firm’s physical capacity as all the input are
variable including plant and capital equipment.
 Out of Pocket and Book Costs:
Out of pocket costs, also known as explicit
costs, are those costs that involve current
payments. E.g, wages, rent, interest etc.
But the book costs are taken into account in
determining the legal dividend payable during a
period. Both are considered for all decisions.
 Fixed Cost and Variable Costs:
Fixed cost is that cost which remains constant
for certain level of output. It is not changed by
the changes in the volume of production. But
fixed cost per unit decrease, when the
production is increased. E.g. salaries, rent on
factory and depreciation on machinery etc.
Variable cost is that which varies directly with
the variation in output. An increase in total
output results in an increase in total variable
costs and decrease in total output results in a
proportionate decline in the total variable costs
E.g Materials, direct labour expenses, and
Routine maintenance expenditure.
 Past and Future Costs:
Past Costs also called historical costs, these are
the actual costs incurred and recorded in the
books of accounts. These costs are useful only
for evaluation and not for decision making.
Future costs are costs that are expected to be
incurred in the future. They are not actual costs.
They are the costs forecast or estimated with
rational methods.
 Traceable and Common Costs:
Traceable cost, otherwise called direct cost, is
one which can be identified with a production
process or product. Raw material, labour
involved in production are examples of
traceable cost.
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3. Me Notes
Common Costs are the costs are the ones that
cannot be attributed to a particular process or
product. It can not be directly identified with
any particular process or type of product.
 Avoidable Costs and Unavoidable
Costs:
Avoidable costs are the costs which can be
reduced if the business activities of a concern
are reduced. E.g. if some workers can be
retrenched with a drop in a product-line, or
volume or production, the wages of the
retrenched workers are escapable costs.
The unavoidable costs are otherwise called sunk
costs. There will not be any reduction in this
cost even if reduction in business activity is
made. E.g when the volume of production is
reduced from 8,000 units to 5,000 units the
present machines has some idle capacity. It
cannot be unavoidable cost.
 Controllable Cost and Uncontrollable
Cost:
Controllable costs are the ones which can be
regulated by the executive who is in charge of it.
It is based on levels of management.
Some costs are not directly identifiable with a
process of product. They are appointed to
various processes or products in some
proportions. These costs are called
uncontrollable costs.
 Incremental Cost and Sunk Costs:
Incremental cost also known as differential cost
is the additional cost due to a change in the level
or nature of business activity. The change may
be caused by adding a new product, adding new
machine, replacing a machine by a better one
etc.
Sunk costs are those which are not altered by
any change. They are the costs incurred in the
past. This cost is the result of past decision and
cannot be changed by future decisions. Once an
asset has been bought or an investment made,
the funds locked up represent sunk costs.
 Total, Average and Marginal Costs:
Total cost is the cash payment made for the
input needed for production. It may be explicit
or implicit. It is the sum total of fixed and
variable costs.
Average cost is the cost per unit of output. It is
obtained by dividing the total cost by the total
quantity produced.
Average Cost = Q
TC
Marginal cost is the additional cost incurred to
produce an additional unit of output. In other
words, it is the cost of the marginal unit
produced.
 Accounting and Economic Costs
Accounting costs are the costs recorded for the
purpose of preparing the balance sheet and
profit and loss statements to meet the legal,
financial and tax purpose of the company.
Economic concept considers future costs and
future revenues which help future planning and
choice. These costs are used on the basis of
management requirements for decision making.
COST OUTPUT RELATIONS
The cost function can be classified two types
 Shot run cost function
 Long run cost function
Short run cost function:
The short-run defined as that period during
which the physical capacity of the firm is fixed
and the output can be increased only by using
the existing capacity more intensively.
The cost concepts, generally used in the cost
behaviour, are total cost, average cost and
marginal cost. Total cost is the actual money
spends to produce a particular quantity of
output. Total cost is the summation of fixed and
variable costs.
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4. Me Notes
TC = TFC+ TVC
Up to a certain level of production total fixed
costs, i.e the cost of plant, building, equipment
etc. remain fixed. But the total variable cost i.e
the cost of labour, raw material etc with the
variation in output. Average cost is the total cost
per unit. It can be found out as follows
Average Cost = Q
TC
The average fixed cost 





Q
TFC
keeps
coming down as the production increases and
the variable cost 





Q
TVC
will remain constant at
any level of output. Marginal cost is the
additional of product. It can be arrived by
dividing the change in total cost by the change
in total output.
MC= 





∆
∆
Q
TC
1 2 3 4 5 6 7 8
Q TFC TVC TC
2+3
AVC
3/1
AFC
2/1
AC
4/1
MC
0 60 - 60 - - - -
1 60 20 80 20 60 80 20
2 60 63 96 18 30 48 16
3 60 48 108 16 20 36 12
4 60 67 124 16 15 31 16
5 60 90 150 18 12 30 26
6 60 132 192 22 10 32 42
The above table represents the cost-output
relation. The table is prepared on the basis of the
Law of Diminishing Marginal returns. The fixed
cost Rs.60 may include rent of factory building,
interest on capital, salaries of permanently
employed staff; insurance etc. fixed cost is same
at all levels of output but the average fixed cost
fall continuously as the output increases.
The variable cost increases but at different rate.
If more and more units are produced with a
given physical capacity the AVC will fall
initially up to 3rd
unit, and being constant up to
4th
unit and then rising.
The average total cost decline and later rises.
But the rise in AC is felt only after the AVC
starts rising. In the table AVC start rising from
the 5th
unit onwards whereas the AC start rising
from the 6th
unit only. If AVC declines AC also
will decline. AFC continues to fall with an
increase in output.
From the above table shows increasing returns
or diminishing cost in the first stage and
diminishing returns or diminishing cost in the
second stage and followed by diminishing
returns or increasing cost in the third stage.
In the above first diagram shows the
relationship between output and total fixed cost,
total variable cost and total cost. The TFE is a
horizontal straight line representing Rs.60,
whatever is the output. The TVC curve slopes
upwards starting from zero, first gradually but
later at a fast rate. The different between TVC
and TC will always be the same as TFC remains
constant. Hence TC curve has the same pattern
or behaviour as TVC curve.
In the second diagram, laws of production more
clearly. The AFC curve continues to fall as
output rises on account of its spread over more
units of output. It is in the shape of rectangle
hyperbola.
TVS increase with increase in production since
more raw materials, labour, power etc., would
be required for increasing output. But AVC
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5. Me Notes
curve first falls and then rises due to the
operation of the law of variable proportions.
The AC curve depends upon the behaviour of
AVC and AFC curve. In the initial stage of
production both AFC and AVC decline and
hence AC also declines. But after a certain point
AVC start rising. If the rise in variable cost is
less than the decline in fixed cost, AC will still
continue to decline otherwise, AC begins to rise.
Thus, the lower end of AC curve turns up and
given it a U-Shape. That is why AC curves are
U-shaped.
MC curve represents the pattern of changes in
both TVC and TC curve as output changes. A
downward trend in MC curve shows increasing
marginal productivity of the variable input and
an upwards trend shoes the decreasing marginal
productivity of the variable input. MC curve
intersects both AVY and AC curves at their
lowest points. When MC decreases it pulls AC
down, and when MC increases it pushes AC up.
If MC is equal to AC, it will pull AC neither up
nor down. Hence MC curve intersects AC curve
at its lowest point.
The relationship between AVC, ATC and AFC
can be summarized as follows.
1. If both AFC and AVC fall, AC will also
fall
2. When AFC falls and AVC rises.
a. Ac will fall where the drop in
AFC is more than the rise in AVC
b. AC remains constant if the drop
ion AFC=rise in AVC
c. AC will rise where the drop in
AFC is less than the rise in AVC
-----
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6. Me Notes
Cost Output Relationship in the Long-
Run
Long run is a period during which all
inputs are variable including the ones which are
fixed in short run. In the long run firm can
change its output according to its demand. Over
a long period, the size of the plant can be
changed, unwanted building can be sold or let
out, and the number of administrative and
marketing staff can be increased or reduced. In
the long run the firm has to bring or purchase
larger quantities of all in inputs. In the long term
all input factors are variable.
In the long run cost out-put relation
therefore implies the relationship between the
total cost and the total output.
• In the long run, a firm has a number of
alternatives in regard to the scale of
operations.
• In the long run average cost curve is
composed of a series of short-run
average cost curves.
• In the short run average cost (SAC)
curve applies to only one plant whereas
the long-run average cost (LAC) curve
takes into consideration many plants.
• The long run cost-output
relationship is shown graphically in the
above with the help of LAC curve.
• To draw an LAC curve we have
to start with a number of SAC curves.
• In this figure it is assumed that
technological there are only three sizes of
plants-small, medium and large, SAC1, for
the small size, SAC2 for the medium size
and SAC3 for the large size plant.
• If the firm wants to produce OP
units or less, it will choose the smallest
plant. For an output OQ, the firm will opt
for medium size plant.
• It does not mean that the OQ
production is not possible with small plant.
Rather it implies that cost of production will
be more with small plant compared to the
medium plant.
• For an output OR the firm will
choose the largest plant as the cost of
production will be more with medium plant.
Thus the firm has a series of SAC curves.
• The LAC drawn will be
tangential to the entire families of SAC
curves i.e. the LAC curve touches each SAC
curve at one point, and thus it is known as
Envelope Curve. And also known as
Planning Curve as it series as guide to an
entrepreneur in his planning to expand the
production in future.
The law of returns to scale shapes the LAC
curve states that if a firm increases the quantity
of all inputs simultaneously and proportionately
the total output initially increases more than
proportionately but eventually increases less
than proportionately.
It implies that when the sale of the firm
expands, per unit cost first decreases but
ultimately increases. This means LAC curve
falls initially and rises subsequently. Like SAC
curve LAC curve also is U-shaped but it will be
always flatter than SAC curves. The U-shape
implies lower and lower average cost in
beginning until the optimum scale of the firm is
reached and successively higher average cost
thereafter. Up to certain point if is going to
increase after that increase production makes
management more difficult and less efficient
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7. Me Notes
resulting in less proportionate increase in
output.
The Long Run Marginal Cost Curve
The long run marginal cost curve
represents the cost of an additional unit of
output where the inputs vary. The long-run
marginal cost curve (LMC) is derived from the
short-run marginal cost (SMC) curves. At the
point A, LAC curve is tangent to SAC1 curve
corresponding to this point A, there is point B
on the SMC1 curve.
If LAC curve is tangent to SAC1 curve
at point A, the corresponding LMC curve will
be equal to SMC1 curve at point B. Thus when
LAC=SAC the LMC=SMC. As LMC is equal to
SMC the LMC curve touches SMC1 curve at
point B. OR units of output can be produced at
the point C. This is the point of tangency
between SAC2 and LAC.
At POINT C, the SAC2 AND SMC2 are
equal. At this pint LMC for output OR is RC
and SMC2 also will be RC. For output OS, the
point of tangency between SAC3 for the output
OS is given by the point E. A curve drawn
through point B, C and E makes LMC curve
which represents the behaviour of marginal cost
in the long-run. LMC curve intersects LAC
curve at its minimum point C. There is only one
plant size whose minimum SAC coincides with
the minimum LAC.
SAC2=SMC2=LAC=LMC
The point C indicates also the optimum scale of
production of the firm in the long-run or
optimum output.
OPTIMUM OUTPUT
Optimum output level of a firm can be
determine with the help of cost curves.
Optimum output level is the level of production
at which the cost of production per unit, i.e. AC,
is the lowest. It is the point where MC curve
intersects from below at the bottom of AC
curve. Thus the optimum point is where
AC=MC. Production beyond or below this point
is sub-optimal. It may be noted that the
optimum level is not the maximum profit level
N.DURGA CHAITANYA PRASAD M.Com., M.B.A (site) 40