Economics for Decision Making, Module-3

Module-3
Cost Analysis & Production Analysis
Introduction:
A business comes in to being with the main objective of earning profit. To achieve optimum
efficiency in production or minimizing cost for a given production is one of the prime concerns
of the business manager, in fact the survival of a firm in a competitive market depends on
their ability to produce at a competitive cost. Therefore, manager of business firm endeavor
to minimize the production cost or what is same things maximize output from a given quantity
of inputs.

Production: “Production” means a process by which resources men material, time etc.)
transformed into different and more useful commodity or services. In general production
means transforming inputs (labour, machines, raw materials, time etc.) into an output.
Various inputs are combined in different quantities to produce various levels of output.”
Inputs and output: An input is a good or service that goes into the process of production.
According to Boumol “An input is a simply anything which the firm buys for use in its
production or other process”. The term inputs needs some more explanation Production
process require wide variety of input depending on the nature of product but Economist have
classified inputs as 1) labour 2) Capital 3)Land 4) Raw materials and Time. All these variables
are flow variable since they are measured per unit of time
Output: An output is any good or service that comes out of production process.
Fixed and Variable inputs: A fixed inputs can be defined as a fixed factor is one that remains
fixed (constant) for certain level of output. A variable input is defined as one whose supply in
the short run is inelastic i.e. labour and raw material etc . the user of such factor can employ
a large quantity in the short run. Technically a variable input is one that change with the
change in output in the long run all inputs are variable
Short Run and long Run
Short run: refer to a period of time in which the supply of certain inputs (e.g plant, building ,
machinery etc) is fixed or inelastic .in short run therefore production of a commodity can be
increased by increasing the use of only variable inputs like labour and raw material
Long run: refer to period of time in which the supply of all the inputs is elastic but not enough
to permit a change in technology that is, in the long run all inputs are variable. Therefore, in
long run production of commodity can be increased by employing more of both variable and
fixed inputs
Production Function: It is a tool to analysis used to explain the input-output relationship. A
production function describes the technological relationship between inputs and output in
physical terms. In other word production Function showing the relationship between the
quantities of inputs used and the output produced. There is a production function for every
good that shows the maximum output you can get from any quantities of inputs. The
production function is the description of the current best technology for making a good.
Production function indicates the highest output that a firm can produce for every
specified combination of inputs given the state of technology. The firm’s production function
for a particular good (q) shows the maximum amount of the good that can be produced using
alternative combinations of capital (k) and labor (l). The production function for two inputs:
Q = F(K,L)
Q = Output, K = Capital, L = Labor

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For a given technology

Characteristics of a Production Function:
➢ Production refers to the transformation of inputs into output;
➢ A production function is a flow concept;
➢ A production function is a physical, technological, or engineering concept, and yet it
has an economic dimension to it; and
➢ In production analysis, factors of production can be separated into fixed and variable
factors.
Short-Run Production with One Variable Input (Labour) or Short Run
Production Function:
In the short run, some inputs (land, capital) are fixed in quantity. The output depends on
how much of other variable inputs are used. For example, if we change the variable input
namely (labour) the production function shows how much output changes when more
labour is used. In the short run producers are faced with the problem that some input
factors are fixed. The firms can make the workers work for longer hours and also can buy
more raw materials. In that case, labour and raw material are considered as variable input
factors. But the number of machines and the size of the building are fixed. Therefore, it
has its own constraints in producing more goods.
In the long run all input factors are variable. The producer can appoint more workers,
purchase more machines and use more raw materials. Initially output per worker will
increase up to an extent. This is known as the Law of Diminishing Returns or the Law of
Variable Proportion. To understand the law of diminishing returns it is essential to know
the basic concepts of production

Amount of Labour(L) Total Capital(K) Output(q)

0 10 0
1 10 10
2 10 30
3 10 60
4 10 80
5 10 95
6 10 108
7 10 112
8 10 112
9 10 108
10 10 100

Observation: with additional workers, output (Q) increases, reaches a maximum, and then
decreases.
Measures of Productivity
Total production (TP): the maximum level of output that can be produced with a given
amount of input.
Average Production (AP): output produced per unit of input AP = Q/L
Marginal Production (MP): the change in total output produced by the last unit of an input

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Short-Run Production with One Variable Input (Labor)

Amount of Amount of Total output (Q) Average Marginal

labour (L) Capital(K) Product Product
0 10 0 0 0
1 10 10 10 10
2 10 30 15 20
3 10 60 20 30
4 10 80 20 20
5 10 95 19 15
6 10 108 18 13
7 10 112 16 4
8 10 112 14 0
9 10 108 12 -4
10 10 100 10 -8

From The above table it is possible to understand the Law of Return. The Total returns are
increasing continuously with the increase in the factor labour. The marginal return remain
constant during fifth and sixth units of labour and it is falling with the additional unit of labour
The law of diminishing return is operating from fourth unit of labour. The marginal physical
product clearly show the operation of the law of diminishing returns. The law of return are
shown with the help of following diagram.

Labour

Relationships Among Total, Average, and Marginal Product Curves

From the above Diagram ox axis measures number of workers and the OY axis measures total
returns. TPC is the total production curve, which is the outcome of increase in number of
workers and total returns. In the first stage of the of the TPC there is a continues and steep
increase in the total production. second stage the total production curve is not that steep
and comparison to first stage. The marginal return is this stage are almost constant. In the
third stage TPC will have a negative slope

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The Law of Diminishing Marginal Returns: As the use of an input increases in equal
increments, a point will be reached at which the resulting additions to output decreases (i.e.
MP declines).The slope of the MP curve in Figure illustrates an important principle, the law
of diminishing marginal returns. As the number of units of the variable input increases, the
other inputs held constant (fixed), there exists a point beyond which the MP of the variable
input declines. Table illustrates this law. Observe that MP was increasing up to the addition
of 4th worker (input); beyond this the MP decreases. What this law says is that MP may rise
or stay constant for some time, but as we keep increasing the units of variable input, MP
should start falling. It may keep falling and turn negative, or may stay positive all the time.
Consider another example for clarity. Single application of fertilizers may increase the output
by 50%, a second application by another 30% and the third by 20% and so on. However, if you
were to apply fertilizer five to six times in a year, the output may drop to zero.
Three stages of production
Increasing Returns: When employment of variable inputs increased, a combination of fixed
factor and variable factor tend to be near the optimum. Thus, in the short run production
function is adjusted to optimization, resulting output tends to be greater proportion to be
increase in the variable factor units.
Diminishing Returns: The reason for diminishing returns is not for seek to increase output by
employing more and more units of variable factors, there by trying to substitute fixed factor
by variable factor. But due to imperfect substitutability of factors, when the fixed factor is
over utilized there emerge internal diseconomies and the diminishing returns follow.
Negative Returns: Stage III is the stage of negative returns , when the inputs of variable factor
is much excessive in relation to the fixed components in the production function. For instance
excessive use of chemical fertilizer on a farm may eventually spoil the farm output
Total Physical Product Marginal Physical Average Physical
Product Product
Stage I
Increasing at an Increases, reaches its Increases and reaches
increasing rate maxiIhum and then its maximum
declines till MR = AP
Stage II
Increases at diminishing Is diminishing and Starts diminishing
rate till it reaches becomes equal to zero
maximum
Stage III
Starts declining Becomes negative Continues to decline

Production Functions with Two Variable Inputs

(Isoquants& LR Production Functions)
We have discussed in the preceding section, the technological relationship between
inputs and output assuming labour to be the only variable inputs capital remain constant. This
is a short run phenomenon. In this section we will discuss the relationship between inputs
and output under condition that both the inputs capital and labour are variable factor this is
long run phenomenon. In this long run, supply of both the inputs is supposed to be elastic and
firms can hire larger quantities of both labour and capital with larger employment of capital
and labour of the scale of production increases the technological relationship between
changing scale of inputs and output is explained under the law of return to scale. Can be

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explained through the production function and isoquant curve technique , The most common
and simple tool of analysis is isoquant curve.
Isoquant curve: A production function with two variable can be represented by a family of
isoquant. The word isoquant simply means equal quantities;
Isoquant curve is defined is a curve representing all various input combinations which
produces the same output (various capital-labor combinations that produces the same
output). Or All those combination of two variable inputs which yield a given quantity of
product Or an isoquant curve is locus of point representing various combination of two inputs
capital and labour yielding same output

Labour,L
Capital, K
1 2 3 4 5 6
1 10 14 17 20 22 24
2 14 20 24 28 32 35
3 17 24 30 35 39 42
4 20 28 35 40 45 49
5 22 32 39 45 50 55
6 24 35 42 49 55 60

The different combination of labour and capital can be used to produce a given level of
output. Thus, if one labour is used and 6 capital needs be employed to produce 24 units of
output alternatively 24 units of output can produce with the help of 1 units of capital and 6
units of labour in between there are another alternative. Alternative combination of labour
and capital that firm can employs in order to produce 24 units of output
Isoquants analyze and compare the different combinations of K & L and output.

An Isoquant is a curve representing all various input combinations which produces the same
output (various capital-labor combinations that produces the same output).Or Isoquants
show combinations of two inputs that can produce the same level of output.

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Properties of Isoquants
All the above-mentioned isoquants are featured with some common properties, which are
as follows:
➢ An isoquant is downward sloping to the right, i.e., negatively inclined. This implies
that for the same level of output, the quantity of one variable will have to be reduced
in order to increase the quantity of other variable.
➢ A higher isoquant represents larger output. that is, with the same quantity, of one
input and larger quantity of the other input, larger output will be produced.
➢ No two isoquants intersect or touch each other. If two isoquant intersect or touch
each other, this would mean that there will be a common point the Two curves; and
this would imply that the 'same amount of two inputs could produce two different
levels of output (i.e., 400 and 500 units), which is absurd.
Production Functions with all variable inputs
A closely related question in production, economics is how a proportionate increase in all the
input factors will affect total production. This is the question of returns to scale, which brings
to mind three possible situations:
• If the proportional increase in all inputs is equal to the proportional increase in output,
returns to scale are constant. For instance, if a simultaneous doubling of all inputs
results in a doubling of production then returns to scale are constant. The following
figure 4.6 shows a constant rate to scale.

• If the proportional increase in output is larger than that of the inputs, then we have
increasing returns to scale. The following Figure 4.7 shows increasing returns to scale.

• If output increases less than proportionally with input increase, we have decreasing
returns to scale. The following Figure 4.8 shows decreasing returns to scale.

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The most typical situation is for a production function to have first increasing then
decreasing returns to scale is shown in Figure 4.9.

The increasing returns to scale attribute to specialisation. As output increases,

specialized labour can be used and efficient, large-scale machinery can be employed in the
production process. However, beyond some scale of operations further gains from
specialization are limited, and co-ordination problems may begin to increase costs
substantially. When co-ordination price is more than offset additional benefits of
specialization, decreasing returns to scale begin.
Returns to Scale and Returns to an Input
Two important features of production functions are returns to scale and returns to input,
which are explained as follows:
Returns to scale: Another important attribute of production function is how output responds
in the long run to changes in the scale of the firm i.e. when all inputs are increased in the
same proportion (by say 10%), how does output change. Clearly, there are 3 possibilities. If
output increases by more than an increase in inputs (i.e.by more than 10%), then the situation
is one of increasing returns to scale (IRS). If output increases by less than the increase in
inputs, then it is a case of decreasing returns to scale (DRS). Lastly, output may increase by
exactly the same proportion as inputs. For example, a doubling of inputs may lead to a
doubling of output. This is a case of constant returns to scale (CRS).

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Returns to input: These describe the impact on the output when only one input is
varied, holding all others constant. These returns may be increasing,' diminishing, or
constant.
Optimal Input Combinations
From the overall discussion so far it is obvious that production function, has a pure
'physical or technological' character. However, it does not tell which input combinations are
optimal. For that purpose, one has to take into account the input prices. The following Figure
4.10 shows the iscost curves.

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Isocost Curves
In this connection, one has to consider yet another but important diagram consisting of iso
cost curves. Here also, the axes represent quantities of the inputs X and Y. Suppose that the
prices of the inputs are given, and there are no quantity discounts for the firm to get larger
quantities at lower prices. The next step will be to plot the various quantities of X and Y which
may be obtained from the given monetary outlays. Figure 4.10 shows the resulting isocost
curyes, which are straight lines under the assumption made here. One isocost showing the
quantities of X and Y that can be purchased for Rs. 1,000 and another isocost curve showing
the quantities of X and Y which can be purchased for an expenditure of Rs. 2,000 and so on.
Now we can easily superimpose the isocost diagram on the isoquant diagram (as the
axes in both the cases represent the same variables). With the help of Figure 4.11, it can be
ascertained that the maximum output for a given outlay, is say Rs. 2,000. The iso quant
tangent represents this maximum output, which is possible with this outlay, to the iso cost
curve. The optimum combination of inputs is represented by point E, the point of tangency.
At this point, the marginal rate6f substitution (MRS, sometimes known as the rate of technical
substitution), between the inputs is equal to the ratio between the prices of the inputs.
Likewise, in order to mini mise the cost for a given output, one may again refer to the
iso quant and iso cost curves in Figure 4.11. In this case one moves along the isoquant
representing the desired output. It should be clear that the minimum cost for this input is
represented by isocost line tangent to the isoquant.

Firm's Expansion Path

A firm's expansion path is defined by the cost-minimising combination of several inputs for
each output level. Thus, the line representing least cost combination for different levels of
output is called firm's expansion path or the scale line shown by
. Economies of Scale: There are Economies of scale in production when the long run average
cost increases as output increases. Economies of scale (increasing returns to scale) are cost
savings associated with larger scale of production. Diseconomies of scale or decreasing
returns to scale refer to the increasing long run average costs as output increases
Diseconomies occur for a number of reasons as the firm increases its size Coordination of a
large firm is more difficult Information costs and communication costs increase as firm
increases
.

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Economies of Scale: The study of economies of scale is of greater importance for all business
manager because it serves as basis for whole process of decision making. The term
economies of scale is a technical term developed by economist to describes the benefits
enjoyed by those firms which produce large scale and participate in long run it will enjoy
certain special benefits which are called economies of scale or
Economies of scale refers to the phenomena of decreased per unit cost as the number of units
of production increase Economies of scale means a reduction in the per unit costs of a product
as a firm's production increases
Capital Land Labour Output TC AC

Scale A 5 3 4 100 57 0.57

Scale B 10 6 8 300 164 0.54

Doubling the scale of production (a rise of 100%) has led to an increase in output of 200% - therefore
cost of production PER UNIT has fallen
Economies of scale have been broadly classified under two group’s
A) Internal Economies B) External Economies
Internal Economies
Internal economies are also Known as operational economies which are obtained during the
date today process of production and hence, they are even called operational economies.
These economies are within the purview of the firm and firm and the firm itself is responsible
for these economies. The important internal economies are:
Labour Economies: Large firm normally employ factor labour in different quantities, and
qualities. Large firms practice the large process of Division of labour which is nothing but
dividing a particular work in too many smaller parts. If a small work is performed repetitively
many fold benefits are obtained to the large business firm. They are like increase in efficiency
of work, increase in productivity, economy of time, improvement in skills, avoiding wastage
of resources etc.
As a result of all these benefits the task performed by worker will be superior quality. Thus,
all labour economies will be enjoyed only by large firm and not by small firm
Technological Economies: Large firm normally adopt capital intensive technology by making
huge investment on plant and machinery. Large firm divided the entire total fixed cost on all
the units of the output. Costly machinery and equipment bring with them both quantity and
quality in production. Large firm will enjoy the benefit of superior technology and benefit of
indivisibility of factor. Latest technological improvement and other benefits will enjoy by large
firm.
Financial Economies: Financial Economies also favor large firm but not small firms.
Normally large firms enjoy the support of stock market, financial institutions and also support
of general public. Large firm obtain fund at cheaper rate of interest with sufficient time of
repayment. Small firm will not enjoy any financial economies.
Managerial Economies: Managerial economies are also called functional economies. Large
firms employ skilled, highly qualified, and specialized personal for both buying and selling.
The functional benefits will be informed of team work, decentralization of power and
adoption of modern management concept like PERT, (Progress evaluation review Technique)
TQM, etc. The large firm during purchase price will be comparatively low with free

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transportation sufficient times for payment are benefits enjoyed during purchase and in sales
too. Large firm also adopt modern technique to market the product through channels of
distribution
Risk Spreading and Survival Economies: Risk spreading is easy for large firm and hence they
survive with whatever be the magnitude of risk and uncertainties. Large firms will diversify
their risk and future they insure against risk. The majority of the activities in the large firms
will be carried out by appropriate massive insurance policy. Large firms meet accidents,
unexpected sticks or events causing damage, risk of transportation etc., effectively. Small
firms will perish due to risk and uncertainties.
External Economies of Scale These are economies made outside the firm as a result of its
location, and occur when: A local skilled labour force is available. Specialist, and local back-up
firms can supply parts or services. An area has a good transportation network. An area has an
excellent reputation for producing a particular good
Diseconomies of Scale
Economies of increasing size do not continue indefinitely. After a certain point, any further
expansion of the size leads to diseconomies of scale. For example, after the division of labour
has reached its most efficient point, further increase in the number of workers will lead to a
duplication of workers. There will be too many workers per machine for really efficient
production. Moreover, the problem of co-ordination of different processes may become
difficult. There may be divergence of views concerning policy problems among specialists in
management
and reconciliation may be difficult to arrive. Decision-making process becomes slow resulting
in missed opportunities. There may be too much of formality, too many individuals between
the managers and workers, and supervision may' become difficult. The management
problems thus get out of hand with consequent adverse effects on managerial efficiency.
The limit of scale economics is also often explained in terms of the possible loss of control
and consequent inefficiency. With the growth in the size of the firm, the control by those at
the top becomes weaker. Adding one more hierarchical level removes the superior further
away from the subordinates. Again, as the firm expands, the incidence of wrong judgments
increases and errors in judgement become costly.
Last be not the least, is the limitation where the larger the plant, the larger is the
attendant risks of loss from technological changes as technologies are changing fast in
modern times.
Concept of Cost
Introduction
Business decisions are generally taken on the basis of money values of the inputs and outputs.
The cost production expressed in monetary terms. It is an important factor in almost all
business decisions, especially those pertaining to (a) locating the weak points in production
management; (b), minimising the cost; (c) finding out the optimum level of output; and (d)
estimating or projecting the cost of business operations. Besides, the term 'cost' has different
meanings under different settings and is subject to varying interpretations. It is therefore
essential that only relevant concept of costs is used in the business decisions.
Concept of Cost
In managerial economics, cost is normally considered from the producer’s point of
view. In producing a commodity, a firm as to employ an aggregate of various factor of
production such as land, labour, capital and entrepreneurship. These factors are to be
compensation is the cost. Thus, the cost of production of a commodity is the aggregate of

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price paid for the factor production used in producing that commodity. A firm’s costs depend
on the rate of output and we will show how these costs are likely to change over time. The
characteristics of the firm’s production technology can affect costs in the long run and short
run.
The Importance of Cost Analysis
Managers seek to produce the highest quality products at the lowest possible cost.
Cost analysis is helpful in the task of finding lower cost methods to produce goods and
services.
Basic Definitions
Profit: The money that business makes: Revenue minus Cost
Cost: the expense that must be incurred in order to produce goods for sale
Revenue: the money that comes into the firm from the sale of their goods
Types of Costs: Short-Run, Short-run total costs (TC), Fixed costs (FC), Short-run variable
costs (VC)
Long-Run. All costs are Variable ‘No fixed costs
Fixed and Variable Costs
Fixed costs are those, which are fixed in volume for a given output. Fixed cost does
not vary with variation in the output between zero and any certain level of output. The costs
that do not vary for a certain level of output are known as fixed cost. The fixed costs include
cost of managerial and administrative staff, depreciation of machinery, building and other
fixed assets and maintenance of land, etc.
Variable costs are those, which vary with the variation in the total output. They are a
function of output. Variable costs include cost of raw materials, running cost on fixed capital,
such as fuel, repairs, routine maintenance expenditure, direct labour charges associated with
the level of output and the costs of all other inputs that vary with the output.
Total, Average and Marginal Costs
Total cost represents the value of the total resource requirement for the production of goods
and services. It refers to the total outlays of money expenditure, both explicit and implicit, on
the resources used to produce a given level of output. It includes both fixed and variable
costs. The total cost for a given output is given by the cost function.
The Average Cost (AC) of a firm is of statistical nature and is not the actual cost. It is
obtained by dividing the total cost (TC) by the total output (Q), i.e.,
TC
AC = Q = average cost

Marginal cost is the addition to the total cost on account of producing an additional unit
of the product. Or marginal cost is the cost of marginal unit produced. Given the cost function,
it may be
defined as
aTC
AC= aQ

These cost concepts are discussed in further detail in the following section. Total,
average and marginal cost concepts are used in economic analysis of firm's producti on
activities.

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Short-run and Long-run Costs

Short-run and long-run cost concepts are related to variable and fixed costs, respectively, and
often appear in economic analysis interchangeably. Short-run costs are those costs, which
change 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.
Long-run costs are, by implication, same as fixed costs. In the long-run, however, even
the fixed costs become variable costs as the size of the firm or scale of production increases.
Broadly speaking, the short-run costs are those associated with variables in the utilisation of
fixed plant or other facilities whereas long-run costs are associated with the changes in the
size and type of plant.
Cost-Output Relations
Cost-output relations play an important role in business decisions relating to cost
minirnisation, profit maximisation and optimisation of output. Cost-output relations are
specified through a cost function expressed as
T(C) = f(Q) (1)
where,
TC = total cost
Q = quantity produced
Cost functions depend on production function and market-supply function of inputs.
Production function specifies the technical relationship between the input, and the output.
Production function of a firm combined with the supply function of inputs or prices of inputs
determines the cost function of the firm. Precisely, cost function is a function derived from
the production function and the market supply function. 'Depending on whether short or
long-run is considered for the production, there are two kinds of cost functions: such as short-
run cost-function and long-run cost function. Cost-output relations in relation to the changing
level of output will be discussed here under both kinds of cost-functions.
Short-run Cost Output Relations
The basic analytical cost concepts used in the analysis of cost behaviour are total average
and marginal costs. The total cost (TC) is defined as the actual cost that must be incurred to
produce a given quantity of output. The short-run TC is composed of two major elements:
total fixed cost (TFC) and total variable cost (TVC). That is, in the short-run,
TC = TFC + TVC (2)
As mentioned earlier, TFC (i.e" the ·cost·of plant, building, equipment, etc.) remains
fixed in the short-run, where as TVC varies with the variation in the output.
For a given quantity of output (Q), the average total cost, (AC), average fixed cost
(AFC) and, average variable cost (AVC) can 'be defined as follows:

TC TFC + TVC
AC = Q = Q

TFC
AFC = Q
TVC
AVC = Q

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and AC = AFC +AVC (3)

Marginal cost (MC) is defined as the change in the total cost divided by the change in the total
output, i.e.,
∆TC aTC
MC = ∆Q or aQ
(4)
Since ∆TC = ∆TFC + ∆TVC and, in the short-run, ∆TFC = 0, therefore, ∆TC=∆TVC
Furthermore, under marginality concept, where ∆Q = 1,MC = ∆TVC.
Cost Function and Cost-output Relations
The concepts AC, AFC and AVC give only a static relationship between cost and output in the
sense that they are related to a given output. These cost concepts do not tell us anything
about cost behaviour, i.e., how AC, AVC and AFC behave when output changes. This can be
understood better with a help of numerical example.
Numerical Example

Output TVC TFC TC MC* ATC AVC AFC

0 0 8500 8500
100 2500 8500 11000 25 110 25 85
200 3800 8500 12300 13 62 19 43
300 4800 8500 13300 10 44 16 28
400 6000 8500 14500 12 36 15 21
500 7500 8500 16000 15 32 15 17
600 9500 8500 18000 20 30 16 14
700 12500 8500 21000 30 30 18 12
800 17000 8500 25500 45 32 21 10.6
900 22500 8500 31000 55 34 25 9.4
1000 32500 8500 41000 100 41 32.5 8.5

*MC is per 100

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From this schedule, the following inferences can be drawn Total cost is rising continuously
in all units of output. The rate of fall in marginal cost is at a faster rate and even it is rising
at an increasing rate. Average cost is falling continuously but the rate of fall is minimum
and even the rising rate is minimum. When compared to the rate of fall and rise, marginal
cost and average cost, marginal cost falls and rises sharply.

Figure 3.2
Cost Curves and the Laws of Diminishing Returns
We now return to the laws of variable proportions and explain it through the, cost
curves. The short-term laws of production, i.e., the laws of diminishing returns. Let us recall
the law: it states that when more and more units of a variable input are applied to those
inputs which are held constant, the returns from the marginal units of the variable input may
initially increase but will eventually decrease. The same law can also be interpreted in terms
of decreasing and increasing costs. The law can then be stated as, if more and more units of
a variable inputs are applied to the given amount of a fixed input, the' marginal cost initially
decreases, but eventually increases. Both interpretations of the law yield the same
information: one in terms of marginal productivity of the variable input, and the other, in
terms of the marginal cost. The former is expressed through production function and the
latter through a cost function.
Figure 3.2 represents the short-run laws of returns in terms of cost of production. As
the figure shows, in the initial stage of production, both AFC and AVC are declining because
of internal economies. Since AC = AFC + AVC, AC is also declining, this shows the operation of
the law of increasing returns. But beyond a certain level of output. while AFC continues to
fall, AVC starts increasing because of a faster increase in the TVC. Consequently, the rate of
fall in AC decreases. The AC reaches its minimum when output increases to 10 units. Beyond
this level of output, AC starts increasing which shows that the law of diminishing returns
comes in operation. The MC, curve represents the pattern of change in both the TVC and TC
curves due to change in output. A downward trend in the MC shows increasing marginal
productivity of the variable input mainly due to internal economy resulting from increase in
production. Similarly, an upward trend in the MC shows increase in TVC, on the one hand,

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and decreasing marginal productivity of the variable input, on the other.

Some Important Cost Relationships
Some important relationships between costs used in analyzing the short-run cost behaviour
may now be summed up as follows:
• As long as AFC and AVC fall, AC also falls because AC = AFC +AVC.
• When AFC falls but A VC increases, change in AC depends on the rate of change in
AFC and AVC then any of the following happens:
 If there is decrease in AFC and increase in A VC, AC falls,
 if the decrease on AFC is equal to increase in Ave, AC remains constant, and
 if the decrease in AFC is less than increase in A VC, AC increases.
• The relationship between AC and MC is of varied nature. It may be described as
follows:
When MC falls, AC follows, over a certain range of initial output. When MCis failing, the rate
of fall in MC is greater than that of AC This is because in case of MC the decreasing marginal
cost is attributed, : to a single marginal unit while; in case of AC, the decreasing marginal cost
is distributed overall the entire output. Therefore, AC decreases at a lower rate than MC.

Similarly, when MC increase, AC also increases but at a lower rate, the reason given in ‘the
above point. There is however a range of output over which this relationship does not exist.
When MC starts increasing, it increases at a relatively lower rate, which is sufficient only to
reduce the rate of decrease in AC, i.e., not sufficient to push the AC up. That is why AC
continues to fall over some range of output even, if MC falls. MC intersect AC at its minimum
point. This is simply a mathematical relationship between MC and AC curves when both of
them are obtained from the same TC function. In simple words, when AC is at its minimum,
then it is neither increasing nor decreasing it is constant. When AC is constant, AC = MC.

Optimum Output in Short-run

An optimum level of output is the one, which can be produced at a minimum or least average
cost, given the required technology is available. Here, the least ‘cost' combination of inputs
can be understood with the help of isoquants and isocosts. The least-cost combination of
inputs also indicates the optimum level of output at given investment and factor prices. The
AC and MC cost Curves can also be used to find the optimum level of output, given the size
of the plant in the short-run. The point of intersection between AC and MC curves determine
the minimum level of AC. At this level of output AC = MC. Production below or beyond this
level will be in optimal. If production is less than 10 units (Figure 3.2) it will leave some scope
for reducing AC by producing more, because MC < AC. Similarly, if production is greater than
10 units, reducing output can reduce AC. Thus, the cost curves can be useful in finding the
optimum level of output. It may be noted here that optimum level of output is not necessarily
the maximum profit output. Profits cannot be known unless the revenue curves of firms are
known.
Long-run Cost-output Relations
By definition, in the long-run, all the inputs become variable. The variability of inputs is based
on the assumption that, in the long run, supply of all the inputs, including those held constant
in the short-run, becomes elastic. The firms are, therefore, in a position to expand the scale
of their production by hiring a larger quantity of all the inputs. The long-run cost-output
relations, therefore, imply the relationship between the changing scale of the firm and the
total output; conversely in the short-run this relationship is essentially one between the total

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output and, the variable cost (labour). To understand the long-run costoutput relations (lnd
to derive long-run cost curves it will be helpful to imagine that a long run is composed of a
series of short-run production decisions. As a' corollary of this, long-run cost curves are
composed of a series of short-run cost curves. We may now derive the long-run cost curves
and study their' relationship with output.
Long-run Total Cost Curve (LTC)
In order to draw the long-run total cost curve, let us begin with a short-run situation. Suppose
that a firm having only one-plant has its short-mn total cost curve as given-by STCl in panel
(a) of Figure 3.3. In this example if the firm decides to add two more plants to its size over
time, one after the other then in accordance two more short-run total cost curves are added
to STCl in the manner shown by STC2 and STC3 in Figure 3.3 (a):. The LTC can now be drawn
through the minimum points of STCl, STC2 and STC3 as shown by the LTC curve
corresponding to each STC.
Long-run Average Cost Curve (LAC)
Combining the short-run average cost curves (SACs) derives the long-run average cost curve
(LAC). Note that there is one SAC associated with each STC. Given the STC 1 STC2, and STC3
curves in panel (a) of Figure 3.3, there are three corresponding SAC curves as given by SAC 1
SAC2 arid SAC3 curves in panel (b) of Figure 3.3. Thus, the firm has a series of SAC curves, each
having a bottom point showing the minimum SAC. For instance, C1Q1 is the minimum AC
when the firm has only one plant. The AC decreases to C2Q2 when the second plant is added
and then rises to C3Q3after the inclusion of the third plant. The LAC caru be drawn through
the bottom of SAC1 SAC2 and SAC3 as shown in Figure·3.3 (b) The LAC curve is also known as
‘Envelope Curve' or 'Planning Curve' as it serves as a guide to the entrepreneur in his planning
to expand production.
Quantity Total Costs of Total Cost of Total Costs = TCL Average Total
Labor Machines + TCM Costs = TC/Q
11 381 254 Rs635 58
12 390 260 650 54

13 402 268 670 52

14 420 280 700 50
15 450 300 750 50
16 480 320 800 50
17 510 340 850 50
18 549 366 915 51
19 600 400 1,000 53
20 666 444 1,110 56

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The SAC curves can be derived from the data given in the STC schedule, from STC
function or straightaway from the LTC-curve. Similarly, LAC can be derived from LTC-
schedule, LTC function or from LTC-curve. The relationship between LTC and output, and
between LAC and output can now be easily derived. It is obvious. from the LTC that the long-
run cost-output relationship is similar to the short-run cost-output relationship. With the
subsequent increase in the output, LTC first increases at a decreasing rate, and then at an
increasing rate. As a result, LAC initially decreases until the optimum utilisation of the second
plant and then it begins to increase. From these relations are drawn the 'laws of returns to
scale'. When the scale of the firm expands, unit cost of production initially decreases, but it

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ultimately increases as shown in Figure 3.3 (b).

Long-run Marginal Cost Curve
The long-run marginal, cost curve (LMC) is derived from the short-run marginal cost curves
(SMCs). The derivation of LMC is illustrated in Figure 3.4 in which SAC3'and LAC are the same
as' in Figure 3.3(b). To derive the LMC3, consider the points of tangency between SAC3 and
the LAC, i.e., points A, Band C. In the long-run production planning, these points determine
the output levels at the different levels of production. For example, if we draw perpendiculars
from points A, Band C to the X-axis, the corresponding output levels will be OQ1 OQ2 and OQ3
The perpendicular AQ1 intersects the SMC1 at point M. It means that at output BQ2, LMC, is
MQ1. If output increases to OQ2, LMC rises to BQ2. Similarly, CQ3 measures the LMC at output
OQ3. A curve drawn through points M3B and N, as shown by the LMC, represents the
behaviour of the marginal cost in the long run. This curve is known as the long-run marginal
cost curve, LMC. It shows the trends in the marginal cost in response to the change in the
scale of production.
Some important inferences may be drawn from Figure 3.4. The LMC must be equal to
SMC for the output at which the corresponding SAC is tangent to the LAC. At the point of
tangency, LAC = SAC. For all other levels of output (considering each SAC separately), SAC >
LAC. Similarly, for all levels of outout corresponding to LAC = SAC, the LMC = SMC. For all
other levels output, i:he LMC is either greater or less than the SMC. Another important point
to notice is that the LMC intersects LAC when the latter is at its minimum, i.e., point B. There,
is one and only one short-run plant size whose minimum SAC coincides with the minimum
LAC. This point is B where, SAC2 = SMC2 = LAC = LMC.
Optimum Plant Size and Long-run Cost Curves
The short-run cost curves are helpful in showing how a firm can decide on the optimum
utilisation of the plant-which is the fixed factor; or how it can determine the least-cost output
level. Long-run cost curves, on the other hand, can be used to show how the management
can decide on the optimum size of the firm. An Optimum size of a firm is the one, which
ensures the most efficient utilisation of resources. Given the state: of technology overtime,
there is technically a unique size of the firm and lever of output associated with the least cost
Concept. This uriique size of the firm can be obtained with the help of LAC and LMCInFigur
3.4 the optimum size consists of two plants, which produce OQ2 units of a produd, at
minimum long-run average cost (LAC) of BQ2.

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The downtrend in the LAC indicates that until output reaches the level of OQ2, the firm
is of non-optimal size. Similarly, expansion of the firm beyond production capacity OQ2 causes
a rise in SMC as well as LAC. It follows that given the technology, a firm trying to minimise its
average cost over time must choose a plant which gives minimum LAC where SAC = SMC =
LAC = LMC. This size of plant assures most efficient utilisation of the resource. Any change in
output level, i.e., increase or decrease, will make the firm enter the area of in optimality.

Possible Size-Cost Relations

Determinants of the Shape of the Long-Run Cost Curve

The law of diminishing marginal productivity does not hold in the long run since all inputs are
variable.
The shape of the long-run cost curve results from the existence of economies and
diseconomies of scale

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 Economics for Decision Making, Module-3

Break Even Analysis

Introduction
An important part of running a company is the determination of how the company should be
financed and how the prices of the products the company sells should be set.
Break-even analysis is a study of Costs, Revenue and sales of a firm and finding out the volume
of sales where the firm’ costs and revenues will be equal. The breakeven point is that level
of sales where the net income is equal to zero
The Breakeven point is the zone of no profit and no loss, as the cost equal revenues
Breaking even is when a firm is just covering its costs, making neither a profit nor a loss.
Variable cost – which vary with the level of activity taking place. These would include the
costs of the raw materials used, the fuel needed for vans or equipment & the wage costs of
people working on the machines
Fixed cost – which remain constant over a given range of activity. These would include the
rent of the premises, insurance on the firm’s vehicles & rates
Break-Even Analysis
Total Costs = Fixed Costs + Variable Costs
Total Variable Costs= Variable costs per unit x number of units produced
Total Revenue is the money received by a firm from the sale of its goods or services
Total Revenue= Selling price x Quantity sold
Contribution
This is a measure of the amount of money that each units sold contributes towards,
covering the fixed cost of a business. Once FC are covered all further contribution is profit.
Break-Even Analysis
Contribution = Total Revenue – Variable cost
Contribution per unit: Selling price per unit – Variable costs per unit
Break-Even: This is the level of output & sales at which a firm generate just enough income
to cover fixed & variable costs, earning neither a profit nor a loss
If the selling price of a product exceeds its variable cost, each unit sold will earn a
contribution towards fixed costs. If total contribution covers fixed costs, the firm breaks
even
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Break-Even Analysis: Break-even point is the level of sales at which the firm breaks even.
Fixed Cost
Break-Even = Contribution Per Unit

Margin of Safety
This is the difference between sales volume & break-even point, & is the amount by which
sales can fall before a firm incurs a loss
Break-Even Charts
Out put in Total Revenue (price Rs 4 Total fixed Total variable Total
units per Units) cost cost cost
0 0 300 0 300
100 400 300 300 600
200 800 300 600 900
300 1200 300 900 1200
400 1600 300 1200 1500
500 2000 300 1500 1800
600 2400 300 1800 2100

Break-even analysis is very commonly presented by means of break-even charts. Break-

even charts are also known as profit-graphs. A break-even chart prepared on the basis of
example 1 above is given in Figure 5.2. In this figure, units of product are shown on the
horizontal axis OX while revenues and costs are shown on the vertical axis OY. The fixed costs
of Rs. 10,000 are shown by a straight line parallel to the horizontal axis. Variable costs are
then plotted over and above the fixed costs. The resultant line is the total cost line, combining
both variable and fixed costs. There is no variable cost line in the graph. The vertical distance
between the fixed cost and the total cost lines represents variable costs. The total cost at any
point is the of Rs. 10,000 plus Rs. 2.00 per unit of variable cost multiplied by the number of
units sold at that point. Total revenue at any point is the unit price of Rs. 4.00 multiplied by
the number of units sold. The break-even point corresponds to the point of intersection of
the total revenue and the total cost lines. A perpendicular from the BEP to the horizontal axis
shows the break-even point in units of the product. Dropping a perpendicular from BEP to the
vertical axis shows the break-even sales value in rupees. The firm would suffer a loss at any
point below the BEP. Total costs are more than total revenue. Above the BEP, total revenue
exceeds total costs and the firm makes profits. Since profit or loss occurs between costs and
revenue lines, the space between them is known as the profit zone, which is to the right of
the BEP, and the loss zone, which is to the Lenth of the BEP. The following Figure 5.2 shows
Break-even Chart.

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The break-even chart remains where the BEP is measured in terms of sales value
rather than in physical units. The only difference is that the volume on the X-axis is measured
in terms of sales value. In that case, a perpendicular from the point BEP to either axis would
show the break-even rupee sales value. The same type of chart could be used to depict the
BEP in relation to full capacity. In this case the horizontal axis would represent the percentage
of full capacity, instead of physical units or the sale value.
Assumptions
1. All costs are either variable or fixed over the entire range of the volume of production.
But in practice, this assumption may not hold well over the entire range of production.
2. All revenue is variable in nature. This assumption may Lot be valid in all cases such as

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 Economics for Decision Making, Module-3

the case where lower prices are charged to large customers.

3. The volume of sales and the volume of production are equal. The total products,
produced by the firm, are sold and here is no change in the closing inventory. In
practice, sales and production volumes may differ significantly. However, these
assumptions are not so unrealistic so as to weaken the validity of the break-even
analysis.
4. In the case of multi-product firms, the product-mix should be stable. For multi-product
firm, the BEP is determined by dividing total fixed costs by an average ratio of variable
profit, also called contribution to’ sales. If each product has the same contribution
ratio, the BEP is not affected by changes in the product-mix.
However, if different products have different contribution ratios, shift in the product-mix may
cause a shift in the break-even point. In real life, the assumption of stable product-mix is
somewhat unrealistic
Managerial Uses of Break-even Analysis
To the management, the utility of break-even analysis lies in the fact that it presents a picture
of the profit structure of a business firm. Break-even analysis not only highlights the areas of
economic strength and weaknesses in the firm but also sharpens the focus on certain in
leverages which can be operated upon to enhance its profitability. Through break-even
analysis, it is possible for the management to examine the profit structure of a business firm
to the possible changes in business conditions. For example, sales prospects, changes in Cost
structure, etc. Through break-even analysis, it is possible to use managerial actions to
maintain and enhance profitability of the firm. The break-even analysis can be used for the
following purposes:
• Safety margin
• Volume needed to attain get profit
• Change in price Change in price
• Expansion of capacity
• Effect of alternative prices
• Drop or add decision
• Make or buy decision
• Choosing promotion-mix
• Equipment selection
• Improving profit performance
• Production planning
Safety Margin
The break-even chart helps the management to know the profits generated at the various
levels of sales. But while deciding the volume at which the firm would operate, apart from
the demand, the management should consider the safety margin associated with the
proposed volume. The safety margin refers to the extent to which the firm can afford a decline
in sales before it starts occurring losses. The formula to determine the safety margin is:

(Sales – BEP) x 100

Safety Margin = Sales

Example : Assume that our sales in Example 1 are 8,000 units.

(8,000-5,000) x 100

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Safety Margin = 8,000 = 37.5%

Before incurring a loss, a business firm can afford to lose sales up to 37.5 per cent of the
present level. A decreasing safety margin indicates that the firm's resistance capacity to avoid
losses has become poorer. A margin of safety can also be negative. A negative safety margin
is the percentage increase in sales necessary to reach the BEP in order to avoid losses. Thus,
it reveals the minimum extent of effort in terms of sales expected by the management.
Suppose in the same example sales are us low as 4,000 units. The safety margin would be:
(4,000-5,000) x 100
Safety Margin = 4,000

= 25%
In other words, the management must strive to increase sales at least by 25 per cent to
avoid losses.
Volume Needed to Attain Target Profit
Break-even analysis is also utilised for determining the volume of sales, necessary to achieve
a target profit. The formula for target sales volume is:
Fixed costs + Target profit
Target Sales Volume = Contribution margin per unit
.
Example : Continuing with the same example, if the desired profit is Rs. 6,000, the target
sales volume would be calculated as follows:
10,000 + 6,000
= 8000 units
2
Change in Price
The management is also faced with a problem whether to reduce the prices or not. The
management will have to consider a number of points before taking a decision related to the
change in the prices. A reduction in price results in a reduction in the contribution margin as
well. This means that the volume of sales will have to be increased to maintain the previous
level of profit. The higher the reduction in the contribution margin, the higher will be the
increase in sales needed to maintain the previous level of profit. However, reduction in prices
may not always lead to an equal increase in the sales volume, which is affected by the
elasticity of demand. But the information about elasticity of demand may not be easily
available. Breakeven analysis helps the management to know the required sales volume to
maintain the previous level of profit. On the basis of this knowledge and experience, it
becomes much easier for -the management to judge whether the required increase it sales
will be feasible or not. The formula to determine the new sales volume to maintain the same
level of profit, given a reduction in price, would be as under:
FC + P
Qn = SPn - VC
where Qn = New volume of sales
FC = Fixed cost
P = Profit
SPn = New selling price
VC = Variable cost per unit (n denotes new)
Example : Continuing with the same example 6, if we propose a reduction of 10 per cent

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in price from Rs. 4.00 to Rs. 3.60, the new sales volume needed to maintain the previous profit
of Rs. 6,000 will be:
10, 000 + 6,000 16, 000
3.60 – 2.00 = 1.60 = 10,000 units

This shows that there is an increase of 2,000 units or 25 per cent in sales. The
management can also easily decide whether this increase in sales volume is profitable for the
business firm or not.
If a firm proposes the price increase, the question to be considered is by how much the
sales volume should decline before profitable effect of the price increase gets eliminated.

Example: If the firm in example 6 considers an increase in price by 12Y2per cent to Rs.
4.50, the new volume to maintain the old profit would be:
10, 000 + 6,000 16, 000
Q2= 4.50 – 2.00 = 2.50 = 6,400 units

In other words, if the fall in sales, due to an increase in price, were less than 1,600 units
or 20 per cent, it would be profitable for the firm to increase the price. But if the decline were
more than 1,600 units, the proposed price increase would reduce the profit.
Limitation of Break-Even analysis
It is static in character: In Breakeven analysis, we keep everything constant. The selling price
is assumed to be constant and cost function is linear in practice it will not be so.
Projection of future with the past is not correct
The profits are a function of not only output relationship is linear is true
Questions
3 Marks
1) What is Cost?
2) What is Total Fixed Cost?
3) What is Total Variable Cost?
4) What Marginal Cost?
5) What is Average Cost?
23) What is Average Revenue?
24) What is Marginal Revenue?
25) What is Production?
26) What is Production Function?
27) What is Total Product (TP)?
28) What is Average Product (AP)?
29) What is Marginal Product (MP)?
30) What is law of variable proportions?
31) What is law of returns to scale?
32) Define producer’s equilibrium?
33) What are Isoquants?
34) What is ISOQUANT Schedule?
35) What is Isocost line?
36) What is MRTS?
37) What is Isoquant Map?
38) What is Economies of Scale?

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39) What is diseconomies of scale?

40) What is Profit?
41) What do you mean by break even analysis?
42) What is Break-even Point?
43) What is Contribution?
44) What is Profit-volume ratio?
45) What is Margin of safety?
46) What is Contribution Margin Ratio?
7 Marks
1) Explain different types of short-run costs.
2) Write a Short note on Long-run average cost curve
3) Why Long-run average cost curve is “U” shaped?
5) Explain different concepts of revenue with example
6) What are the factors affecting production?
7) Explain relationship between Average Product and Marginal Product
8) Explain Isoquant schedule
9) Explain ISOQUANT Curve
10) Explain properties of Isoquant Curve.
11) Explain internal economies of scale.
12) Explain external economies of scale.
13) Explain internal diseconomies of scale.
14) Explain external diseconomies of scale.
15) What is the Use of Break-even analysis in decision making?
16) What are the limitations of Break-even Analysis?
10 Marks
1) What are the Different types costs?
3) Explain different types of factors of production
4) Explain short-run Production Function?
5) What are the three stages of law of variable proportions? Explain with example
6) Explain Producers equilibrium (Isoquant analysis).
7) What are the three stages of law of returns to scale? Explain with example
8) Explain types of economies of scale
9) Explain diseconomies of scale.
10) Explain different types of profits?
11) What are the functions of the profit?
12) What is Break even Chart? Draw a breakeven chart and explain its elements.

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