MEANING OF PRODUCTION

Production means transformation of inputs into output. For instance, a sugar factory uses such
inputs as raw-material viz, sugarcane, labour, capital such as machinery and factory building to
produce sugar.
The process of transformation can be:
(1) A change in form (ie., cloth into garment)
(2) A change in space (ie., by road or rail transportation)
(3) A change in time (ie., by warehousing or cold storage).
Accordingly, production may be defined as 'transformation of inputs leading to creation or
addition of value in a good'. Chart below illustrates the Production Process

Thus we see that production process involves of inputs into outputs so that the value of output is
greater than the value of inputs. In other words, production means creation or value addition.

FACTORS OF PRODUCTION
The inputs used in production have been traditionally called as factors of production, also
called Agents of Production.
Economists have identified five factors of production as under:
1. Land- Land is the most basic factor. It includes all resources gifted by nature. Thus land does
not mean only the land surface but also includes all natural resources underneath or above the
land surface. For example, land covers the entire land surface, all material resources beneath the
ground, forests, hills and mountains, rivers and seas, water, air, light and rains.
2. Labour- Labour is the active factor of production. In economics, any work done by body or
mind for remuneration is called labour. If money or reward is not paid for any type of labour,
manual or mental, it is not labour in economics.
3. Capital- Capital does not mean money alone. In economics, capital refers to man-made
resources. It is also called 'produced means of production'. Thus, all those means/factors that
have been produced by human effort and which are being further used for production
activity is capital. As such, machinery, building, plant and equipment, roads, railways, bridges
are all capital.
4. Organization- Production is possible only by coordinating various inputs. There will be larger
production if all the inputs are properly coordinated. For this purpose, there is an organizer who
does the work of coordination. A manager generally does the job of coordination or organization.
5. Enterprise- Enterprise, also called entrepreneurship means taking or assuming risk of a
business. When a person or a business firm makes investment in any sphere, there is risk of loss
or profit. An entrepreneur is a person who performs this function of risk-bearing and is prepared
to take the loss if it materializes. Entrepreneurship involves a variety of activities viz.
(1) Deciding to undertake a particular activity
(2) Bearing the risk and uncertainty of production.
(3) Undertaking innovation.

Characteristics of Factors of Production

Certain characteristics of factors of production are worth noting:
1. Complementarity: All factors of production are complementary to each other. If any one
factor is absent, production is not possible.
2. Substitutability: Factors of production are also substitutes for each other. But this
substitutability is limited. That is, one factor of production can replace another factor to
some extent and not fully. This can be called limited substitutability.
3. Specificity: Specificity means that some factors can be used for a specific product and not
for others. For instance, some land is good only for producing wheat and nor for paddy.
Likewise, labourer or machine can also be specific for a particular product or industry. If factors
are specific, this reduces their mobility.
4. Mobility: Mobility is yet another feature of factors of production. It means ability to move.
There are two types of mobility: (i) Occupational, and (i) Spatial or Locational.
Occupational mobility means ability of a factor of production to move from one occupation
business or industry to another. For instance, a laborer has Occupational mobility if he can
shift from a textile mill to a jute mill. Unskilled labor has greater mobility than skilled labor.
Knowledge workers generally move from one industry to another with ease. Likewise, an
industry specific machine has lower occupational mobility than a multi-purpose machine.
Specificity or specialization reduces occupational mobility.
Spatial Mobility means ability to move from one place to another. Land does not have spatial
mobility but labor has, workers often moving from one place to another for employment. Plant,
machinery and equipment have limited mobility. Capital in the form of money has considerable
spatial mobility. Entrepreneurship also has lesser spatial mobility since an entrepreneur generally
prefers to stay at a place where he has established himself. He feels comfortable there and does
not easily shift to another place.

Ch 11 Theory of Production and Supply Analysis

INTRODUCTION
Production is the process whereby inputs are transformed into outputs. The economic unit that
performs the production activity is known as the producer or the firm. The primary aim of
each rational producer or a firm is to maximize its profits. Profits for a firm depend upon its
costs of the inputs used and the revenue derived from the sale of output. Since production is
possible with the help of different proportions of different inputs. In this endeavor, it manipulates
the different proportions in which the different factors can be used. It may also change the scale
of production, if it helps the firm in realization of his objective of 'Least cost combination'.
Production theory, therefore, concerns itself with the problem of combining various factors
inputs, given the state of technology, in order to produce a stipulated output at the minimum cost.
According to Ferguson, "The theory of production consists of how the producer, given the
state of technology combines various inputs to produce a definite amount of output in an
economically efficient manner."

PRODUCTION FUNCTION
A Production Function is a physical relation between a firm's inputs of resources and its output
of goods and services per unit of time. Inputs are factors of production like raw materials, labour,
capital, organization, fuel etc. Quantity of production is output. This output is the result of inputs.
Thus, the functional relationship between physical inputs and physical output is called
Production Function.
Definitions
According to Prof. Leontief, "A Production Function is a description of the quantitative
relationship between the inputs observed and the outputs emerging from a particular production
process."
Prof. Watson defines it as, "Production means the transformation of inputs into outputs. The
production function is the name for the relationship between the physical inputs and the physical
outputs of a firm."
The production function in its simple and general form is given below:

Where P is the rate of output of a good or service and a, b, c, d etc., are different factors of
production used per unit of time. Production function is a technical relationship between two
factors of production and their output, while the technique and other factors remain constant.

Production function can be explained in Fig. Labor is measured on X- axis and capital on Y-axis.
In the beginning 2 unit of labour and 2 unit of capital produce 5 unit of output, with 4 units of
labor and 4 units of capital output increases to 10 units and with 8 unit of labour and 8 units of
capital production is 22 units. Joining all these production points we get Production Process
Path. In this way various Production Process paths can be drawn such as 1 and 3. In path 1 more
labour and less of capital is used and in Path 3 more of capital and less of labour is used.

TYPES OF PRODUCTION FUNCTION

Economic Theorists analyze two kinds of input-output relations in production function: First the
relation where quantities of some inputs are fixed while quantity of other inputs vary; second
where all the inputs are variable and the relationship is between changes in the amounts of all
inputs and the resulting outputs.
Production function can be divided into two parts.
1. Short Run Production Function
In the short run, increase the quantities of one input while keeping the quantities of other
inputs constant in order to have more output. This aspect of the production function is known
as the law of variable proportions. When a producer brings a change in his production by
changing only one factor of production and as a result there is a change in the proportion
of combination of factors of production, then this proportional relationship between production
(output) and factors of production (Inputs) is referred to as Law of Returns to a Factor.

2. Long Run Production Function

In the long run, it is possible for a firm to change all inputs up or down in accordance with its
scale. This is known as returns to scale. When a producer changes all the factors of
production in the same proportion, the proportional relationship between production and
factors of production is referred to as Law of Returns of Scale.
Two types of Production Function can be shown in the following chart :

LAWS OF RETURNS
Laws of Returns are classified into two categories:

LAW OF VARIABLE PROPORTIONS

In short period, when one input is variable and all other inputs are fixed, the firm's production
function exhibits the law of variable proportions. If the number of units of a variable input is
increased, keeping other inputs constant, how output changes is the concern of this law. The law
states that as the quantity of a variable factor is increased by equal doses, keeping the
quantities of other factors constant, the total production at first increases more than
proportionately, then equi-proportionately and finally less than proportionately. When
more and more units of the variable factor are used, holding the quantities of fixed factors
constant, a point is reached beyond which the marginal product, then the average and finally the
total product will diminish. The law of variable proportions (or the law of non-proportional
returns) is also known as the law of diminishing returns.
Definitions
According to Leftwitch, "The law of variable proportions states that if the input of one resource
is increased by equal increments per unit of time, while the other inputs of other resources are
held constant, total input will increase, but beyond some point, the resulting output increases will
become smaller and smaller."
In the words of Samuelson, "The law states that an increase in some inputs relative to other
fixed input will, in a given state of technology, cause total output to increase; but after a point the
extra output resulting from the same addition of extra inputs is likely to become less and less."
Prof. Stigler defines, "If the quantity of one productive factor is increased by equal increments,
the quantities of other productive factors remaining fixed, the resulting increments of product
will decrease after a point."

Assumptions
The law of variable proportions holds good if the following assumptions are fulfilled:
(1) One of the factors is variable, while all other factors are fixed.
(2) All units of the variable factor are homogeneous. It means all its units are equally efficient.
(3) The proportion of the factors of production can be changed. For example, 2 hectares of
land with one laborer or 2 hectares of land with 4 laborers etc.
(4) Level of technology and methods of production are constant.
(5) It is a short period operation. The law does not apply in long period when all factors
become variable.
Explanation of the Law – law of variable proportions can be explained with the help of Table.
When on the fixed input the land of 4 acres, units of the variable factor labor are employed, the
resultant output is obtained. First three columns of the table reveal the production function.
The average and marginal product columns are derived from the total product column. The
average product is obtained by dividing the column (3) by the column (2). The marginal
product is the addition to total product by employing an extra laborer.
An analysis of the table shows that total, average and marginal products increase in the
beginning, reach a maximum and then start declining. The total product reaches its
maximum when 7 units of labor are employed and then it declines. The average product
continues to rise till the 4th unit while the marginal product reaches its maximum at the 3rd
unit of labor, then it also falls. The marginal product starts declining first, the average
product follows it and the total product is the last to fall.

Diagrammatic Representation

In this figure quantities of AP, MP and TP are shown on y-axis and number of laborers on x-axis.
TP is the total product curve. The TP curve first rises: at an increasing rate and then reaches
the highest point at an output then increases at a decreasing rate and then starts falling
slowly. At points a the slope of TP is the highest, at b it is less than a and at c it becomes zero.
The MP curve reaches its maximum point at d when the slope of the TP curve is maximum
at point a, the maximum point on the AP curve is e where it coincides with b on TP curve,
from where the TP starts a gradual rise. When the TP curve reaches its maximum point c, the
MP curve becomes zero at point f, and when TP starts declining, the MP becomes negative.
Three Stages of the Law
1. First Stage - In this stage, average product reaches the maximum and equals the marginal
product when 4 laborers are employed, as shown in Table. This stage is portrayed in Fig. from
the origin to point where the MP and AP curve meet. In this stage, total output increases at an
increasing rate and the total product curve also increases rapidly. Thus, this stage relates to
increasing average returns.
The main reason for increasing returns in first stage is that in the beginning the fixed factors are
larger in quantity than the variable factors. When more units of variable factors are applied to
a fixed factor, the fixed factor is used more intensively, division of labor and specialization
will be possible on fixed factors, being indivisible they will be put to maximum use, thereby
the production increases rapidly. Hence, the law of increasing returns sets in.

2. Second Stage - The second stage goes from the point where the average output is maximum
to the point where the marginal output is zero. After having attained the optimum
combination of the fixed inputs and the variable input, if the firm increases still further the
quantity of the variable input, the total output increases but only at a diminishing rate. This
is the crucial stage for the firm, because it is within this stage that the firm determines its level
of actual operation. In Table the second stage of the law of variable proportions operates
between the stage when 5 and 8 units of laborers are employed. In Fig, the second stage lasts
till point f is reached.

3. Third Stage - In this stage, the total product starts declining and the marginal product
becomes negative. This is also known as the stage of negative returns. In the Table, the
employment of the 9th worker actually causes a decrease in total output from 22 to 21 and makes
the marginal product minus 1. In Fig. the third stage operates beyond the point 'f' where the
MP curve is below the x-axis. Here, the workers are too many in relation to the available land,
making it absolutely impossible to cultivate it. In this stage, the total output, after having
reached the maximum of c at the beginning of its stage, begins to fall. Thus, in this stage, the
total output, average output and marginal output all fall.

The Stage of Operation or the Best Stage of Operation

During the first stage, the marginal output rises and ultimately begins to fall. The average output
on the other hand rises. During this stage, the quantity of the fixed factor is more relative to
the quantity of the variable factor, so that if some units of fixed factors are withdrawn, the
total product will rise, the marginal product of the fixed factor is negative. No producer
will like to operate in this stage, even if the fixed factors are supplied to him free of cost
because the fixed factors only bring in negative marginal returns.
Similarly, during the 3rd stage, the marginal product of the variable factor becomes
negative, implying that a producer will not like to operate in this stage also. The first and the
third stage are also known as stages of economic absurdity or 'economic nonsense’. A
producer will always seek to operate in the second stage. At which point the producer will
operate in this stage, will depend upon the prices of the factors.

Causes of The Operation of Law of Variable Proportion

1. Indivisibility of Factors-The main reason for the stage of increasing returns is
indivisibility. Indivisibility means that due to technological requirements, a minimum
amount of resources must be employed whatever the level of output. Thus, as more units of
variable factor are employed to work with an indivisible fixed factor, output greatly
increases due to fuller and more effective utilization of resources.
2. Division of Labour or Specialisation - In the beginning, due to sufficient quantity of variable
factor, it becomes possible to introduce specialization or division of labor which results in
higher productivity. The greater the quantity of variable input, the greater the scope of
specialization. Hence greater will be the level of productivity.
3. Imperfect Substitute - This reason is mainly responsible for the stage of diminishing
returns. One factor can not be used in place of the other factor. When fixed and variable
factors are not combined in an appropriate ratio, marginal returns of variable factor begins to fall.
4. Change in Factor Ratio - The main cause of the operation of the stage of diminishing
returns is that one of the factors of production is variable while others are fixed. When this
variable factor is used with fixed factors, their ratio compared to variable factor fall. When an
additional unit of a variable factor has to be produced with the help of a relatively less units
of fixed factor, the marginal return of the variable factor begins to diminish.

LAW OF DIMINISHING RETURNS

This law states that when with a fixed amount of any factor of production, successive units of
any variable factor of production are employed then total output will increase but at a
diminishing rate.
Definitions
According to Boulding, "As we increase the quantity of any one input which is combined with
fixed quantity of other inputs, the marginal physical productivity of the variable inputs must
eventually declines."
In the words of Prof. Benham "As the proportion of one factor in a combination of factors is
increased, after a point the marginal and average products of that factor will diminish."
Mrs. Joan Robinson defines, "The law of diminishing returns states that with a fixed amount of
any one factor of production successive increase in other factor will after a point yield a
diminishing increase of output."
Assumptions of the Law
The law of diminishing returns is based on the following assumptions:
1. Short Run: The law is based on the assumption of short-run. Because in the long-run, all
factors are variable.
2. Fixed and Variable Factors: Some of the factor inputs are fixed and some are variable.
3. Homogeneous: It is assumed that the different units of a variable factor of production are
homogeneous and identical in quality and quantity.
4. Change in the Factor Proportions: The law assumes the proportions in which the factors of
production are put to use are changeable. It is possible to change the ratio of the variable
factor to the fixed factors of production.
5. Constant Technology: The state of technology is given and remains constant.
6. No Change in Price: The law can be stated in terms of costs only if the prices of variable
inputs and the price of output remain constant.

Explanation – The law can be explained in two ways:

(i) In terms of Diminishing Returns;
(ii) In terms of Increasing Costs.
(i) In Terms of Diminishing Returns:
The table is prepared on the assumption that a farmer produces with the help of two factors i.e.
land and labour. Land is a fixed factor and labour is a variable factor. With a view to increase
his production, the farmer employs more units of variable factor on a given piece of land.

It is clear from table that as more and more units of labour are applied to a given plot of land
(a) total output increases at a diminishing rate (b) marginal product goes on diminishing.
In Fig Labour is shown on x-axis and marginal produce on y-axis. The DR curve represents
diminishing returns. It slopes downward from left to right. It indicates that as more and more
laborers are employed, each successive laborer yields less marginal returns than its
proceeding worker.
(ii) In Terms of Increasing Costs: Law of diminishing returns also known as the law of
increasing costs. If returns are diminishing, costs are increasing. When more and more units of
labour are applied to a plot of land, their marginal returns diminish, then there is a
tendency for the average cost of production to increase. That is why in terms of cost, this law
is called the law of increasing cost.

Table shows land as a fixed factor. Units of labor have been considered as a variable factor.
Average cost of production of first unit is Rs. 2, when second unit of the variable factor is used,
average cost goes upto Rs. 2.20 and with the application of third, fourth and fifth units, average
cost rises to 2.50, 2.80 and 3.30 respectively. In this way average cost is increasing with every
addition to the variable factor used.
In figure, the upward sloping IC curve represents increasing cost. It shows that average cost is
increasing with the use of more and more variable factors or production.

Causes of the Operation of the Law of Diminishing Returns.

Main causes of the operation of the law of diminishing returns are as under:
1. Fixed Factors of Production: When additional unit of a variable factor has to be produced
with help of a relatively fixed factor, then marginal return of variable factor begins to diminish.
2. Beyond the Optimum Capacity: The optimum point of production is reached when the
available factors of production are being put to their best use. The combination of the fixed
factors and the variable factors is in the best proportions. If this combination is disturbed,
every additional unit of a variable factor will bring in less than proportionate return ie.,
marginal return will fall.
3. Imperfect Substitute: Upto a certain stage, factors of production can be substituted for each
other. But beyond a limit, it is not possible to substitute these factors of production. Beyond
the optimum limit, the factors become imperfect substitutes for each other. It is at this stage the
law of diminishing returns sets in.

LAW OF INCREASING RETURNS

Law of Increasing Returns states that when more of a variable factor is employed, total
production increases at a higher rate than the rate of increase in the employment of a
variable factor.
The law was propounded by seventeenth century economist Antonia Seera. The law rests upon
the idea that when the size of production is increased, productivity of factor inputs also
increases. Total production increases with the employment of every additional unit of a variable
factor. The law when explained in terms of costs is called 'The Law of Diminishing Costs'. If
returns are increasing, costs are decreasing.
Definitions
According to Marshall, "An increase of labour and capital leads generally to improved
organisation, which increases the efficiency of the work of labour and capital. Therefore, in those
industries which are not engaged in raising raw produce, an increase in labour and capital
generally gives a return increased more than in proportion."
According to Benham, "As the proportion of one factor in a combination of factors is increased,
up to a point, the marginal productivity of the factor will increase."
In the words of Mrs Joan Robinson, "The law of increasing returns states that when an
increased amount of any factor of production is devoted to certain use, it is often the case that
improvements in organization can be introduced which will make physical units of the factors
(men, acres or money capital) more efficient so that an increase in the physical amount of
factors."
Assumptions
The law of increasing returns rests upon the following assumptions:
(1) There is scope of improvement in technique of production and organization of production.
(2) At least one factor of production is indivisible.
(3) Some factors of production are supposed to be divisible.

Explanation of the Law – The law can be stated in terms of:

(i) Increasing Returns (ii) Diminishing Costs.
(i) In Terms of Increasing Returns-

It is clear from this table that when 1st unit of variable input (labour) is put to work with 2 units
of capital which is a fixed factor of production, the total production of pens is 10 dozen. When an
additional unit of labor is employed, total production increases to 25 dozen. In this way, marginal
produce of the 2nd unit is (25–10=15 dozen). Similarly, with the use of 3rd, 4th and 5th units of
labor marginal produce increases further. It becomes evident that due to increased employment
of labor, marginal produce increases and total produce increases at the increasing rate.

The IR curve which rises upward from left to right, depicts increasing returns. It shows that
as more and more units of the variable input i.e. labour are put to work, their marginal
produce goes on increasing. This is the law of increasing return.
(ii) In Terms of Diminishing Costs - According to the law of increasing returns, when total
output increases, average cost per unit goes on diminishing.

Average cost can be calculated by dividing total cost by total produce. As we go on using more
and more units of labour, average cost goes on falling. When 1st unit of labor is used, average
cost is Rs. 10.00 with every increase in variable factor of production, average cost is falling from
10 to Rs. 8, 6.66, 5.71 and 5.00 respectively.

'DC' is the average cost curve falling downward from left to right. It shows that average cost
is falling as we use more and more doses of the factor labor.

Causes of Operation of the Law

The law of increasing returns operates due to following reasons:
1. Indivisibility of Factors: In the production process, there are some indivisible factors
engaged. So other factors are required to a certain extent to utilise these factors fully.
Before the stage of their full utilisation, every increase in variable factor will increase
marginal and average products and the average cost will come down.
2. Specialization: When a large number of workers are employed to do a job, it becomes
possible to divide a job in different parts. Each person is held responsible for a particular part
only. This is known as the process of division of labour, which results in specialisation. Every
person becomes expert at his job i.e., efficiency increases. Higher efficiency implies more
production.
3. Fixed Factors: The cost of fixed factors remains the same whatever the size of output may be.
So,when a few variable factors are used with these fixed factors and production is on small scale,
average cost is higher. But when more of variable factors are applied to these fixed factors to
increase the size of production, average cost falls.
4. Economies of Large Scale Production: When more of variable factors are used and size of
production increases, many economies of large scale production occur. For example, when
production is done on a large scale, raw material can be purchased from wholesale markets
at cheaper rates. This reduces costs. Similarly, production can be sold in wholesale markets.
Many other economies of large-scale production result in the falling of average cost.

THE LAW OF CONSTANT RETURNS

According to the law of constant returns, as more and more units of the variable factor
(labour) are applied with the fixed factor (capital) marginal product tends to remain
constant, Consequently, total output increases at the constant rate. In this case, marginal
and average production remains the same.
For instance, if the first dose of labour and capital produces 50 kilogram of sugar, two doses may
produce 100 kilograms, three doses 150 kilograms and four doses 200 kilograms so that the
marginal and average returns to each dose is 50 kilograms.
Definitions
According to Prof. Marshall, "If the actions of the law of increasing and diminishing returns are
balanced, we have the law of constant returns."
The law is the intermediate stage between initial stage of the increasing returns and the ultimate
stage of the diminishing returns and applicable to all sorts of production to a certain extent.
According to Stigler, "When all the productive services are increased in a given proportion, the
product is increased in the same proportion."

Explanation of the Law

The law can be stated in terms of: (i) Constant Returns (ii) Constant Costs.
(i) In Terms of Constant Return: In terms of constant returns the law can be explained with the
help of a table and a diagram as under:

Table shows that as a firm increases the input of labor along with the fixed factor (capital), total
production of blankets increases constantly by the same amount. When units of labor are
doubled, production of blankets is also doubled. Likewise, when units of labor are increased five
times, total production of blankets is also increased five-fold i.e., 25 blankets. Thus, both
marginal and average products remain constant.
Fig – CR curve is parallel to x-axis signifying that marginal product increases at a constant rate
with increase in units of labor. It means output increases constantly by the same amount as
more and more units of the variable factor are employed.
(ii) In Terms of Constant Costs: average and marginal cost of production remain constant
as a result of additional application of variable factors along with the fixed factor of production.
In the Table below, it should be Total Product (blankets) and not total cost (blankets).

The table shows that total production and total cost, increase in the same proportion
consequently, there is no change in average cost due to increase in production. Average cost
remains constant i.e., Rs. 40.00 per piece of blanket.

In Fig, CC curve represents constant cost. It means as production increases, average cost
remains constant.

THE LAW OF RETURNS OF SCALE

The law of Returns of Scale is a long run concept. Returns to scale explains the behaviour of
output when the quantities of all factors of production are raised simultaneously in a given
proportion. The responsiveness of output to such change in inputs is called returns to scale.
Definitions – According to Koytosyiannis, "The term 'returns to scale' refers to the change in
output as all factors change in the same proportions."
In the words of Liebhafasky, "Returns to scale relates to the behaviour of total output as all
inputs varied and is a long-run concept."

Explanation
Law of returns to scale refers to increase in output as a result of increase in all factors in the
same proportion. Such an increase in output is called Returns to Scale.
Supposing, initial production function is as follow:
Q = f (L, K)
If both the factors of production i.e. labour (L) and capital (K) are increased in the same
proportion (a) we will be able to obtain a new level of output Q₁, which is higher than Q then:
Q₁ = f (aL, aK)

(1) If Q₁ increases in the same proportion as increases in factors of production, ie then

it will be an example of Constant Returns to Scale.

(2) If Q₁ increases less than proportionately as increase in factors of production i.e.

then it will be an instance of Diminishing Returns to Scale.

(3) If Q₁ increases more than proportionately as increase in factors of production, ie.

then it will be an instance of Increasing Returns to Scale.

(i) The column (2) ie. percentage increase in labor and capital can be derived as follows:

Similarly percentage increase in capital is determined in the same manner

The percentage increase in labour and capital is same since both change in the same proportion.
(ii) The column (4) i.e. percentage increase in total production is determined as follows:

Why do returns to Scale First Increase, become Constant and then Diminish?
1. Increasing Returns to Scale: It occurs when a given percentage increase in all factor
inputs (in some constant ratio) causes proportionately greater increase in output.

Fig. shows that 10% increase in all factor inputs causes 15% increase in output. Likewise, 15%
increase in factor inputs causes 25% increase in output. Thus, any percentage increase in input is
causing a greater percentage increase in output. Increasing returns to scale are thus operative.
The main cause of its operation is that when scale of production is increased then due to division
of labour and specialization, many types of 'internal economies' are available. For instance,
it may be able to install better machines, sell its product more easily, borrow money cheaply,
procure the services of more efficient managers and workers etc. All these economies help in
increasing the returns to scale more than proportionately. Not only this, a firm also enjoys
increasing returns to scale due to external economies. When a large number of firms are
concentrated at one place, skilled labour, credit and transport facilities are easily available,
subsidiary industries crop up to help the main industry, research and training centres appear
which help in increasing the productive efficiency of the firms. Thus, these external economies
are also the cause of increasing returns to scale.
2. Constant Returns to Scale: it occurs when a given percentage increase in all factor inputs
(in some constant ratio) causes equal percentage increase in output.
The Fig. shows that 10% increase in all factor inputs causes 10% increase in output. Likewise,
20% increase in inputs causes 20% increase in output. Thus, any percentage increase in output is
matched with equal percentage increase in output. The OQ line accordingly, forms a 45° angle
from the origin, indicating the occurrence of constant returns to scale.
The increasing returns to scale do not continue indefinitely. Hence, the stage of constant return
to scale arises, when after reaching a certain level of production, as the firm is enlarged
further, internal and external economies are counter (balanced) by internal and external
diseconomies of scale. In mathematical terminology, that production function which reflects
constant returns to scale is called Homogeneous Production Function or Homogeneous
Function of the first degree. This function states that if labor and capital are increased in equal
proportion then output will also increase in the same proportion.
3. Diminishing Returns to Scale - it occurs when a given percentage increase in all factor
inputs (in some constant ratio) causes proportionately lesser increase in output.

The Fig. shows that 15% increase in all factor inputs causes only 10% increase in output.
Likewise, a 25% increase in factor inputs causes only 15% increase in output. Returns to scale
are thus diminishing. Constant returns to scale is only a passing phase, for ultimately returns to
scale start diminishing. The main cause of its operation is that internal and external
diseconomies outweigh economies of scale. For instance, indivisible factors may become
inefficient and less productive. Business may become unwieldy and produce problems of
supervision and coordination. Large size of the establishment creates difficulties of control. To
these internal diseconomies are also added some external diseconomies e.g. land, labour, capital
etc. become expensive. Prices of raw-material also go up. Transport and marketing difficulties
emerge. All these factors tend to raise costs and the expansion of the firms leads to diminishing
returns to scale.
RETURNS TO SCALE AND ISO-QUANT APPROACH
Return to scale can also be shown through the iso-quants. If 100 percent increase in output can
be achieved by less than 100 percent increase in inputs, it is increasing returns to scale (IRS).
If 100 percent increase in output can be achieved by just 100 percent increase in inputs, it is
constant returns to scale (CRS); and if 100 percent increase in output can be achieved by 'more
than 100 percent’ increase in inputs, it is decreasing returns to scale (DRS).
1. Constant Returns to Scale- Constant Returns to scale refers to situations in which expansion
in output happens to just proportionate to the expansion in factor inputs. In other words, constant
returns to scale means that the size of inputs and the size of the output increases in the same
proportion. Doubling the input doubles the output.

Fig shows CRS. Compare points A and B on the two iso-quants. These points lie on the straight
line OAB. The ratio between the two inputs is constant as we move along the ray, but the total
quantity of inputs is higher on every point to the right. Point B is the same distance from A as A
is from O. In other words OA = AB , If A and B are placed in this manner it signifies that at B all
inputs are doubled as compared to A. At A the input combination is 1K + 1L.
At B it is 2K + 2L. At A output level is 100 units and at B it is 200 units. So between A and B, if
OA = AB these are CRS.
2. Increasing Returns to Scale - Increasing returns to scales refers to a situation in which
output increases by a greater proportion than increase in factor inputs or when increase in
scale of operation is proportionately less than the increase in output. Under increasing returns to
scale, doubling of resources more than doubles the level of output.

Fig. shows IRS. Point B here lies at a lesser distance from A as compared to the distance
between O and A. It means AB is less than OA. It further means that at B, input level is less
than double of input level at A. At A, the input combination is 1K + 1L. At B the input
combination is "less than (2K + 2L)" but greater than 1K + 1L (compare it with C where input
level doubles). At B the output level is double than that at A. So ' less than double' of inputs
produce double the output. So at B, if AB < OA, there is IRS.
3. Diminishing Returns to Scale - Diminishing Returns to scale refers to a situation in which
output increases in lesser proportion than increase in factor inputs or when increase in the
scales of operations is proportionately greater than the increase in output. In other words, if a
given change in factor inputs results in proportionally smaller changes in output, it is a case of
diminishing returns to scale.

Fig. shows DRS. Point B here lies at more distance from A as compared to the distance between
O and A. It means AB is greater than OA. It also implies that input level at B is more than
double the input level at A. At A the input combination is 1K + 1L. At B it is "more than (2K +
2L)" (compare it with C where it is 2K + 2L). At B the output level is double than that at A.
So "more than double the input" produces double the output. So at B, if AB > OA, there DRS.

Varying Returns to Scale - The three returns to scale can be shown in one diagram (above Fig).
The increasing returns to scale operators when the distance between successive iso-quants
decreases i.e., OA > AB > BC . Constant returns to scale operates when the distance between
successive iso-quants is same i.e., BC = CD = DE. Decreasing returns to scale operates when
the distance between successive iso-quants is increasing i.e., DE < EF < FG < GH.

LAW OF VARIABLE PROPORTIONS WITH THE HELP OF ISO-QUANTS

It is shown that given the fixed factor, if an equal increment in total output is secured by
increasing variable factor at diminishing rate it is said to be increasing returns to factor. Since
BC < AB < KA, K to C is the stage over which increasing returns to factor operates.
If an equal increment in total output is secured by increasing the variable factor at an
increasing rate, it is said to be diminished returns to factor. Since EF > DE> CD and thus C
to F is the stage over which diminishing returns to factor operates.
If an increment in the variable factor results in the decrease of the total output, it is said to
be negative returns to factor. In Figure the increase in labour from L6 to L7 results in the
decline in total output from 600 units to 500 units. Hence, from F to G is the range over
which negative returns to factor operates.
The Law of Variable Proportion can also be explained with the help of IQ curves in an
alternative given diagram below.

In the diagram, it is shown that capital is fixed i.e. OK and labor is variable. OA is the upper
ridge line which is drawn by joining the points at which Marginal Productivity of capital is
zero. OB is the lower ridge line at which Marginal Productivity of Labour is zero.
Upto point P, it is shown that as units of labor increases with the fixed quantity of capital, to
increase Production by 100 units each time, amount of labor used decreases in proportion than
before or to increases production from 100 to 200 units MN labor is required which is less
than KM amount of labor which was required to produce first 100 units of output.
Similarly for Production from 200 to 300 units, NP amount of labor is required which is less
than MN amount of labor. Hence K to P shows the application of 1st stage of production in
Law of Variable Proportion. From point P to S, there is second stage of production. In this
stage, for every 100 units of output, quantity of labor is increasing i.e. RS > QR > PQ. But in
this region MPL is + ve. Beyond point S negative returns stage applies as quantity of labor
used is ST but output falls from 600 to 500 units. Hence MPL is negative.
Thus, the three stages of production are:
(i) K to P 1st stage of Production
(ii) P to S IInd stage of Production
(iii) S to U IIIrd stage of Production
The best stage of production is the second stage. Every producer wants to operate in this stage.