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Subject
COMMERCE
Paper No and Title
2. Managerial Economics
Module No and Title
13. Theory of Production: Law of Diminishing Returns
Module Tag
COM_P2_M13
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PAPER No. 2: Managerial Economics
MODULE No.13 : Theory of Production: Law of Diminishing Returns
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TABLE OF CONTENTS
1.
2.
3.
4.
5.
Learning Outcomes
Introduction
Some Basic Concepts of Production Theory
Production Function
Production Function with One Variable Input
5.1. Relationship between TPL, APL and MPL Curves
6. The Law of Variable Proportions or Diminishing Marginal Returns
6.1. Assumptions
6.2. Stages of Production
7. Summary
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PAPER No. 2: Managerial Economics
MODULE No.13 : Theory of Production: Law of Diminishing Returns
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1. Learning Outcomes
After studying this module, you would be able to
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Know about the Production Function.
Derive the relationship between AP, MP& TP
Learn about the Law of Variable Proportions.
Learn about Stages of Production.
PAPER No. 2: Managerial Economics
MODULE No.13 : Theory of Production: Law of Diminishing Returns
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2. Introduction
Today, one of the key concerns of the business managers is to achieve optimum efficiency in
production or minimizing cost for a given output. In competitive market, a firm can survive only if
it is able to produce goods and services at a competitive cost. Hence, business managers should
make an effort to minimize the cost of production or maximize output for a given level of inputs.
There are some basic questions which managers are confronted with while endeavoring to minimize
the production cost. These are:
1.
2.
3.
4.
How does output change with the increase in quantity of inputs?
How can production be optimized to achieve reduction in cost?
How does technology helps in minimizing the cost of production?
How to achieve the least cost combination of inputs for a given output?
The theory of production seeks to explain answer to these questions with the help of economic
models that are built under hypothetical conditions. The production theory provides various tools
and methods to analyze relationship between input and output which provide directions to find
solutions to practical business problems.
3. Some Basic Concepts Of Production Theory
Production
In economics, the transformation of resources (men, material, time and so on) into a different &
more useful commodity through a process is called production. In general, the production function
is limited to only ‘manufacturing’ in which inputs (labour, machine, raw material, time & so on)
are transformed into an output.
In economics sense, there are different forms of production other than manufacturing. When a
commodity is transferred from one place to another for consuming in the production process is
production. For eg. When sand is transferred from the river bank to construction site by the sand
dealer, this activity, too, is production. When a commodity is stored for future consumption or sale,
this is also called production.
It is not necessary that only physical conversion of inputs into tangible goods take place in
production process. Some types of production involves conversion of an intangible input into
intangible output. For e.g. both input and output are intangible in the production of medical, legal,
social and consultancy services.
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MODULE No.13 : Theory of Production: Law of Diminishing Returns
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Fixed and Variable Factors of Production
A variety of goods and services are used by a firm in the process of production called factors of
production or inputs such as land, labour, raw material, plant and machinery, factory premises,
tools and equipment etc. These factors of production can be classified into two parts:
1. Fixed factors
2. Variable factors
Fixed factor is one whose quantity remains the same irrespective of the level of output. Its quantity
cannot be readily changed in the short run. On the other hand, a variable factor is one whose
quantity changes with the changes in the level of output. In the short run, a larger quantity can be
employed by the users of such factors. For example: a firm wants to increase the production of
books from 1000 to 2000 daily. To do so, it will need more factors of production. But, there are
some factors whose supply cannot be increased immediately e.g. printing press, building etc.
Therefore, the firm will have to use those factors whose quantity can be increased immediately
such as labour, raw material etc. In the given example, printing press and building are fixed factors
of production, labour and raw material are variable factors of production.
Short run and Long run
Short run refers to that time period in which supply of certain factors is fixed i.e. it cannot be
increased or decreased. For e.g. plant, machinery, building etc. Therefore, a firm can increase the
production of a commodity in the short run, by increasing the use of variable factors such as labor
and raw materials.
Long run refers to that time period in which supply of all factors i.e. fixed and variable is elastic,
but not sufficient to allow a change in technology. In the long run, no factor is a fixed factor, all
factors are variable. Therefore, a firm can increase the production of a commodity in the long run
by increasing the use of both variable and fixed factors of production.
There is another term ‘very long run’ used by economists which refers to that time period in which
technology of production can also be changed. The production function also changes in the very
long time period.
4. Production Function
Production function is a mathematical statement used to explain the technical relationship between
input and output in physical terms over a given period of time.
According to Koutsoyiannis, “ the production function is purely a technical relation which connects
factor inputs and output.
The general form of production function tells that output of any commodity depends on quantity of
inputs and techniques of production. Given the state of technology, several methods using different
combination of factors are used in the production of a commodity. For e.g. the production of cloth
requires cotton or polymer or silk as raw material with power loom, handloom or even
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PAPER No. 2: Managerial Economics
MODULE No.13 : Theory of Production: Law of Diminishing Returns
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computerized machines. The same product can be produced in several possible ways using different
kinds of raw materials and technology options. Thus, there can be various technically efficient
methods of production. Production function incorporates all such technically efficient methods.
Production function is a schedule showing maximum output of a commodity produced per unit of
time with each combination of inputs and with the given state of technology. A different set of
inputs are used to produce a given level of output and each of these sets may be technically efficient.
Suppose, a manufacturing firm employs only two factors- Labour (L) and Capital (K) in
manufacturing steel chairs. Then, general form of its production function can be written as:
Q= f (L, K)
Where Q= Quantity of steel chairs produced
L= Labour
K= Capital
The above production function shows that quantity of steel chairs produced depends on the quantity
of Labour (L) and Capital (K) employed. The production of steel chairs can be increased by
increasing K and L. The time period (i.e. short run or long run) considered for increasing production
is used to decide whether both K and L or only L will be increased.
In the short run, production of steel chairs can be increased by employing more of labour only. The
production in the long run can be increased by employing more of both capital and labour as all
factors are variable in the long run.
Accordingly, production function can be of two kinds:
1. Short run production function
2. Long run production function
The short run production function can be written as:
Q= f (K, L)
Where K means that capital is fixed in amount.
The long run production function can be written as:
Q= f (K, L)
The production function is based on some assumptions. These are:
1.
2.
3.
4.
5.
There is perfect division of both inputs and output.
Only two factors of production are employed- capital and labour.
Imperfect substitution between labour and capital.
Technology is given and constant.
In the short run, supply of fixed factors is inelastic.
The production function will have to be changed, if there is some change in these assumptions.
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PAPER No. 2: Managerial Economics
MODULE No.13 : Theory of Production: Law of Diminishing Returns
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5. Production Function with One Variable Input
In the short run, producers can change the output by changing variable factors only. Let us suppose
a firm uses two factors, labour and capital where labour is variable and capital is the fixed factor.
If labour is increased to increase the output keeping the amount of capital unchanged, then there
will be a change in the ratio in which these factors are used. Thus, output can be changed through
a change in labour only. This type of production function is also known as variable proportion
production function. It is essentially a short run production function which shows maximum output
that can be produced by changing the quantity of variable factors keeping other factors fixed.
The short run production function can be written as:
Q= f (K, L)
Total Product (TP)
It can be defined as total quantity of goods that can be produced by a firm during a specified time
period. TP of a firm can be raised by utilizing more and more units of the variable factor i.e. labour.
As can be seen in fig. 1.1, TPL increases at an increasing rate in the beginning with the employment
of more and more of variable factor. After a point, it starts increases at a decreasing rate with further
increase in the use of the factor. It is not necessary that total product will always increase with the
increase in the quantity of variable factors. For example, if a firm employs labours that are beyond
the capacity of the factory then they will not be in a position to work efficiently. Thus, TP L curve
slopes steeply upward at first, reaches a maximum and then starts declining.
Marginal product (MP)
Marginal product is defined as change in total production due to use of an extra unit of a variable
factor. For example, when 10 labours were employed in a firm, total production of chairs was 1000.
Now, if one extra labour is employed, total production increases to 1050 chairs attributable to 11
labours. Since 11th labour has added 50 chairs to the total production, the marginal product of 11th
labour is 50 chairs.
The marginal product of labour can be written as:
MPL = Change in Total Product
Change in Labour
= Δ TPL
ΔL
The formula for calculating MPL is
MPL for nth unit =TPn – TPn-1
n= number of labour units
In fig 1.1, marginal product rises in the beginning. When total product is maximum, it become zero.
Here total product is not increased with the use of extra units of variable factor. Ultimately,
marginal product becomes negative when total product declines.
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MODULE No.13 : Theory of Production: Law of Diminishing Returns
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Fig 1.1: The TPL curve and the derivation of APL and MPL curves
Average Product
Average product of an input is total product divided by the total quantity of labour employed to
produce this output. It measures on an average how much output is produced by each labour. Thus,
APL = Total Product
Labour Input
As can be seen in fig. 1.1, like marginal product, average product also rises initially and then falls.
It is inverted U-shape curve and can never be zero or negative.
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MODULE No.13 : Theory of Production: Law of Diminishing Returns
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5.1 Relationship between TPL, APL, and MPL Curves
With the help of TPL curve, we can derive APL and MPL curve as graphically illustrated in fig. 1.1.
TPL is total product of labour curve. Here it is assumed that only variable factor is labour and the
amount of capital is fixed (K). TPL rises when quantity of labour increases but the increase become
smaller and smaller.
Relationship between TPL and APL Curves
1. APL at a point is given by the slope of the straight line from the origin upto a point on the
TPL curve. Till point a, the value of the slope increases and after that it declines.
2. In the beginning, APL curve increases, becomes maximum and then declines.
3. APL is positive as long as TPL is positive.
4. It is always greater than zero.
Relationship between TPL and MPL Curves
1. MPL at any point on total product curve is the slope of the tangent at that point or MPL
between two points is the slope of the line joining the two points on TPL curve. Till point
c, the value of the slope increases, then declines until TPL is maximum. MPL is zero at that
points and after that it becomes negative.
2. In the beginning, MPL increases, becomes maximum when the slope of the tangent is
steepest and then falls.
3. MPL is zero, when TPL is maximum and become negative when TPL declines.
4. Area under MPL curve gives TPL.
Relationship between APL and MPL Curves
1. In the beginning, when both APL and MPL curves are increasing, MPL increases greater
rate than APL curve. Both curves increase till fixed input (K) is underutilized.
2. Both APL and MPL curves decline, but MPL curve declines at a higher rate than APL curve.
3. MPL is equal to APL, when APL curve is maximum.
4. When MPL starts falling, APL continues to increase.
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MODULE No.13 : Theory of Production: Law of Diminishing Returns
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6. The Law of Variable Proportions or Diminishing Marginal Returns
In the traditional theory of production, the law that studies the input output relations with one
variable factor (say, labour) keeping the quantity of other factor (say, capital) constant, is called the
law of variable proportions.
The law of variable proportions states that when the quantity of variable factor is increased, keeping
the quantity of fixed factor constant, then increase in total product will eventually decline. In other
words, total output increases at an increasing rate upto a certain point but after that point it increases
at diminishing rate.
According to G.L.Thirkettle in “Basic Economics”, “if increasing quantities of one factor of
production are used in conjunction with fixed quantity of other factors then, after a certain point,
each successive unit of a variable factor, will make a smaller and smaller addition to the total
product.”
6.1 Assumptions
This law is based on certain assumptions. These are:
1. There is only one variable factor, other factors are held fixed or constant.
2. The variable factors are homogenous i.e. each unit is equal in efficiency.
3. It is possible to change the proportion in which the various factors are combined.
4. The short run time period is assumed as in long run it is possible to vary all factor inputs.
5. The state of technology is given and constant.
6. There is no change in prices of factor of production.
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MODULE No.13 : Theory of Production: Law of Diminishing Returns
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6.2 Stages of Production
In the short run, a firm can change the output by changing the quantities of the variable factors
while quantities of other factors remain unchanged. The behavior of output can be explained in
three stages which is given below:
Fig 1.2: Stages of Production
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MODULE No.13 : Theory of Production: Law of Diminishing Returns
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Stage I: Stage of Increasing Returns
In this stage, TPL increases at an increasing rate upto point ‘c’. MPL rises in the beginning and
reaches its maximum point. APL pulls up due to rising MPL.
Beyond point ‘c’, TPL increases at a decreasing rate. MPL starts declining but is positive. The point
‘c’ is known as the point of inflexion. After this point, APL continue to increase because MPL is
higher than APL. The stage I ends when APL reaches its maximum and is equal to MPL.
In stage I, the amount of fixed factor is abundant in relative to the variable factor. Since fixed factor
is not fully utilized therefore producer has an incentive to increase the output by employing more
and more units of the variable factor. This will result in more efficient use of fixed factor. Thus, a
rational producer will not choose to operate in this stage because by expanding the level of output,
he can further reduce its average cost.
Causes for Increasing Returns
The two important reasons for increasing returns are given below:
1. Indivisibility of Fixed Factor- It means a minimum size of fixed factor need to be employed
irrespective of the level of output. In initial stages, the minimum size of fixed factor is too
large than its actual utilization. This results in underutilization of fixed factor. By
employing more and more units of the variable factor, the fixed factor is utilized effectively
and efficiently. This causes output ton increase at an increasing rate.
2. Specialization- Specialization is theanother reason for increasing returns. When the
quantity of variable factor increases, the scope of specialization also increases. The various
advantages offered by specialization include productivity, efficiency, better skill etc.
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MODULE No.13 : Theory of Production: Law of Diminishing Returns
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Stage II: Stage of Diminishing Returns
In stage II, TPL increases at a decreasing rate and reaches its maximum point when this stage ends.
Both APL and MPL declines but not negative. This is the reason why this stage is known as stage of
diminishing returns. APL is greater than MPL throughout this stage. The stage comes to an end
where MPL is zero and TPL is maximum. Stage II is the relevant stage of operation for producer as
efficiency of the scarce factor i.e. labour can be maximized.
Causes for Diminishing Returns
The two important reasons for diminishing returns are given below:
1. The Non Optimal Proportion between Fixed and Variable Factors- Once the optimum
combination of variable and fixed factors is reached, further employment of labour leads
to non-optimal proportion of fixed factor with the variable factor. As a result, efficiency of
variable factor starts decreasing as fixed factor or indivisible factor is being used to full
extent.
2. Elasticity of Substitution between the Factors is Finite – If the fixed factor is perfectly
substituted by the variable factor, then the inadequacy of the former could be compensated
by increasing the use of latter. But, elasticity of substitution between factors is finite.
Therefore, if firm employs additional variable factors beyond the optimum combination,
then productivity of variable factors decline as the availability of indivisible factor per unit
of variable factor decreases.
Stage III: Stage of Negative Returns
In this stage, total product falls. MPL becomes negative and falls below the X- axis. APL falls
continuously but is non- negative. A rational producer would not like to operate in this stage as the
efficiency of both fixed and variable factors decreases and the proportion between factors is highly
sub optimal.
Causes for Negative Returns
The two important reasons for negative returns are given below:
1. Sub Optimal Ratio – In this stage, the quantity of variable factor is too much in relative to
the fixed factor. As a result, the efficiency of not only variable factor but also fixed factor
starts declining. As a result, total product starts falling.
2. Moving beyond Optimum Degree of Specialization- If the limit to optimum degree of
specialization is crossed, then the efficiency of variable factor declines
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PAPER No. 2: Managerial Economics
MODULE No.13 : Theory of Production: Law of Diminishing Returns
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7. Summary
 The transformation of resources (men, material, time and so on) into a different & more
useful commodity through a process is called production.
 Fixed factor is one whose quantity remains the same irrespective of the level of output.
Its quantity cannot be readily changed in the short run.
 A variable factor is one whose quantity changes with the changes in the level of output.
 Short run refers to that time period in which supply of certain factors is fixed i.e. it
cannot be increased or decreased. For e.g. plant, machinery, building etc.
 Long run refers to that time period in which supply of all factors i.e. fixed and variable
is elastic, but not sufficient to allow a change in technology.
 Production function is a mathematical statement used to explain the technical
relationship between input and output in physical terms over a given period of time.
 Production function can be of two kinds: (a) Short run production function (b) Long
run production function.
 Total Product is total quantity of goods that can be produced by a firm during a
specified time period.
 Marginal Product is defined as change in total production due to use of an extra unit of
a variable factor.
 Average Product of an input is total product divided by the total quantity of labour
employed to produce this output.
 The law of variable proportions states that when the quantity of variable factor is
increased, keeping the quantity of fixed factor constant, then increase in total product
will eventually decline.
 The behavior of output can be studied in three stages: (a) stage of increasing returns
(b) stage of diminishing returns (c) stage of negative returns.
 Stage II is the relevant stage of operation for producer.
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PAPER No. 2: Managerial Economics
MODULE No.13 : Theory of Production: Law of Diminishing Returns