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TOPIC FOUR: PRODUCTION THEORY;

PART ONE: INTRODUCTION: Factors of production: Land, labour, capital and enterprise. Mobility of factors
of production and specialization.
PART TWO: Production function defined:

-Short- run changes in production; Total, Average and marginal products, stages of production and the law of
diminishing returns:

-Long-run changes in production; The least-cost factor combination; concepts of isoquants, isocosts and the
Marginal rate of technical substitution (MRTS);- Returns to scale-,

PART THREE: Theory of the Firm: Costs of production: Total, average and marginal costs, relationship
between cost curves in the short run and long run. Economies and diseconomies of scale: Revenue and profits

…………………………………………

Introduction

Production can be defined as the transformation of resources into products or the process whereby
inputs are turned into outputs through technological innovations. The efficiency of this process
depends upon three factors

 The proportion in which the various inputs are employed

 The absolute level of each input
 The productivity of each input at different input levels and ratios.

Various concepts in production

 Factors of production: There are four factors of production – Land, Labour, Capital and
Organization. Additionally, we can categorize the factors of production as variable inputs and
fixed inputs.
 Fixed inputs: A fixed input is defined as one whose quantity cannot be readily changed when
market conditions indicate that an immediate change in output is desirable. Although no input is
ever absolutely fixed but frequently for analytical simplicity we hold some inputs fixed.
 Variable inputs: A variable input is the one whose quantity can be changed almost
instantaneously in response to desired changes in output. Example can be labour hours.
 Short run: In a short run the quantities of one or more factors of production cannot be changed.
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 Long run: Long run production corresponds to the time that is needed to make all production
inputs variable. Usually long run represents the scenario when firms decide to expand the scale of
operations or branch out into new products.
 Fixed vs Variable proportions: variable proportion production implies that output can be
changed in the short run by changing the amount of variable inputs used in co-operation with the
fixed inputs. Naturally as the amount of one input is changed the other remaining constant, the
ratio of inputs changes too. Secondly, when production is subject to variable proportions, the
same output can be produced by various combinations of inputs – i.e. by different input ratios.
This may apply only to the long run but it is relevant to the short run when there is more than one
variable input.

THEORY OF PRODUCTION

THIS IS DIVIDED INTRO THREE PARTS

PART ONE: INTRODUCTION

In economics, a production function relates physical output of a production process to physical inputs
or factors of production. It is a mathematical function that relates the maximum amount of output that
can be obtained from a given number of inputs – generally capital and labor etc.

Meaning of Production Function: In simple words, production function refers to the functional
relationship between the quantity of a good produced (output) and factors of production (inputs).

(A) FACTORS OF PRODUCTION:

Production is the result of co-operation of four factors of production viz., land, labour, capital and
organization. Therefore, the producer combines all the four factors of production in a technical
proportion. The aim of the producer is to maximize his profit. For this sake, he decides to maximize
the production at minimum cost by means of the best combination of factors of production. Factors of
production are the resources people use to produce goods and services; they are the building blocks of
the economy.
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a) Land as a Factor of Production

Land is short for all the natural resources available to create supply. It includes raw property and
anything that comes from the ground. It can be either renewable or non-renewable resource. Once man
changes it from its original condition, it becomes a capital good. For example, oil is a natural resource,
but gasoline is a capital good. Farmland is a natural resource, but a shopping center is a capital good.
The income earned by owners of land and other resources is called rent. these resources can be
renewable, such as forests, or non-renewables such as oil or natural gas. Although land is undeniably
crucial to most forms of production, just how essential it is, varies depending on the industry. For
instance, land is a central focus of virtually all agriculture but is much less important to a tech
company that is quite literally operating in the virtual sphere. Characteristics of Land as a Factor of
Production are

 The land is a free gift of nature. (ii) The land has no cost of production.
 It is immobile. (iv) The land is fixed and limited in supply.

b) Labor as a Factor of Production

Labor is the work done by people. The value of the workforce depends on workers' education, skills,
and motivation. It also depends on productivity that measures how much each hour of worker time
produces in output. The reward or income for labor is wages. Labor, as a factor of production, involves
any human input..

labor range from the very physical to primarily mental work that goes into production. On the mental
side of this factor of production are laborers like artists producing art, or programmers creating
software etc. On the more physical side of labor might be food service workers, construction workers,
or factory workers. If someone has ever paid you for a job, you have contributed labor resources to the
production of goods or services. In production, wages are paid based on workers’ skill levels as well as
the time invested in work. Laborers with a great deal of training and education are considered to be
“highly skilled” and are paid higher wages than less trained workers. So-called skilled or highly-
trained workers are described as “human capital”. Nations with high levels of such human capital tend
to be more efficient and productive than countries with lower levels of this valuable resource.
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Characteristic are: It is a human factor. (ii) One cannot store labour. (iii) No two types of
labour are the same.

c) Capital as a Factor of Production

Capital is short for capital goods. These are man-made objects like machinery, equipment, and
chemicals that are used in production. That's what differentiates them from consumer goods. For
example, capital goods include industrial and commercial buildings, but not private housing. A
commercial aircraft is a capital good, but a private jet is not. The income earned by owners of capital
goods is called interest. Here capital refers not to money (which is not a factor of production), as you
might expect, but to manufactured resources such as factories and machines. These are man-made
goods used in the production of other goods. Their use in commercial production is what separates
them from more widely used consumer goods.

Some other examples of capital include hammers, forklifts, conveyor belts, computers, and delivery
vans. But it is not just this kind of machinery; office furniture like conference tables and desk chairs
also fall under the umbrella of capital. An increase in capital goods means an increase in the
productive capacity of the economy.

Note that personal and private capital is distinct from the capital we are describing here. For instance,
your personal vehicle is not a capital good in this sense; however, a taxi or other vehicle used in some
form of business is considered to be a capital good.

Characteristics

i) Capital is a manmade factor of production. ii) It is highly mobile.

ii) It is a passive factor of production.

d) Entrepreneurship as a Factor of Production : Entrepreneurship is the drive to develop an idea

into a business. An entrepreneur combines the other three factors of production. The most
successful are innovative risk-takers. The income entrepreneurs earn is profits.

An entrepreneur is someone who takes on the economic risk involved in bringing the other three
factors of production together. Entrepreneurs are a vital engine of economic growth at all scales,
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helping to build many of the largest firms in the world as well as some of the small businesses in your
neighborhood. Entrepreneurs help contribute to economic growth, so governments typically do their
best to encourage entrepreneurship using the right combination of policies to make starting a business
accessible. Characteristics

 He has imagination.
 He has great administrative power.
 An entrepreneur must be a man of action.
 An entrepreneur must have the ability to organize.
 He should be a knowledgeable person.
 He must have a professional approach.

PRODUCTION FUNCTION ANALYSIS

The main objective for most firms is profit maximization. Business objectives might include: • to
break even(TR=TC) • to increase market share• to survive• to make returns to shareholders
(dividends)• to increase sales• to provide a good service. When firms produce goods and services, they
use resources (factors of production – land, labour, capital and enterprise).
Production Function: “production function is an indicator of the physical relationship between the
inputs and output of a firm. Production function reflects how much output we can expect if we have so
much of labour and so much of capital. The production function of a firm depends on the state of
technology. With every development in technology the production function of the firm undergoes a
change.

A basic relationship between inputs and outputs may be expressed as:

Q = f( L, K, Ln, effort, time, technology…) Where Q = Quantity of output, L = Labour, K=

Capital, and Ln = Land.

Hence, the level of output (Q), depends on the quantities of different inputs (L, K, Ln) available to the
firm.

In the simplest case, it is given as

Q = f(L, K)

where there are only two inputs, labour (L) and capital (K) and one output (Q)
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Following are the main features of production function:

1. Substitutability: The factors of production or inputs are substitutes of one another which make it
possible to vary the total output by changing the quantity of one or a few inputs, while the quantities of
all other inputs are held constant. It is the substitutability of the factors of production that gives rise to
the laws of variable proportions.

2. Complementarity: The factors of production are also complementary to one another, that is, the two
or more inputs are to be used together as nothing will be produced if the quantity of either of the inputs
used in the production process is zero. The principles of returns to scale is another manifestation of
complementarity of inputs as it reveals that the quantity of all inputs are to be increased
simultaneously in order to attain a higher scale of total output.

3. Specificity: It reveals that the inputs are specific to the production of a particular product. Machines
and equipment’s, specialized workers and raw materials are a few examples of the specificity of
factors of production. The specificity may not be complete as factors may be used for production of
other commodities too. This reveals that in the production process none of the factors can be ignored
and in some cases ignorance to even slightest extent is not possible if the factors are perfectly specific.

NOTE: The production function is defined in the short run and in the long run and the distinction is
extremely relevant in microeconomics. The distinction is based on the nature of factor inputs. Those
inputs that vary directly with the output are called variable factors. These are the factors that can be
changed. Variable factors exist in both, the short run and the long run. Examples of variable factors
include daily-wage labourers, raw materials, etc. On the other hand, those factors that cannot be varied
or changed as the output changes are called fixed factors. These factors are normally characteristic of
the short run or short period of time only. Fixed factors do not exist in the long run.

Consequently, we can define two production functions: short-run and long-run. The short-run
production function defines the relationship between one variable factor (keeping all other factors
fixed) and the output. The law of returns to a factor explains such a production function.

The long-run production function is different in concept from the short run production function. Here,
all factors are varied (these are fixed and variable) in the same proportion. The law that is used to
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explain this is called the law of returns to scale. It measures by how much proportion the output
changes when inputs are changed proportionately.

PART 2 A: THE SHORT RUN PRODUCTION FUNCTION

Short run production function examines the relationship between one variable factor and output,
keeping the quantities of other factors fixed. Thus in the short run production it is important to assume
factor input is fixed.

The business firm is basically termed as a technical unit where the inputs are converted into outputs
and then into a sale. In the long run, it is essential for having a better understanding of the marginal
return received on the marginal product. A secured relationship between all the physical outputs of the
production process and its input constitutes the production function theory. A firm product function
shows the relationship between amounts of resources employed and total product.

A production process minimizes the waste and brings out the product in the market in the most
effective manner. The economic growth of any country largely depends on the manufacturing growth
implies a country manufacturing growth should be high if it has high economic growth. With this
inception, the theory of production function determines the income generated by the production
process is the economic physical input value deducted from the economic value of physical output.

Fixed and Variable Resources: -Resources such as labour are categorized as variable resources because they
can be varied quickly and have the ability to change the output range, whereas the adjustment in these resources
consumes much more time. On the other side, resources such as the size of the building can’t be altered quickly
so they fall under the category of fixed resources. Output generated from the production process varied as per
time required to change the quantity. Thus, in the short run, at least one resource is fixed (contradictory no
resources are fixed in long run projects). So the output can be changed just by adjusting the resources as
the size and firm are stable in short-run cases. The length of the long run projects differs greatly
because of the production efforts.

So the output can be changed just by adjusting the resources as the size and firm are stable in short-run
cases. The length of the long run projects differs greatly because of the production efforts.

THE STAGES OF PRODUCTION PROCESS in the short run

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The three stages of production are characterized by the slopes, shapes, and interrelationships of the
total products, marginal product, and average product curves.

a). Total Output/ Total Product (TP): The short run production function gives the total (maximum)
output obtainable from different amounts of the variable input given a specified amount of the fixed
input. Total output can also graphically be described as the locus of different output levels produced
by using different combinations of factor inputs. Output is plotted on the vertical axis and input is
plotted on the horizontal axis. A total product curve first rises slowly, then more rapidly and finally
reach the maximum value and then begins to decrease. This curvature represents the law of
diminishing marginal returns.

b). Average Product (AP): Average product represents the quantity of output produced per unit of a
particular input. For example, average product for labour will be

APL = TPL/QL

The average product is given by the slope of the line drawn from the origin to the corresponding point
on the total product curve.

c). Marginal product (MP): Marginal product represents the quantity of additional units of output
produced by one additional unit of input. In other words, the marginal product of an input is the
addition to total product attributable to the addition of one unit of the variable input, keeping the fixed
inputs constant.

The marginal product at a point is given by the slope of the total product at that point. Marginal
product is positive as long as output is increasing but becomes negative when output is decreasing.

MPL = dTPL/dQL

Economists recognize three distinct stages of production, which are defined by a concept known as the
law of diminishing marginal returns. The idea of the three stages of production helps companies set
production schedules and make staffing decisions

The Three Stages of Production Process-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: The
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stages are given by the relation among Average product (AP), Marginal product (MP) and Total
product (TP)):

In the short-run production function-

-let the variable factor be labour

-land be the fixed factor (fixed at one acre)

The origin of stage 3 starts from the maximum point of the TP curve. In this stage, the marginal
product is declining and its negative, also both TP and AP are declining at the same time.

In this stage: TPL increases at an increasing rate up the point of inflection. APL Starts at the same
point as the TPL, It rises reaching a maximum at the end of stage one. MPL rises in the beginning and
reaches its maximum point before and then it starts to decline. MPL intersects the APL at its
maximum point.

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.

The two important reasons for increasing returns at this stage are:
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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

Stage II:

In stage II (Stage of Diminishing Returns): TPL increases at a decreasing rate and reaches its
maximum point when this stage two. Both APL and MPL declines, however, PML declines to zero
when TPL is a maximum. This is the reason why this stage is known as stage of diminishing returns.
At this stage APL is greater than MPL throughout this stage. The stage comes to an end when MPL is
zero.

Stage II is the relevant stage of operation for producer as efficiency of the scarce factor i.e. labour can
be maximized.

The two important reasons for diminishing returns are given below:

1. 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.

In stage 111: TPL starts to decline. APl also decline, however it will remain positive as long as TPL is
positive although declining. MPL becomes negative and falls below the X- axis. 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.

The two important reasons for negative returns are given below:
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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

The Law of Diminishing Marginal Returns: The law of diminishing marginal returns is one of the
fundamental principles of economics and is important for finding the right balance in production
within an organization. Regardless of the nature of the company, understanding the law of diminishing
marginal returns will have a direct impact on its efficiency. Finding the right balance between factors
of production is essential, but it takes knowledge and effort. As accepted by economist, there are
significant stages of production under which all the production process is defined by the law of
diminishing marginal returns.

The law of diminishing returns is an economic principle stating that as investment in a particular area
increases, the rate of profit from that investment, after a certain point, cannot continue to increase if
other variables remain at a constant. As investment continues past that point, the rate of return begins
to decrease.

For example, the law states that in a production process, adding workers might initially increase
output. However, at a certain point the optimal output per worker will be reached. Beyond that point,
each additional worker's efficiency will decrease because other factors of production remain
unchanged, such the available resources.

The Law of diminishing marginal returns/Law of Variable Proportions concerns itself with the way the
output changes when you increase the number of units of a variable factor. Hence, it refers to the
effect of the changing factor-ratio on the output.

The law of diminishing marginal returns states that in any production process, a point will be reached where
adding one more production unit while keeping the others constant will cause the overall output to decrease

OR The law states that keeping other factors constant, when you increase the variable factor, then the
total product initially increases at an increases rate, then increases at a diminishing rate, and
eventually starts declining” OR: “when more and more units of a variable input are employed on a
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given quantity of fixed inputs, the total output may initially increase at increasing rate and then at a
decreasing rate, then at a constant rate, but it will eventually be diminishing”.

It’s also called "the law of increasing costs" because adding one more production unit diminishes the
marginal returns and the average cost of production inevitably increases.

The law of diminishing marginal returns predicts when some optimal capacity is already achieved then
the additional factor added to the production actually responsible for smaller increases in the output.
For instance, if a company employs workers to achieve the optimal capacity, and when it achieves,
then even after adding additional employees the optimal level will also result in less efficient
operations. Henceforth, the law of diminishing marginal returns can be considered as the most
important feature in short-run projects

The assumptions law of diminishing returns are as follows:

a) Assumes the state of technology to be constant. Changing the technological tools used in
production would change the marginal and average cost and value of a product. This would negate
the premises of the law of diminishing returns by changing more than one production variable.
b) Outputs must not vary proportionately. Only one input must vary, while others remain constant at
all times. This eliminates production situations where some or all inputs vary proportionately to
each other.
c. Short Period: The law is applicable in the short run as supply of one or the other factor cannot be
increased within the short span of time. Thus, they are considered fixed.
d. Homogeneous Units: All units of variable factors of production are assumed to be homogeneous.

d). Assumes that input prices are given.

Causes for the Operation of Law of Diminishing Returns

(i) Fixed Factors of Production: The law of diminishing returns applies because certain factors of
production are kept fixed. All factors of production, land, labour, capital or enterprise cannot be
increased every time. As we know that production is the result of the effective combination of factors
of production, every factor will have to be increased for obtaining production at increased rates. If
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certain factor becomes fixed, the adjustment of factor of production will be disturbed and the
production will not increase at increasing rates and thus law of diminishing returns will apply.

(ii). Scarce Factors: In case of certain factors especially land which is itself limited cannot be
increased the law of diminishing return will apply. It may also happen in case of other factors of
production. For example, sometimes, labour, specially technical or capital or even enterprise cannot be
increased in individual cases. As a result, the adjustment of factors of production will be disturbed and
the output cannot be achieved at increasing rates.
(iii) . Lack of Perfect Substitutes: There is another reason due to which the law of diminishing returns
does not apply i.e., lack of perfect substitutes of factors of production. It means that one factor of
production cannot be substituted for another factor. Substitute for every factor of production is not
always available. In the absence of such substitute, the law of diminishing returns will apply.
(iv). Optimum Production: If the perfect adjustment of the factors of production has been made,
certainly optimum production will be returned. After this optimum level of production, more and more
variable factors will result in less efficient combination of fixed as well as variable factors of
production. In other words, this, will reduce the marginal product and hence the law of diminishing
returns will operate.

Significance of Law of Diminishing Marginal Returns: The law of diminishing returns applies
quickly to agriculture, mining, forests, fisheries and building industries. In case of land, it applies to
both in its intensive and extensive form of cultivation. This is because the inputs in agriculture
production are natural, while in industrial production, inputs are generally man-made. Therefore, if
increasing variable input is applied to fixed inputs, then the marginal returns start declining.

a. Application of the Law in Agriculture: In agriculture, nature dominates, so the law of dominates, so
the law of diminishing returns applies quickly. In agriculture, more and more doses of labour and
capital can be employed with the fixed factor (i.e. land) to produce more. Land being fixed cannot be
increased or reduced as per the choice of the agriculturist. Thus as more and more variable factors are
employed with the fixed factors, the marginal product falls and hence the law of diminishing returns
apply.
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b. Application in Extractive Industries: The law of diminishing returns applies quickly to the extractive
industries like:

(i) Mines: As more and more minerals are extracted from the mines, the levels of minerals go down.
For deep extraction, there is need of light, oxygen, water, more labourers etc. All this would involve
more expenses and hence the law of diminishing returns would operate quickly.

(ii) Fisheries: In a river or in a sea, as we go on catching more and more fish, the number of fish would
fall around the bank or shore. Now for more catch of the fish, we have to go deep into river or sea.
This would involve wastage of time in going into deep water and then coming back to the bank or
shore. Also in deep sea, the number of catching may not be too big. Thus it is clear that the law of
diminishing returns apply quickly to fisheries.

(iii) Buildings: The law of diminishing returns applies quickly to multi-storey building. As the more
and more storeys are built, the expenses on upper storeys increase as compared to lower storeys. Thus
the law of diminishing returns apply to buildings too.

3. Application in Industries: In industries, labour and capital play more role than land and these can be
increased to any level. It is due to this reason that the law of increasing returns apply in industries. But
this does not continue for very long. A stage reaches when the quality of these variable factors
deteriorates or the prices of these variable factors increase. These two factors result in diminishing
returns.

Thus it is clear that the law of diminishing returns apply to all types of production; sooner or later.
That is why it is called, ‘Universal law,

“The Law of Diminishing Returns is a law of life and can be applicable anywhere and everywhere”.

……………………………

PART TWO B: LONG RUN PRODUCTION ANALYSIS

The long-run is a period of time in which all factors of production and costs are variable. In the long
run, firms are able to adjust all costs, whereas, in the short run, firms are only able to influence prices
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through adjustments made to production levels. In the long run production function, the relationship
between input and output is explained under the condition when both, labor and capital, are variable
inputs.

In the long run, the supply of both the inputs, labor and capital, is assumed to be elastic (changes
frequently). Therefore, organizations can hire larger quantities of both the inputs. If larger quantities of
both the inputs are employed, the level of production increases. In the long run, the functional
relationship between changing scale of inputs and output is explained under returns to scale.

The returns to scale can be explained with the help of isoquant technique.

Isoquant Curve: “An isoquant is a curve showing all possible combinations of inputs physically
capable of producing a given level of output” OR, “An isoquant curve may be defined as a curve
showing the possible combinations of two variable factors, labor and capital that can be used to
produce the same total product

Following are the assumptions of isoquant curve:

i. Assumes that there are only two inputs, labor and capital, to produce a product

ii. Assumes that capital, labor are divisible in nature

iii. Assumes that capital and labor are able to substitute each other at diminishing rates because they
are not perfect substitutes

iv. Assumes that technology of production is known

On the basis of these assumptions, an isoquant curve can be drawn with the help of different
combinations of capital and labor. The combinations are made such that it does not affect the output
level.
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IQ1 is the output for four combinations of capital and labor. Figure shows that all along the curve for
IQ1 the quantity of output is same that is, 200 with the changing combinations of capital and labor.
The four combinations on the IQ1 curve are represented by points A(L1,K1), B(L2,K3), C(L3,K4),
and D(L4,K1).

Some of the properties of the isoquant curve are as follows:

i. Negative Slope: Implies that the slope of isoquant curve is negative. This is because when capital
(K) is increased, the quantity of labor (L) is reduced or vice versa, to keep the same level of output. As
the quantity of labor is increased from one unit to two units, the quantity of capital is decreased from
four to three, to keep the level of output constant, which is 200.

ii. Convex to Origin: Shows the substitution of inputs and diminishing marginal rate of technical
substitution (which is discussed later) in economic region. This implies that marginal significance of
one input (capital) in terms of another input (labor) diminishes along the isoquant curve.

iii. Non-intersecting and Non-tangential: Implies that two isoquant curves (as shown in Figure-4)
cannot cut each other. The two isoquants intersect at point A implying that they give the same level of
satisfaction. but the intersection of two isoquants implies that BL2 and CL2 are equal with respect to
their output, which is not possible. Therefore, it is stated that isoquant curves cannot intersect;
otherwise the law of production would not be applicable.
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iv. Upper isoquant have high output: Implies that upper curve of the isoquant curve produces more
output than the curve beneath. This is because of the larger combination of input result in a larger
output as compared to the curve that is beneath it.

Marginal Rate of Technical Substitution(MRTS):

“The marginal rate of technical substitution is the amount of an input that a firm can give up in order
to increasing the amount of the other input by one unit and still remain on the same isoquant.”

Marginal Rate of Technical Substitution (MRTS) is the quantity of one input (capital) that is reduced
to increase the quantity of the other input (L), so that the output remains constant. The MRTS is equal
to the slope of isoquants.

The principle of marginal rate of technical substitution (MRTS ) is based on the production function
where two factors can be substituted in variable proportions in such a way as to produce a constant
level of output.
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The isoquant reveals that as the units of labour are successively increased into the factor-combination
to produce 100 units of good X, the reduction in the units of capital becomes smaller and smaller. It
means that the marginal rate of technical substitution is diminishing.

Marginal rate of factor substitution: As one moves down the isoquant, output remains the same.
Therefore the output gained from employing more labour must equal the output lost from employing
more capital. This can be depicted in mathematical form as

The marginal rate of substitution is the amount of one factor (e.g. K) that can be replaced by one factor
(e.g. L). If 2 units of capital could be replaced with one-factor labour,

RETURNS TO SCALE:

Returns to scale describes the relationship between variable inputs and output when all the inputs, or
factors are increased in the same proportion. It has been observed that when there is a proportionate
change in the amounts of inputs, the behavior of output varies.

In the long run all factors of production are variable. No factor is fixed. Accordingly, the scale of
production can be changed by changing the quantity of all factors of production

The changes in output as a result of changes in the scale can be studied in 3 phases. They are:
Increasing returns to scale, Constant returns to scale and Decreasing returns to scale
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a) Increasing Returns to Scale:

Increasing returns to scale or diminishing cost refers to a situation when all factors of production are
increased, and output increases at a higher rate. It means if all inputs are doubled, output will also
increase at a faster rate than double. Hence, it is said to be increasing returns to scale. This increase is
due to many reasons like division of labour and external economies of scale.

A movement from a to b indicates that the amount of input is doubled. Now, the combination of inputs
has reached to 2K+2L from 1K+1L. However, the output has increased from 10 to 25, which is more
than double. Similarly, when input changes from 1K+1L to 3K + 3L, then output changes from 10 to
50, which is greater than change in input. This shows increasing returns to scale.

There a number of factors responsible for increasing returns to scale.

Some of the factors are as follows:

i. Technical and managerial indivisibility: implies that there are certain inputs, such as machines and
human resource, used for the production process are available in a fixed amount. These inputs cannot
be divided to suit different level of production. For example, an organization cannot use the half of the
turbine for small scale of production.
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ii. Specialization: Implies that high degree of specialization of man and machinery helps in increasing
the scale of production. The use of specialized labor and machinery helps in increasing the
productivity of labor and capital per unit. This results in increasing returns to scale.

iii. Concept of Dimensions: Refers to the relation of increasing returns to scale to the concept of
dimensions. According to the concept of dimensions, if the length and breadth of a room increases,
then its area gets more than doubled. For example, length of a room increases from 15 to 30 and
breadth increases from 10 to 20. This implies that length and breadth of room get doubled. In such a
case, the area of room increases from 150 (15*10) to 600 (30*20), which is more than doubled.
b. Diminishing Returns to Scale:

Diminishing returns or increasing costs refer to that production situation, where if all the factors of
production are increased in a given proportion, output increases in a smaller proportion. It means, if
inputs are doubled, output will be less than doubled. If 20 percent increase in labour and capital is
followed by 10 percent increase in output, then it is an instance of diminishing returns to scale.

(NOTE: The Horizontal Axis Should Read Diminishing Returns to Scale –NOT CONSTANT)

When the combination of labor and capital moves from point a to point b, it indicates that input is
doubled. At point a, the combination of input is 1k+1L and at point b, the combination becomes
2K+2L, However, the output has increased from 10 to 18, which is less than change in the amount of
input. Similarly, when input changes from 1K+1L to 3K + 3L, then output changes from 18 to 24,
which is less than change in input. This shows the diminishing returns to scale.
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Diminishing returns to scale is due to diseconomies of scale, which arises because of the managerial
inefficiency. Generally, managerial inefficiency takes place in large-scale organizations.

Another cause of diminishing returns to scale is limited natural resources. For example, a coal mining
organization can increase the number of mining plants, but cannot increase output due to limited coal
reserves.

c. Constant returns to scale

Constant returns to scale or constant cost refers to the production situation in which output increases
exactly in the same proportion in which factors of production are increased. In simple terms, if factors
of production are doubled, output will also be doubled. In this case internal and external economies are
exactly equal to internal and external diseconomies. This situation arises when after reaching a certain
level of production, economies of scale are balanced by diseconomies of scale.

When there is a movement from a to b, it indicates that input is doubled. Now, when the combination
of inputs has reached to 2K+2L from IK+IL, then the output has increased from 10 to 20.

Similarly, when input changes from 1K+1L to 3K + 3L, then output changes from 10 to 30, which is
equal to the change in input. This shows constant returns to scale. In constant returns to scale, inputs
are divisible and production function is homogeneous.
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Calculating constant returns to scale is important because it helps companies measure the correlation
between their inputs and outputs to notice how their processes are affecting the average cost of production in
the long run. A constant return to scale is the goal of most companies because it means their investments are
generating consistent returns. As they invest more capital, resources and labor into a project, they're seeing
the benefits returned to them at the same rate

Production of Maximum Output With A Given Level Of Cost (Equilibrium)

How does the firm decide the most optimal or efficient level of production?
In the long run, a specific firm has the freedom of choice to make several business decisions.

Whatever output a firm chooses to produce, the production manager desires producing it at the lowest
possible cost. To accomplish this objective, the production process must not only be technically
efficient but economically efficient, as well. So the production process has to be organized in the most
efficient manner.

Note 1 : The firm’s cost, in its turn, depends on two key factors, viz.:

(1) The technical relation between inputs and output (i.e., how outputs vary as inputs vary), and

(2) Factor prices (i.e., the price of labour or the wages, the price of capital or the interest rate and so
on).

To analyze the maximum output of a firm we use the isoquant and the isocost curve analysis.

An isoquant curve may be defined as a curve showing the possible combinations of two variable
factors, labor and capital that can be used to produce the same total product

An isocost line is a graph showing various possible combinations of inputs (labor and capital) that can
be purchased for an estimated total cost. Any combination of inputs on an isocost line provides the
same total cost for the output.

OR An isocost line is a locus of points showing the alternative combinations of factors that can be
purchased with a fixed amount of money. In fact, every point on a given isocost line represents the
same total cost. To construct isocost lines we need information about the market prices of the two
factors

ILLUSTRATION OF AN ISOQUANT
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Let a unit of labour cost 6600 pounds and that a unit of capital cost 6,000 pounds. If the total outlay of
the firm to be spent on the two inputs is 400,000 pounds

 If the firm spends all its outlay on labour, then it is able to buy 400,000/6,000 = 60.6 units of
labour
 If the firm spends all its outlay on capital, then it is able to buy 400,000/6,000 = 60.6 units of
capital.

These lines are straight lines because factor prices are constant and they have a negative slope equal to
the factor-price ratio, Its slope is given by the ratio of the prices of the two factors. It is known as the
actual rate of factor substitution, the rate at which the firm can substitute labour by capital in the
market place.

EXERCISE: Let a unit of labour cost Sh. 500 and a unit of capital cost Sh. 1000. If the total outlay of
the firm to be spent on the two inputs is Sh. 10,000

 If the firm spends all its outlay on labour, then it is able to buy 10,000/500 = 20 units of labour
 If the firm spends all its outlay on capital, then it is able to buy 10,000/1000 = 10 units of
capital.
Draw the isocost curve
Diagram.
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For Profit Maximisation: To maximize profits, a firm will wish to produce at the point of the highest
possible isoquant and minimum possible isocost.
Combining Isoline and Isoquants in order to get the best possible output level where the firm will be in
equilibrium

Four hypothetical isoquants are shown. Clearly, at the given level of cost, output level Q 3 is unattain-
able. And, neither output level Q0 nor level Q1 would be chosen, since higher levels of output can be
produced with the fixed cost outlay. The highest possible output with the given level of cost is
produced by using Lo amount of labour and K0 amount of capital.

At point A, the given isocost line is tangent to the highest attainable isoquant, ie, isoquant Q2. Thus, in
the case of constrained output maximization, the MRTS of capital for labour equals the factor-price
ratio (the price of labour to the price of capital).

Thus in order either to maximize output subject to a given cost or to minimize cost subject to a given
output, the production manager must employ factors in such amounts as to equate the MRTS with the
factor price ratio.

.…………………………………..END…………………………