Unit – 3: Production Function
Law of Variable Proportion
Meaning:
The law of variable proportion is one of the
fundamental laws of economics. It is also known as the 'Law of Diminishing
Marginal Returns' or the 'Law of Diminishing Marginal Productivity.' This Law
of variable proportion shows the input-output relationship or production
function with one variable factor, i.e., a factor, which can be changed, while
other factors of production are kept constant.
In short-period when the output of a good is sought to be
increased by way of additional application of the variable factor, law of
variable proportions comes into operation. When the number of one factor is
increased while all other factors remain constant, then the proportion between
the factors is altered. On account of change in the proportion of factors there
will also be a change in total output at different rates. In economics, this
tendency is called Law of Variable Proportions. The law stats that as the
proportion of factors is changed, the total production at first increases more
than proportionately, then equi-proportionately and finally less than
proportionately.
According to Samuelson,
“The law states than 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.”
Assumptions: The law of variable proportions functions is based on
following assumptions:
a)
Constant technology: The technology is
assumed to be constant because technological changes will result into rise of
marginal and average product.
b)
Snort-run: The law operates in the short-run
because it is here that some factors are fixed and others are variable. In the
long-run, all factors are variable.
c)
Homogeneous input: The variable input
employed is homogeneous or identical in amount and quality.
d)
Use of varying amount of variable factor: It
is possible to use various amounts of a variable factor on the fixed factors of
production.
Explanation of the Law: Law
of variable proportion can be explained with the help of following table and
diagram:
Units of Land
|
Units of Labour
|
Total Product
|
Marginal Product
|
Average Product
|
1
|
1
|
2
|
2
|
2
|
1
|
2
|
5
|
3
|
2.5
|
1
|
3
|
9
|
4
|
3
|
1
|
4
|
12
|
3
|
3
|
End of the first State Beginning of the
Second Stage
|
||||
1
|
5
|
14
|
2
|
2.8
|
1
|
6
|
15
|
1
|
2.5
|
1
|
7
|
15
|
0
|
2.1
|
End of the Second Stage Beginning of the
Third Stage
|
||||
1
|
8
|
14
|
-1
|
1.7
|
Explanation: From
the above Table and Diagrams drawn on the assumption that production obeys the
law of variable proportions, one can easily discern three stages of production.
These are elucidated in the following table:
Three
States of Production
States
|
Total Product
|
Marginal Product
|
Average Product
|
1. Stage
|
Initially
it increases at an increasing rate. Later at diminishing rate.
|
Initially
increases and reaches the maximum point. The starts decreasing.
|
Increases
and reaches its maximum point
|
2. Stage
|
Increases
at diminishing rate and reaches its maximum point.
|
Decreases
and becomes zero.
|
After
reaching its maximum begins to decrease.
|
3. Stage
|
Begins to
fall
|
Becomes
Negative.
|
Continues
to diminish.
|
Causes of Applicability: Main
causes accounting for the application of the law of variable proportions are as
follows:
1)
Under utilization of Fixed Factor: In the initial stage of production, fixed factor of production
like land or machine is under-utilized. More units of variable factor, like
labour are needed for its proper utilization. Thus, as a result of employment
of additional units of variable factor there is proper utilization of fixe
factor. Consequently, total production begins to increase.
2)
Fixed Factors of production: The
principal cause of the operation of this law is that some of the factors of
production are fixed during the short period. When the fixed factor is used
with variable factor, then its ratio if compared to variable factor falls.
Production is the result of the cooperation of all factors. Consequently,
marginal return of the variable factor begins to diminish.
3)
Optimum Production: After making
the optimum use of a fixed factor if it is combined with increasing units of
variable factor, then the marginal return of such variable factor begins to
diminish.
4)
Imperfect Substitute: It is the
imperfect substitution of factors that is mainly responsible for the operation
of the law of diminishing returns. One factor cannot be used in place of the
other factor. Consequently, when fixed and variable factors are not combined in
an appropriate ratio, the marginal return of the variable factors begins to
diminish.
Postponement of the Law: Postponement
of the law of variable proportions is possible under the following conditions:
1)
Improvement in Technique of Production: Operation of the law can be postponed if along with the increase
in variable factors technique of production is improved.
2)
Perfect Substitute: The law can
also be postponed if factors of production are made perfect substitutes, i.e.
when one factor can be substituted for the other.
Isoquants and its Properties
The
word an
isoquant is a locus of points, representing different
combinations labour and capital .An isoquant Curve. ‘ISO’ is of Greek origin
and means equal or same and ‘quant’ means quantity. An isoquant may be defined as a
curve showing all the various combinations of two factors that can produce a given level
of output. The
isoquant shows- the whole range of alternative ways
of producing- the same level of output. The modern economists
are using isoquant, or ‘ISO’ product curves for determining the optimum factor
combination to produce certain units of a commodity at
the least cost.
Properties or Features of Isoquant
The following are the important
properties of isoquants:
1. Isoquant is downward sloping to
the right. This means that if more of one factor is used less of the other is
needed for producing the same output.
2. A higher isoquant represents
larger output.
3. No isoquants intersect or touch
each other. If so it will mean that there will be a common point on the two
curves. This further means that same amount of labour and capital can produce
the two levels of output which is meaningless.
4. Isoquants need not be parallel
to each other. It so happens because the rate of substitution in different
isoquant schedules need not necessarily be equal. Usually they are found
different and therefore, isoquants may not be parallel.
5. Isoquant is convex to the
origin. This implies that the slope of the isoquant diminishes from left to
right along the curve. This is because of the operation of the principle of
diminishing marginal rate of technical substitution.
6. No isoquant can touch either
axis. If an isoquant touches X axis then it would mean that without using any
labour the firm can produce output with the help of capital alone. If an
isoquant touches Y axis, it would mean that without using any capital the firm
can
produce output with the help of labour alone. This is impossible.
7.Isoquants have negative slope.
This is so because when the quantity of one factor (labour) is increased the
quantity of other factor (capital) must be reduced, so that total output
remains the same.
Ridge Lines - The Economic Region of Production:
An isoquant represents combinations of two inputs that yield the
same level of output. However, not all points of an isoquant are relevant for
production. Such points may be called infeasible points. One should consider
only feasible portions of an isoquant. This is because of the fact that no
rational producer will produce where marginal product of an input is either
zero or negative.
If the isoquant is backward bending and upward sloping, marginal
product of any input will be negative, and, hence, this portion of the isoquant
may be considered as economically non-sensible region of production. Only the
negatively sloped segment of the isoquant is relevant for production or
economically feasible.
This is shown in Fig. 3.5 where we have drawn three isoquants showing
different levels of output for different labour-capital combinations. This
diagram separates economic region of production from uneconomic region of
production. Region in which marginal products of all inputs are positive
constitutes economic region of production.
Or the region in which input substitution takes place may be
called economic region of production. In an uneconomic region, as marginal
product of an input becomes either zero or negative, the question of input
substitution does not arise. Production in such region is, for obvious reasons,
unprofitable or infeasible.
At point A on IQ1, the firm
employs certain units of labour and capital. Since the tangent to IQ1 at point A is parallel to the vertical axis,
marginal product of capital (MPK) is zero. If
more capital is used, marginal product of capital should be negative. In other
words, beyond point A, MPK is
negative. At point B on IQ1, MPL is zero and beyond point B on IQ1, MPL is
negative.
Thus, points between A and B represent positive marginal
productivities of both labour and capital. Here substitution between two inputs
takes place. Similarly, points A1and A2 on IQ2 and IQ3describe zero MPL while
points beyond A1 and A2 describe negative MPK. Points B1and B2 on IQ2and IQ3 represent zero MPK and
beyond B1and B2 describe
negative MPL.
A rational producer will produce in that region where marginal
productivities of inputs are positive. By joining points A, A1 and A2 (i.e.,
points of zero marginal products) we get OR line and by joining points B, B1 and B2 (points of
zero marginal products) we get OL line. These lines are called ridge lines.
They give the boundaries of the economic region of production where input
substitution takes place.
Any
point on the Isoquants outside the upper ridge line OR and the lower ridge line
OL constitute uneconomic region of production. Production must take place
inside the ridge lines. Note that the ridge lines separate the relevant (i.e.,
negatively sloped) from the irrelevant portions (i.e., positively or zero
sloped) of the Isoquants.
Producer’s Equilibrium or Optimum Combination
of Factors or Least Cost Combination
The producer’s equilibrium refers to the situation in which a
producer maximizes his profits. In other words the producer is producing given
amount of output with least cost combination of factors. The least cost
combination of factor’s also called optimum combination of the factor or input.
Optimum combination is that combination at which either:
a) The output derived from a given level of inputs is maximum OR
b) The cost of producing a given output is minimum.
For producer’s equilibrium or optimum combination, it must fulfill
following two conditions as:
(i) At the point of equilibrium the iso-cost line must be tangent
to isoquant curve.
(ii) At point of tangency i.e., iso-quant curve must be convex to
the origin or MRTSLk must be falling.
The iso-cost line gives information regarding factor prices and
financial resources of the firm.
With a given outlay and prices of two factors, the firm obtains
least cost combination of factors, when the iso-cost line becomes tangent to an
iso-product curve. Let us explain it with the following Fig. 15.
In Figure 15, P1L1 iso-cost line has become tangent to
iso-product curve (representing 500 units of output) at point E. At this point,
the slope of the iso-cost line is equal to the iso-product curve. The slope of
the iso- product curve represents MRTS of labour for capital. The slope of the
iso-cost line represents the price ratio of the two factors.
Slope of Iso-quant curve = Slope of Iso-cost curve
MRTSLk = – ∆L/∆L = MPL/MPK = PL/PK
[where ∆K → change in capital, ∆L → change in labour, MPL →
Marginal Physical Product of Labour, MPk – Marginal Physical Product of
capital, PL Price of Labour, and PK → Price of capital, MRTSLK =Marginal Rate of
Technical Substitution of labour and capital.]
The firm employs OM units of labour and ON units of capital. The
producing firm is in equilibrium. It obtains least cost combination of the two
factors to produce 5 00 units of the commodity.The points such as H, K, R and S
lie on higher iso-cost lines. They require a larger outlay, which is beyond the
financial resources of the firm.
Expansion Path
As financial resources of a firm increase, it would like to
increase its output. The output can only be increased if there is no increase
in the cost of the factors. In other words, the level of total output of a firm
increases with increase in its financial resources.
By using different combinations of factors a firm can produce
different levels of output. Which of the optimum combinations of factors will
be used by the firm is known as Expansion Path. It is also called Scale-line.
In the words of Stonier and Hague, “Expansion path is that line
which reflects least cost method of producing different levels of output.”
Expansion path can be explained with the help of Fig. 16. On
OX-axis units of labour and on OY-axis units of capital are given.
The initial iso-cost line of the firm is AB. It is tangent to IQ
at point E which is the initial equilibrium of the firm. Supposing the cost per
unit of labour and capital remains unchanged and the financial resources of the
firm increase.
As a result, firm’s new iso-cost-line shifts to the right as CD.
New iso-cost line CD will be parallel to the initial iso-cost line. CD touches
IQ1 at point E1 which will
constitute the new equilibrium point. If the financial resources of the firm
further increase, but cost of factors remaining the same, the new iso-cost line
will be GH.
It will be tangent to Isoquants
curve IQ2 at point E2 which will be the new
equilibrium point of the firm. By joining together equilibrium points E, E1 and E2, one gets a line
called scale-line or Expansion Path. It is because a firm expands its output or
scale of production in conformity with this line
Laws of Return to Scale
It is a Long run concept. All factors of production are variable
in the long period. No factor is a fixed factor. Accordingly, scale of
production can be changed by changing the quantity of all factors.
According to Koutsoyiannis “The term returns to scale refers to
the changes in output as all factors change by the same proportion.”
There are three aspects to Laws of Return to Scale:
a)
Increasing Return to Scale.
b)
Constant Returns to Scale.
c)
Diminishing Returns to Scale.
Increasing Returns to Scale: When inputs
are increased in a given proportion and output increases in a greater proportion,
the returns to scale are said to be increasing. In other words, proportionate increase
in all factors of production results in a more than proportionate increase in output
It is a case of increasing returns to scale. Thus, if by
100 percent increase in factors of production, output increases by 120 percent
or more, it will be an instance of increasing returns to scale.
If the industry is enjoying
increasing returns, then its marginal product increases. As the output
expands, marginal costs come down. The price of the product also comes down.
Constant Return to Scale: When inputs
are increased in a given proportion and output increases in the same proportion,
constant return to scale is said to prevail. For example, if inputs are
increased by 25% and output also increases by 25%, the return to scale
are said to be constant ( = 1). This may be called homogeneous
production function of the first degree. In case of constant returns to
scale the average output remains constant. Constant returns to scale operate
when the economies of the large scale production balance with the
diseconomies.
Decreasing Returns to Sale: Decreasing
returns to scale is otherwise known as the law of diminishing returns. This
is an important law of production. If the firm continues to expand
beyond the stage of constant returns, the stage of diminishing returns to
scale will start operate. A proportionate increase in all inputs results
in less than proportionate increase in output, the returns to scale is said to
be
decreasing. For example, if inputs are increased by 20%, but output
increases by only 10%, ( = < 1), it is a case of decreasing return to scale.
Decreasing return to scale implies increasing costs to scale.
Internal and External Economies
Now-a-days,
goods are produced on a very large scale in modern factories. When the
production is carried on a large scale the producer derives a number of
advantages or economies. These advantages of large scale production are called
economies of scale. This is the reason why entrepreneurs try to expand the size
of their factories. Marshall divides the economies of scale into groups – (i)
internal economies and (ii) external economies.
1.
Economies of Concentration
2.
Economies of Information
3.
Economies of Disintegration
1. Labour Economies
2. Technical Economies
3. Inventory Economies
4. Selling or Marketing
Economies
5. Managerial Economies
6. Transport and Storage
Economies
A.
Internal Economies: Internal Economies: A producer drives a number of advantages when he expands the size
of his factory. These advantages are called internal economies. They arise
because of increase in the scale of production (i.e. output that can be
produced). These are secured only by the firm expanding its size. They are
dependent on the efficiency of the organizer and his resources. So internal
economies are those advantages which are obtained by a producer when he
increases or expands the size of his firm. Internal economies are divided into
various classes as follows. When a firm increases its scale of production it
enjoys several economies. These economies are called internal economies.
Types
of Internal Economies: There are two types of internal
economies:
a)
Real Economies: Real economies
are those which are associated with a reduction in the physical quantity of
inputs, raw materials, various types of labour and various types of capital.
Real economies can be of six types –
1)
Labour Economies or Specialization: Specialization means to perform just one task repeatedly which
makes the labour highly efficient in its performance. This adds to the
productivity and efficiency of the labour.
2)
Technical Economies: Technical
economies are those economies which are related with the fixed capital that
includes all types of machines & plants. Technical economies are of three
types:
a)
Economies of Increased Dimension.
b)
Economies of Linked Processes.
c)
Economies of the use of
By-Product.
3)
Inventory Economies: A large size
firm can enjoy several types of inventory economies; a big firm possesses large
stocks of raw material.
4)
Selling or Marketing Economies:
A firm producing a large scale also enjoys several marketing economies in
respect of scale of this large output.
5)
Managerial Economies: A firm
producing on large scale can engage efficient & talented managers.
6)
Transport and Storage Economies:
A firm producing on large scale enjoys economies of transport & storage.
b) Pecuniary
Economies: Pecuniary economies are economies
realized from playing lower prices for the factors used in the production and
distribution of the product due to bulk-buying by the firm as its size
increases.
B.
External Economies: When the
number of factories producing the same commodity like sugar increases, we say
that the particular industry (sugar industry) has developed. When the industry
as a whole develops, every firm in the industry derives man advantages. These
advantages are called external economies. They are enjoyed by all the firms in
the industry. They are not the property or monopoly of any firm. The following
are the main types of external economies:
1)
Economies of Concentration: When
several firms of an industry establish themselves at one place, then they enjoy
many benefits together, e.g. availability of developed means of communications
and transport, trained labour, by products, development of new inventions
pertaining to that industry etc.
2)
Economies of Information: When the
number of firms in an industry increase, then it becomes possible for them to
have concerted efforts and collective activities.
3)
Economies of Disintegration:
when an industry develops, the firms engaged in its mutually agree to divide
the production process among themselves.
Internal and External Diseconomies of
Scale
The term diseconomies of scale refer to a situation where an increase
in the size of the firm leads to a rising average cost. Diseconomies of scale may be classified into internal diseconomies and external diseconomies
of scale.
The major
internal diseconomies of scale arise from its size of the firm, technical causes and managerial problems. When a
firm achieves a size where it is producing at
the lowest possible average cost it is said to be at its optimum size. The optimum size will
very over time as technological
progress change the technique of
production. In addition to this, more loaded men and machinery
leads to machine fault and human failure cause
breakdown of production. When the size increases management becomes more
complex and difficult. Managerial function of co-ordination, consultation and
interdepartmental decision making will get delayed due to the size. There will be possibility of delay in implementation of decision
within the organization. Delay in communication will reduce the involvement of
the employees.
There are
some external diseconomies of scale in the form of disadvantages:
Ø There
is shortage of labour which causes a wage rise.
Ø Increase
in the demand for raw materials will also bid up prices.
Ø When
there is heavy localization of industries, the land for expansion will become increasingly scarce.
Scarcity will cause an increase in the price to purchase land or to rent.
Ø Transport
costs may also rise because of increased congestion.
The change in output will cause a
movement along the long run average cost curve. One of the most significant
influences is external economies of scale. If external economies are experienced, the long
run average cost will shift down (output will be now be cheaper to
produce). Whereas external diseconomies of scale are encountered
the long run average cost curve will move up (output will now be costlier to produce). Improved technology
would lower the long run average cost curve.