Production Function and The Law of variable proportions
Production Function and Analysis
The term, “production” means the transformation of physical
‘inputs’ into physical ‘output’ Or we can say that production is concerned with
the way in which resources [inputs] are employed to produce a firm’s products
[outputs].
The term ‘inputs’ or ‘factors of production’ includes all
those things which are required by the firm to produce a particular product.
Economists have classified input as
labour, capital, land, and organization. Along with these four factors, there
are some more factors added to the factors of production, for example, raw
materials, power, fuel, technology, time and services like transports and communications, warehouse, marketing,
banking, shipping and insurance, etc. Thus the term ‘input’ has a wider meaning
in economics.
While ‘Output’ refers to finished products.
Production Function: A production function describes the technological
relationship between inputs and output in physical terms. It specifies a flow
of output resulting from a flow of inputs during a specified period of time.
A production function can be represented in the form of
mathematical equation as
Q=f [L, N, K..etc.] where Q stands for the quantity of output
per unit of time and L, N, K, are the various factors inputs like land, labour,
capital etc which are used in the production of output.
There are two types of factor inputs:
Fixed Inputs: A fixed input is one whose
supply is inelastic in the short run such as land, machinery, etc. It can not be
increased in the short-run. In a technical sense, a fixed factor is one that
remains fixed or constant for a certain level of output.
Variable Inputs: A variable input is one whose supply is elastic in the
short-run such as labour and raw material, etc. All the users of such factors
can employ a larger quantity in the short run. Technically, a variable input is
one that changes with the change in the output.
In the long run, all inputs are variable.
Thus, there are two types of production function as follows:
Short-run production function: The short-run refers to a period of
time in which the supply of certain inputs such as plant, building, machinery,
etc is fixed or is inelastic.
Quantities of all inputs both fixed and the variable will be kept
constant and the production of a commodity can be increased by increasing the use
of only one variable input like labour or raw materials. For example, the law of
variable proportion.
Long-run production function: The long-run refers to a period of time in
which the supply of all the inputs is elastic thus in the long run all the
inputs are variable. In this case, the producer will vary the quantities of all
factor inputs, both fixed as well as a variable in the same proportion. For
example, the law of returns to scale.
Production Function with Fixed factors and one Variable Input
The Law of variable proportions: The law of variable proportion
explains the behaviour of production as the proportion between fixed and
variable inputs are changed, by increasing the quantity of the variable factor.
The law of variable proportions states as follows:
The marginal product of a variable input (which is being
added to other inputs that are fixed in quantity) will eventually decline.
The law of variable proportion states that as the quantity of
a variable factor is increased, keeping the quantities of other factors
constant, the total production at first increases more than proportionately,
then in equal proportion and finally less-than-proportionately.
According to Professor Marshall, an increase in the quantity
of a variable factor added to fixed factors, at the end results in a less than the proportionate increase in the amount of product, given technical conditions.
Thus, it states that when more-and-more units of a variable
input is applied to a given quantity of fixed inputs, the total output may
initially increase at an increasing rate and then at a certain rate, but it
will eventually increase at diminishing rates.
Assumptions:
1 Only one factor is variable while other factors are held constant.
2 Different units of a variable factor are homogeneous.
3 No change in technology.
4 There are possibilities for varying the proportions in which different inputs are combined.
5 The law will hold good only for a short and a given period as in long run all factors are variable.
|
No of units of Variable Inputs |
Total Product in units (TP) |
Marginal Product in units (MP) |
Average Product in units (AP) |
Stages of Production |
|
1 |
20 |
20 |
20 |
First Stage |
|
2 |
48 |
28 |
24 |
|
|
3 |
78 |
30 |
26 |
|
|
4 |
104 |
26 |
26 |
Second Stage |
|
5 |
120 |
16 |
24 |
|
|
6 |
132 |
12 |
22 |
|
|
7 |
140 |
8 |
20 |
|
|
8 |
144 |
4 |
18 |
|
|
9 |
144 |
0 |
16 |
|
|
10 |
140 |
-4 |
14 |
Third Stage |
Total product or Output: Total output is the sum of marginal
output. It is the output derived from all units of factors. The total product goes
on increasing as long as the marginal product is positive. It is the highest when
MP is zero and declines when MP becomes negative.
Marginal Product or output: It is the output derived from an additional
unit of a variable factor. MP increases, in the beginning, reaches the highest
point, diminishes and becomes negative at the end.
Average Product or Output: It can be obtained by dividing total
output by the number of a variable factor. AP has the same tendency as the MP.
In the beginning, MP will be higher than AP but At the end, AP will be higher
than MP.
Stage One: In this stage, the output can be
increased by increasing the variable input relative to the fixed input. The
first stage comes to an end when the MP curve cuts the AP curve at the point where AP
is maximum. TP increases at an increasing rate until MP reaches its highest
point. This stage is called the stage of increasing returns.
Stage Two: In this stage, TP increases at a diminishing rate as both MP and AP fall,
but both are positive. This stage extends from the end of stage 1 [at the point
where MP and AP are equal] to the point
where MP is zero and TP is maximum. This stage is also known as the stage of
diminishing returns. In this stage, the firm maximizes its total output.
Stage Three: In this stage, the variable factor
is excessive related to the fixed factors, MP is negative & TP also declines.
It is completely irrational to produce in this stage.
A ration producer will not select
either the stage one or stage three because in stage-one there is
an opportunity to increase the output by employing more units of the variable
input. And in stage-three, MP is negative and TP declines. The stage-one &
stage-three are described as a non-economic region. The producer will select only
the stage-two because this is the most economic region, where the producer can
maximize the output.
Reason for the application of this
law
In the short term, the producer cannot
increase the quantities of all the factors of production. That is why there is the only
possible to increase one variable factor, keeping other factors fixed. The proportion of the factors
becomes more suitable after increasing the quantity of a variable factor and leads
to more efficient utilization of the fixed factors. During the initial stage, the total production rises at an increasing rate because of the increase in the marginal product. Eventually, beyond the points of optimum combination, if the
producer continues increasing the units of the variable factor, the factor proportion
becomes ineffectual. Therefore, the marginal product starts decreasing and becomes
negative. At this point, the total product also decreases.
This law helps a producer to select
the most ideal combination of factor inputs or the least cost combination of
factor inputs.
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