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Lesson – 17
Production Function
Summary
The concept of production function is the subject matter of producers`
behaviour who play an important role in the production of goods and service
by establishing physical relationship between input and output. This is
evident from the fact that no single commodity can be produced without the
help of any one of these four factors of production. Therefore, the producer
combines all the four factors production i.e. land. Labour, capital and
entrepreneur for producing variety of goods and services in a technical
proportion which, in turn, provides the basis of studying the concepts of cost
of production, different market forms, concept of supply etc. Let us discuss
about various concepts like TPP, APP, MPP, short run and long run production
function, law of variable proportion in this topic.
Meaning of Production It can increase only the level
output by increasing the
Production is defined as the quantity of a variable factor
process of creating goods and and making intensive use of
services with the help of the existing fixed factors.
factors of production or inputs Long run refers to the time
for satisfaction of human period in which the firms can
wants. increase the scale of output
In other words, by increasing the quantity of
‘transformation of inputs into all the factor inputs
output’ whereby value is simultaneously and in the
added, is broadly called same proportion.
production.
Different Concept Related to b. Fixed factors and variable
Production Function – factors
Fixed factors are those
a. Short run and long run factors of production whose
Short run refers to a time quantity can not be hanged
period in which a firm does with change in the level of
not have sufficient time to output.
increase the scale of output.
Learner`s Guide, Sr. Sec. Economics,(318)
For example, the quantity of between inputs and output
land, machinery etc. can not under given technology.
be changed during short run. Ox = f (L, K)
Variable factors are those
factors of production whose Where, Ox=Quantity of commodity X
quantity can easily be hanged
with change in the level of f is the function and L and k
output. L = Unit of Labour
For example, we can easily
change the quantity of labor to K = Unit of Capital
increase or decrease the
production. Short run production function
c. Level of production and scale A short run production
of production function that shows the
When firm changes production changes in output when only
with change in quantity of one one factor is changed while
factor while other factors other factor remains constant
remains constant , it is known is termed as a short run
production function. In the
as change in level of above example of production
production. function.
It provides the basis for ‘Law of The underlying theory to the
Variable Production’. short run production function
When the firms increase is the “Law of variable
production by increasing the proportion or Returns to a
quantity of all the factors of factor”.
production simultaneously and
in the same proportion, it Long run production function
increases the scale of A long run production
production. function studies the impact on
It provides the basis of for ‘Law output when all the factors of
of Returns to Scale’. production can be changed
simultaneously and in the
Definition of Production same proportion.
Function
The underlying theory to the
Production function refers to long run production function
the physical relationship is the ‘Returns to Scale’.
Contd..
Learner`s Guide, Sr. Sec. Economics,(318)
Three Measures of Production Relationship among TPP, APP
and their Relationship and MPP
Total Physical Product (TPP) Units of Units of TPP in APP MPP in
Labour Capital Units in Units
TPP is the total amount of a Units
1 1 2 2 2 MP
commodity that is produced 2 5 2.5 3 1ST
with a given level of factor 3 9 3 4 Stage
inputs and technology during
a given period of time. 4 12 3 3 MP
nd
5 14 2.8 2 2
Formula, = ∑ 6 15 2.5 1 Stage
7 15 2.1 0
Or = + + +
1 2 3 8 14 1.7 -1 MP
⋯
(-ve)
rd
3
Average Physical Product (APP) Stage
APP is the output produced
per unit of input employed. It
can be obtained by dividing
TPP by the number of units of
variable input.
Formula, =
L = no. of Variable Unit
Marginal Physical Product (MPP)
MPP of an input is the
additional output that can be Relationship between TPP and MPP
produced by employing one As long as MPP increases, TPP
more unit of that input while increases at an increasing rate.
keeping other inputs constant
= ∆ When MPP falls but remains
positive, TPP increases but at a
∆
Where, ∆ = Change in TPP diminishing rate.
When MPP becomes zero, TPP
And ∆ = Change in Unit of Labour is maximum.
If MPP becomes negative, TPP
= −
−1 starts decreasing.
P
Learner`s Guide, Sr. Sec. Economics,(318)
Relationship between APP and There are three phases of returns to
MPP a variable factor which are
As long as MPP is greater than discussed below –
APP, APP increases. Phase I: Increasing Returns
When MPP is equal to APP, APP is to a factor - In this phase TPP
maximum and constant. increases at an increasing
When MPP is less then APP, APP rate and marginal product of
decreases. variable factor increases.
MPP can be zero and negative Phase II: Diminishing
but APP is never zero or Returns to a factor - In this
negative. phase TPP increases at an
increasing rate and marginal
product of variable factor
Law of Variable Proportion
increases.
The law states that if you go Phase III: Negative Returns
on using more and more units to a factor - In this phase,
of variable factor (labour) with MPP declines and it becomes
fixed factor (capital), the total negative. Here the TPP also
output initially increases at an starts falling.
increasing rate but beyond a
certain point, it increases at a Schedule for Law of Variable
diminishing rate and finally it Proportion
falls. Units Units TPP MPP Phases
Assumptions of the law- of of in in
Capital Labour Units Units
1 1 2 2 TPP increases
There is no change in 2 5 3 at increasing
rate, MPP also
technology of production. 3 9 4 increases
The production process allows TPP increases
the different factor ratios to 4 12 3 at a
5 14 2 diminishing
produce different levels out rate, and MPP
6 15 1 falls but
output. 7 15 0 remains
positive
There is no change in
technology of production. 8 14 -1 TPP falls and
MPP becomes
All the units of variable factor negative
are equally efficient.
Full substitutability of factors Graphical presentation Law of
of production is not possible. Variale Proportion
Learner`s Guide, Sr. Sec. Economics,(318)
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