Production
Function and Returns to a Factor
here
are four factors of production: Land, Labour, Capital and Entrepreneurship. For
contributing their factor services, factor payments for the four factors of
productions are as follows: Rent (land), wages and salaries (Labour), Interest
(capital) and Profit (entrepreneurship).
I. Production Function:
Production function is the function relationship between physical inputs and
physical output of a commodity for a given technology. It is purely a technical
relationship.
Production function is expressed in terms of the
following equation:
QX = f (L, K)
For
example, if physical inputs (say 10 units of capital and 5 units of labor) are
required to produce physical output(say 100 units of the commodity), the
production function for the same will be written as : 100X = f(5L, 10K).
II. Fixed Factors and Variable Factors
Factors
of productions are classified as:
(i) Fixed factors
(ii) Variable Factors.
(i) Fixed factors: Fixed
factors are those the application of which does not change with the change in
quantity of the output. Fixed
factors like machines are, in fact, installed before output actually starts.
Therefore, a fixed factor is there even when the output is Zero.
(ii) Variable Factors: Variable
factors are those the application of which varies with the change in the
quantity of output. Labour is an example of variable factor. You need more
labour to produce more units of a commodity.
III. Short Run Production Function and
Long Run Production function
(i) Short Run is a period
of time when production can be increased only by increasing the application of
variable factor(s). For example, once a plant (of a particular production
capacity) is installed, it cannot be changed during the short-run period. Short
period is too short to change it.
Short
run production function is written as under:
QX = f (L,K
)
Where, QX= Output of Good
X, L= Labour a variable factor, &
=
capital, a fixed factor
Also, consider these equations: 40X = f (5L, 4
) and 45X
= f (6L, 4
)
In short run, output can be increased only by increasing the
variable factor.
(ii) Long Run: Long
Run is a period of time when the distinction between “fixed factor” and the
variable factor vanishes. All the factors become variable factors. Long period
is long enough to even increase the production capacity of a firm by changing
the plant size or installing more plants.
QX
= f (L, K)
40X = f
(5L, 4K)
and 80X = f
(10L, 8K)
In the long run, output can be increased only by increasing the
application of both the factors.
|
Short Run Production Function
|
Long Run Production Function
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It
is a production function in which factor ratio tends to change with change in
the volume of output.
|
It
is a production function in which factor ratio does not change with change in
the volume of output.
|
|
Output
is increased by increasing the application of one variable factor only.
|
Output
is increased by increasing the application of all factors.
|
|
Scale
of output remains constant, no matter what the level of output is.
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Scale
of output tends to change with the change in the level of output.
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Short
period production function is studied with reference to “Returns to a factor.
|
Long
period production function is studies with reference to Returns to scale.
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Some
basic concepts:
(i)
Total Product (TP): TP is the sum total of output produced by all the units of
a variable factor along with some constant amount of the fixed factors used in
the process of production.
(ii)
Marginal Product (MP): MP refers to change in TP when one more unit of variable
factor is used, fixed factor remaining constant. TP is the sum total of MP
corresponding to each unit of the variable factors. Please note that TP is the
sum total of MP corresponding to each unit of the variable factor.
(iii)
Average Product (AP): AP is the output per unit of the variable factor. It is
estimated as: AP
= TP/L
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