Production shows the relationship between input resources utilized to produce the product and output that is in the form of ready product. This product is ready to sell in the market which consumer consume. Production function determines the efficiency of production process. following statements explains the production function better.
- Technical proportion of factors of production versus output
- Appropriate combination of inputs to obtain given level of output.
- It is the technical ratio between input and output
- Maximum or expected output obtained by specific combinations of input.
Production function expresses the efficiency of input resources such as labour, material, men utilized to produce expected or standard output. The proportion or ratio of all these input can express in a function that is known as production function. The mathematical expression that shows the relationship between input resources and output that is production as follows
Q= f(L1, C, L2)
Where,
L1= Labor
L2= Land
C= Capital
Above input resources used to produce agriculture produce.
Example,
A farmer can produce rice in expected(average) quantity using the various inputs such as labor, land(farm) and capital(includes, equipment, purchasing of seeds, fertilizers etc.)for the production of specific level of output which is near to the expectation.
Types of Production function
- Cobb-Douglas Production Function
- Leontief Production Function
- The CES Production Function\
Cobb-Douglas production function
This function shows the constant rate of return which means proportion of input changes directly proportional to in output. When Input increases the output will proportionally increases. It is also known as linear homogeneous production function.
Cobb-Douglas production function expressed in mathematical form as follows
Q=ALKβ
Where,
L is input labor
K is input capital
& β are the positive parameters
Cobb-Douglas production function indicated in three states depends upon the values of & β.
- α + β >1: Increasing returns to scale
- α + β =1: Constant returns to scale
- α +β <1: Decreasing returns to scale.
Leontief production function
Leontief production function used to represent the constant change means fixed multiples of quantity of inputs utilized for the production of output. Following examples shows how it can be utilized.
Example,
Manufacturing of two wheeler or car requires tyres , shock-ups and the like many spare parts as the input material which needed in fixed multiples numbers such as tyres used in the multiples of two in case of two wheeler manufacturing.
In car manufacturing the tyres used in multiples of 4. The mathematical expression of CES production function as follows
Q=f(L1/a, L2/b)
Where,
Q is output or production quantity
L1 is input-1
L2 in input-2
a and b are the constant used depends upon the product type.
Hence the Leontief production function certain proportion of input which do not have substitutability.
The CES production function
CES(Constant elasticity substitution) indicate the constant return to scale. Increase in the input in n-times will tends to increase in the output in n-times.