Production Function
Blog post description.
10/22/20252 min read
Production illustrates how the resources used in creating a product relate to the outcome of that process. Customers can purchase and consume this item in stores. The effectiveness of the production process is based on the production function. The production function is better explained by the following sentences.
The technical ratio of the sources of production to the output
The right mix of inputs is necessary to get a certain amount of output.
This is the technical ratio between what goes in and what comes out.
The maximum or projected output that can be obtained from a certain set of inputs. The production function shows how well inputs like work, materials, and men are used to make the standard or expected output. A function known as a production function can display the amount or percentage of all these inputs. This equation shows the relationship between inputs and outputs:
Q = f(L1, C, L2)
Where,
L1 = Labor
L2 = Land
C = Capital
Above are input resources used to produce agricultural produce.
Example,
A farmer can produce rice in the expected (average) quantity using the various inputs such as labour, land (farm), and capital (which includes equipment, purchasing of seeds, fertilisers, etc.) for the production of a specific level of output, which is near the expectation.
Types of Production Function
Cobb-Douglas Production Function
Leontief Production Function
The CES Production Function\
Cobb-Douglas production function
This function displays the constant rate of return. This implies a direct relationship between the percentage changes in input and the changes in output. When the input goes up, the output will go up by the same amount. This function is also called a linear uniform production function.
Cobb-Douglas production function expressed in mathematical form as follows:
Q=ALError! Filename not specified. Kβ
Where,
L is input labour.
K is the input capital
Error! Filename not specified. & β are the positive parameters
The Cobb-Douglas production function indicated in three states, depends upon the values of Error! Filename not specified. & 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's production function shows that the amount of inputs used to make output is always changing by set multiples of that amount. The examples below show how it can be used.
An example
Two-wheeler and car manufacturers need a lot of different parts, like tires, shock absorbers, and other spares. These parts need to be ordered in set multiples, like two tires for a two-wheeler manufacturer.
When making cars, the tires are used in groups of four. This is how the CES generation function is written in math:
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 constants used, depending upon the product type.
Hence, the Leontief production function has a certain proportion of input that does not have substitutability.
The CES production function
CES (constant elasticity of substitution) indicates the constant