Production Function

Production Function is the relationship between physical inputs (land, labour, capital, etc.) and physical outputs (quantity produced). It is a technical relationship (not an economic relationship) that studies material inputs on one hand and material outputs on the other hand. Material inputs include variable and fixed factors of production.

In the words of Watson, “Production Function is the relationship between a firm’s production (output) and the material factors of production (input).”

Algebraic and Graphical Representation of Production Function


In a standard equation, the Production function is represented by Q, Labour (Variable element) is represented by L, and Capital (Fixed element) is represented by K.

For example, When there are 4 units of labour and 5 units of capital, the equation for the production function is Q = f(4,5).

production function

 

In the above graph, X-axis represents inputs that are being used in the production process and Y-axis represents outputs that get produced. Q is the Production Function.

Variable Factors are the factors that can be changed during the course of the short run. Variable factors vary with the level of output. An increase in variable factors leads to more production and vice-versa. Employment of variable factors is not required when there is no production. Variable factors include labour, power, fuel, etc. 

Fixed Factors are the factors that can not be changed in the short run. The number of fixed factors always remains constant even when is zero production. Fixed factors include land, capital, building, etc. 

 Types of Production Function

Production function on the basis of the time period can be divided into two categories: Short Run Production Function and Long Run Production Function. 

In these production functions, the combination and behaviour of variable factors and fixed factors are different.

1. Short Run Production Function:

Short Run is a period of time where output can only be changed by changing the level of variable inputs. In the short run, some factors are variable and some are fixed. Fixed factors remain constant in the short run like land, capital, plant, machinery, etc. Production can be raised by only increasing the level of variable inputs like labour. Therefore, the situation where the output is increased by only increasing the variable factors of input and keeping the fixed factors constant is termed as Short Run Production Function.

2. Long Run Production Function:

Long Run is a span of time where the output can be increased by increasing all the factors of production whether it is fixed (land, capital, plant, machinery, etc.) or variable (labour). Long run is enough time to alter all the factors of production. All factors are said to be variable in the long run. Therefore, the situation where the output is increased by increasing all the inputs simultaneously and in the same proportion is termed Long Run Production Function.

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