Production Function: Meaning, Features, and Types

What is 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 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.

Q = f(L,K)

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

Production is a process that business uses to convert inputs into outputs. Production involves a series of activities that convert the inputs into outputs that people can use for the fulfilment of their needs. Production is basically the transformation of inputs into output. Input is anything that is utilised in the creation of a commodity and Output is something that gets produced at the end of the production process. The relationship between inputs and outputs is defined using the Production Function.

Assumptions of Production Function

• Both inputs and outputs are divisible.
• There are only two factors of production, i.e., land (Variable element) and capital (Fixed element).
• Factors of production are imperfect substitutes.
• Technology is constant.

Graphical Representation of Production Function

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).

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. 

Note: Production in the short run can only be increased by increasing the variable factor.

Features of Production Function

1. Complementary: A producer will have to combine the inputs to produce outputs. Outputs can not get generated without the use of inputs.

2. Specificity: For any given output, the combination of inputs that may be used is clearly defined. What type of factors are needed for the production of a particular product is clearly mentioned before the actual production gets started.

3. Production Period: The period of the production process is clearly explained to the production unit. Each stage of production is given some specific time. Production generally gets completed over a long period of time.

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. This relationship is explained by the ‘Law of Variable Proportions.’

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. This relationship is explained by the ‘Law of Returns to Scale.’

Concept of Product

Product or output refers to the volume of the goods that the company produces using inputs during a specified period of time. The concept of product can be looked at from three different angles: Total Product, Marginal Product, and Average Product.

1. Total Product: Total Product (TP) refers to the total quantity of goods that the firm produced during a given course of time with the given number of inputs. Total Product is also known as Total Physical Product (TPP) or Total Output or Total Return. For example, if 6 labours produce 10 kg of wheat, then the total product is 60 kg. A company can increase TP in the short term by focusing primarily on the variable components. But over time, both fixed and variable elements can be increased to raise TP. 

2. Average Product: Average Product refers to output per unit of a variable input. AP is calculated by dividing TP by units of the variable factor. For example, if the total product is 60 kg of wheat produced by 6 labours (variable inputs), then the average product will be 60/6, i.e., 10 kg. 

Average Product = [Tex]\frac{Total~Product}{Units~of~Variable~Factor}[/Tex]

3. Marginal Product: Marginal Product refers to the addition to the total product when one more unit of a variable factor is employed. It calculates the extra output per additional unit of input while keeping all other inputs constant. Other names of Marginal Product are Marginal Physical Product (MPP) or Marginal Return.

MP_n = TP_n – TP_n-1

Here, 

MP_n  = Marginal product of n^th unit of the variable factor, 

TP_n = Total product of n units of the variable factor, and 

TP_n-1 = Total product of (n-1) units of the variable factor