Production function is a concept in economics that explains the relationship between physical output and input. Output refers to the number of goods or services produced in a given time period. Input, on the other hand, is the number of resources or materials that are used to produce output. While production is simply the process of creating goods and services for consumption, production function is the concept explaining the quantitative relationship between input and output. There are four main components of the production function. 

Overview of Production Function

• It refers to the relationship between the quantities of output of production and the input or factors of production. 
• It explains the amount of output that can be produced according to the quantity of input. 
• Four main factors of production exist: land, labour, capital, and entrepreneurship.
• There are two types of factors of production: Fixed factors and Variable factors.
• Fixed factors refer to those aspects of production that remain the same regardless of changes in the output.
• Variable factors are those that may change as output changes. 
• The formula for production function is Q= f(K, L), where Q is the output, f refers to function, K is the capital and L stands for labour. 
• There are two kinds of production functions: Long Run and Short Run Production Function. 

Types of Production Function

• Short Run Production Function and Long Run Production Function are two types of production function.
• Short run production function is the relationship between the specific variable input and quantity of output. 
• In the short run production function, only one factor is variable, while others remain fixed. 
• Long run production function explains the relationship between all inputs and the quantity of output. 
• In the long run production function, all factors of production, or inputs are variable.  

Total Product, Marginal Product, Average Product

• Total Product refers to the total amount of goods and services produced in a given period of time within a given input.
• Marginal Product is the quantity of total goods and services when an additional unit of the variable factor is used. 
• Average Product refers to the total product per unit of variable factors or input. 
• The relationship between total product and marginal product is:

1. An increase in total product at an increasing rate results in an increase in marginal product.
2. The increase of total product at a diminishing rate causes the marginal product to decrease. 
3. Finally, as the total product begins to decrease, the marginal product falls and becomes negative. 

• The relationship between average product and marginal product can be explained as:

1. When the average product is greater than the marginal product, the average product increases.
2. As the marginal product becomes more than the average product, the average product decreases.
3. As both marginal and average product fall, the marginal product falls at a greater rate and eventually becomes negative, while average product remains positive.

The Law of Variable Proportions

• The Law of Variable Proportions states that as the quantity of only one input increases, the total product first rises at an increasing rate, then at a decreasing rate, finally the total output ends up falling.
• Total product refers to the total amount of goods and services produced within the given input in a specific period of time.
• The Law has some assumptions:

1. Only one input will be variable, others are fixed.
2. It operates on the short run production function.
3. The condition of technology is given and is fixed.
4. The price of input or factors of production are fixed.
5. The proportion of variable factor units can be changed. 

• There are three phases of this law:

1. Increasing Returns: In this phase, the increase in one input leads to increase in the quantity of output at an increasing rate until it reaches its highest point. This phase sees an increase in both the total product and the marginal product.
2. Diminishing Returns: This stage is when the quantity of output increases but at a decreasing or diminishing rate. In the second phase, the total product increases but the marginal product starts decreasing but is positive. 
3. Negative Returns: In this phase, the output begins to decrease at a diminishing rate. Here, both total product and marginal product decrease. The marginal product becomes negative.

• There are several reasons for the law of variable proportions, three of which are: 

1. Increasing Returns: It states that a better utilisation of factors leads to an increase in the efficiency of these factors and thus increases overall output. 
2. Diminishing Returns: This happens as the combination of factors becomes less optimum and because the variable and fixed factors become imperfect substitutes of one another. 
3. Negative Returns: This happens as the efficiency of both negative and fixed factors falls and the quantity of fixed factors begins to decrease or fall.

Conclusion

Production function is a concept that explains the relationship between quantities of input and the output. Its formula is Q=f(K,L). Production function is of two types: short-run and long-run, depending on the number of fixed factors. Products can be of three kinds: Total product, Average product, and marginal product. There is a specific relationship between total product and marginal product as well as marginal product and average product. Production function is also used in the Law of Variable Proportions which states that as the quantity of one variable input increases, the total product first increases at an increasing rate, then decreases at a decreasing rate, and ultimately falls and the marginal product becomes negative.