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The production function is the Technical relationship telling the maximum amount of output capable of being produced by each and every set of specified inputs. It is defined for a given set of technical knowledge.”

A production function is a mathematical and sometimes graphical way to measure the efficiency of production by considering the relationships between two or more variables, meaning two or more factors that are relevant when producing a good or service, such as raw materials and labor. Once a business has determined the factors for production, it can begin building the production function. For our castaway Carl, his factors of production would be his labor compared to the number of coconuts he collects.

According to Stigler, “the production function is the name given to the relationship between the rates of input of productive services and the rate of output of product. It is the economist’s summary of technical knowledge.

Production is the transformation of inputs into outputs. Inputs are the factors of production — land, labor, and capital — plus raw materials and business services.

The transformation of inputs into outputs is determined by the technology in use. Limited quantities of inputs will yield only limited quantities of outputs. The relationship between the quantities of inputs and the maximum quantities of outputs produced is called the “production function.”

But how do these outputs change when the input quantities vary? Let’s take a look at an example of a production function.

In general, we would allow for varying amounts of land, labor and capital. However, in this example, labor will be the only input, for the sake of simplicity.

The main theme of production function is to get the maximum production with the present given set of variable.

Eg: a firm can use the more labour and less machines OR it can use less labour and more machines to get maximum production. Here which is suited best and how to find the best alternative choice is the main aim of production function.

In a general mathematical form, a production function can be expressed as:

• Q=output/quantity
• LB = Land & Buildings.
• L = Labour.
• K = capital.
• M = raw material.
• t= time.

Types of Production Function

Short Run Production Function: In short run production function one factor of production remains constant and one factor of production changes. As in short run we can make changes in labour only the other factor that is capital remains constant as in short period we cannot immediately make changes in the capital only labour can be changed.

Long Run Production Function: In long run production function all factors of production changes. As in long run we can make changes in labour as well as the other factor that is capital also. So in long run all factor of production are variable. Output can be increased by increasing all the factors of production.