The functional relationship between the physical input (or factor of production) and therefore the output is named a production function. It assumed the input as an explanatory or independent variable and the output as a dependent variable. Mathematically, you can write this as:
Q=f(L,K)
Where”Q”represents the output,”L”and”K” are the inputs, respectively, labour and capital (such as machinery). Note that there may be many other factors, but we are assuming a two-factor input here. Production functions in the short term and in the long term are different. This distinction is crucial in microeconomics. This distinction is based on the nature of the factor input.
Factors
Variable factors includes inputs that change directly with the output. These are factors that can change. Fluctuating factors exist both in the short term and in the long term. Examples of variable factors include daily labour and raw materials.
On the other hand, factors that cannot change or change as the output changes are called fixed factors. These factors are usually characteristic only for a short or short period of time. There are no fixed factors in the long term.
Therefore, production functions can be defined: short-term and long-term. A short-term production function defines the connection between one variable factor (keeping all other factors fixed) and therefore the output. The law of regression to factors explains such a production function.
For example, suppose that a company has 20 units of Labour and 6 acres of land, and initially uses only Labour units (variable coefficients) for that land (fixed coefficients). Thus, the ratio of land and labour is 6: 1. Now, if the company chooses to adopt 2 labour units, then the ratio of land to Labour will be 3: 1 (6: 2).
Here, all factors change in the same proportion. The law used to explain called the law of return to scale. It measures how much of the output changes when the input changes proportionally.
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