Everything You Must Know About Production Function & Law of Variable Proportion

Production functions are equations that describe how inputs are used to produce outputs. It is an essential concept in economics as it helps explain the relationship between using different combinations of inputs and getting different output levels. The law of variable proportion explains how, when more of one input is added, eventually, its marginal productivity will decrease, and a point where total production will not increase anymore will be reached.

This article will provide details about what is production functions and explain the law of variable proportion explanation, and why they matter in economics.

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What is Production Function?

The production function is a mathematical formula that describes the relationship between inputs (labour, capital, land etc.) and outputs (goods or services produced). It helps to identify the optimal combination of inputs that will lead to maximum output. The production function also highlights how the firm can use different combinations of these inputs to produce more efficient output. 

Understanding this relationship is essential for businesses as it allows them to increase their profits by studying their current production processes and tweaking them accordingly. By understanding what increases or decreases productivity, firms can decide whether they should increase investments in specific resources, which in turn leads to improved profit margins.

What is the Law Of Variable Proportion?

The Law of Variable Proportions is an economic law that explains how the proportion of inputs used in production changes when one input increases while other inputs are held constant. This law states that as the amount of a factor of production, such as labour or capital, is increased while the amounts of other factors remain constant, eventually diminishing returns will occur. 

In other words, at some point, increasing one input will not produce commensurate increases in output. This can be seen when extra labourers are added to a factory, but productivity does not increase due to limited resources and space for workers to work effectively. Businesses need to understand this concept to make cost-effective decisions about investments and production methods.

Importance of Production Functions and Law of Variable Proportion

Production functions and the Law of Variable Proportions are two critical economic concepts. Production functions describe how the output is related to inputs, while the law of variable proportions states that as one input increases, the output will not necessarily increase proportionally. This law applies when a firm uses more than one input type in production processes.

The importance of production function lies in its ability to quantify economic efficiency. Economists can measure the most efficient way a firm should use resources for maximum profits or minimal costs by applying techniques such as marginal analysis or total cost-output analysis. Similarly, understanding the Law of Variable Proportions allows firms to identify their optimal level of resource usage given fixed quantities and prices for different available inputs. 

Moreover, both these concepts help managers make decisions by providing information on how changes in input affect outputs and what types of inputs can be used to obtain desired output levels efficiently. They also provide insight into modern theories about monopolies, where inefficient producers may gain an advantage over rivals by exploiting differences between productive capabilities due to economies of scale or other factors present within certain markets.

Stages of Law of Variable Proportion

This law applies in most production functions, but four distinct stages can be observed when this law is put into practice. 

Stage 1: The first stage occurs when one factor increases while all others remain constant. In this scenario, total output increases at an increasing rate as multiple units of the same factor are added until it reaches its maximum production capacity. This increase in output due to each additional unit is known as increasing returns to scale (IRS). 

Stage 2: The second stage begins after IRS has been achieved and continues until diminishing returns take effect. During this period, total output still rises with each additional unit; however, not at nearly the same rate as during Stage 1. 

Stage 3: After diminishing returns have begun taking effect on production processes, any further addition of the variable factor leads to even lower levels of output growth or negative returns altogether. This reduction in marginal productivity results from having too much utilisation of resources relative to what demand requires.

Stage 4: Finally, upon reaching its long-run equilibrium point where further additions lead only towards negligible gains, if any at all, no benefit accrues by adding extra units anymore, and profit maximisation goals become unachievable without compromising on quality standards or reducing per-unit cost structures substantially which may be difficult under some circumstances, e.g., labour market deficiencies etc.


The production function explains the law of variable proportions in detail. It states that as more and more units of a single input are used, at some point, the marginal productivity of that input begins to diminish and eventually reaches zero. This is because all inputs have limited capacities, so when we reach their maximum capacity, no additional output can be produced from them. As such, it is crucial for businesses to understand what is production function and explain the law of variable proportion. Consider this law carefully when deciding how much they should produce with each type of input available to them.

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