The law of variable proportions or diminishing returns has been stated by Bentham in the following manner.
"As the proportion of one factor in a combination of factors is increased, after a point, first the marginal and then the average production of that factor will diminishing".
The behaviour of output as a result of change in the proportion of variable factors to the fixed factor can be studied through three stages.
Assumptions of the Law:
The behaviour of these total, average and marginal products of the variable factor as a result of the increase in its amount is generally divided into three stages.
Stage-I (Increasing Return)
Total Product increases at an increasing rate to a particular point say F. Corresponding to the point F Marginal Product increases up to this level. From the point F Total Product goes on rising at a diminishing rate and Marginal Product starts falling -but is still higher than Average Product and the AP continues to rise. 1st stage ends where MP curve cuts AP curve from above.
Stage-II (Diminishing Return)
The second stage begins from the point of intersection of AP and MP curves and ends at that point where" MP is zero. At this stage both MP and AP go on falling and both of them are positive. The total product goes on rising at a diminishing rate. This stage is known as the stage of diminishing return. This is stage where a firm wishes to operate.
Stage-III (Negative Return)
In the third stage Marginal Product of variable factor is zero. MP curve cuts the OX-axis at point M. In this stage the Total Product starts diminishing. Total Product continues to decline. As MP is negative this stage is also known as the stage of negative return.
Causes of law of variable proportions
conduction, convection, and radiation
the average variable cost curve and average cost curve are u- shaped because of the law of variable proportions.
The law of variable proportions, often discussed in economics, describes how the output of production changes as one input variable is modified while others remain constant. In mathematics, this concept can be applied to analyze relationships between variables in functions, particularly in calculus and optimization. For example, by examining how changes in one variable affect the output of a function, mathematicians can derive insights about marginal returns, similar to how the law of variable proportions informs economic production processes. Thus, both fields explore the dynamics of change and proportionality in their respective contexts.
what is relationship between change in input and output. In the return's to scale (long term concept) all the factor are variable but in the variable proportions are some factor variable and some factors are fixed.
All factors of production are variable in the long run.
A chemical combination of two or more substances in variable proportions is called a mixture. Mixtures can be either homogeneous (uniform composition throughout) or heterogeneous (non-uniform composition).
The law you are referring to is the Law of Definite Proportions. This law states that a chemical compound always contains the same elements in the same proportions by mass, regardless of the source of the compound.
The law of definite proportions was developed by Joseph Proust in 1806.
The law of multiple proportions was proposed by John Dalton in 1804; today this law has not a general validity.
At a point of inflexion in the law of variable proportions, the maximum output or productivity of a factor of production occurs when the marginal product of that factor begins to decline. This point indicates a shift in the relationship between input and output, where the addition of more of a variable input (while keeping others constant) leads to diminishing returns. Consequently, the total product curve changes from increasing at an increasing rate to increasing at a decreasing rate, highlighting the transition in production efficiency.
Dalton\'s principle of compounds supports the law of definite proportions.