Law of variable proportion or returns to variable factor -

This law state that keeping other factors of production constant, when only one variable factor is increased, in the beginning total physical product increases at an increasing rate, then increases at a decreasing rate and ultimately decline. This law is applicable in short period only. 

This law has three phases-

I- Increasing returns to a factor - In this phase MPP increases so TPP increases at an increasing rate. Reasons for increasing returns to a factor are - better utilisation of fixed factor, increase in efficiency of variable factor, indivisibility of fixed factors. 

II- Diminishing returns to a factor - In this phase MPP decreases but positive so TPP increases at decreasing rate .This phase ends when MPP is zero & TPP is maximum. Reasons for diminishing returns is that factors of production are imperfect substitutes of each other and after optimum combination of factors when more and more units of variable factors are increased, pressure of production start falling on fixed factors and MPP start decreasing. 

III-Negative returns to a factor - In this phase MPP becomes negative so TPP decreases. It happens when variable factor become too much as compared to fixed factors then coordination between variable and fixed factor become very poor and efficiency of factors decrease. 

Explanation: The law of variable proportion can be explained with the help of a schedule and a diagram as follows.