The law of variable proportion

                                                                 ECONOMICS NOTE

The law of variable proportion:

The law of variable proportion analyzes the short run production phenomenon. In the short run ,the volume of production can be changed by altering the variable factors of production . Generally, labour is considered as variable and other factors are assumed constant. 

                      This law states that when more and more unit of variable inputs are used with the given fixed inputs, then the total output may initially increase at an increasing rate upto some extent and it increases at decreasing rate and it reaches to maximum level then it starts to decline.

         The law of variable proportion operates under the following  assumptions:

·         The state of technology remains constant.

·         Labour is single variable factor and it is homogeneous.

·         There must be possibility of varying the proportion of factors of production.

This law can be explained by the help of table and figure.

Fixed input	No.of labour	Total product	Average product=TP/L	Marginal product=	Stage of Returns
2      2 2 2	1 2 3 4	8 20 36 48	8 10 12 12	8 12 16 12	Ist stage
2 2 2	5 6 7	55 60 60	11 10 8.6	7 5 0	IInd stage
2 2	8 9	56 45	7 5	-4 -11	IIIrd stage

The table shows that, production changes due to change in variable factor (i.e. labour). As the number of labor increases, initially TP_L  increases at an increasing rate and starts to increases in decreasing rate , APL and MPL increases different rate and equal at particular point, it is the Ist stage .In second stage TPL increases at decreasing rate and reaches at maximum level , APL starts to decline and MPL also decline , APL declines continuously and MPL starts to decline  negatively.

          The law of variable proportion can be explained by the following figures.

In the above Y-axis measures  TP_L, MP_L and  AP_L ,and X-axis measures unit of labour. As the  quantity of labor increases by keeping all other factors constant ,there may arise three different stages.

First stage: First stage covers upto OL2.In this stage, TP_L increase at increasing rate upto point of inflexion, then it increases at decreasing rate .MP_L increases  gradually and becomes maximum at point of inflexion then it begins to fall. At the end of this stage both MP_L and AP_L are equal .

 In the first stage , increasing returns to scale crop up due to increase in efficiency of fixed factor and increase in efficiency of labor.

Second stage : This stage begins with the L₂ to L₃ . In this stage TP_L increases at decreasing rate until it reaches to the maximum point. AP_L and MP_L decline but positively. MP_L sharply declines and becomes zero when TP_L is maximum. AP_L is greater than MP_L.

 In this stage decreasing returns to scale crop up due to the imperfect substitutability of the factors of production and scarcity of fixed factor.

Third stage : This stage begins with L₃ , where TP_L starts to decline. AP_L gradually declines and MP_L declines negatively.

In this stage negative returns to scale crop up due to excessive amount of variable factor over the limited fixed factor.

-A rational producer will always produce in II^nd stage where both APL and MPL are positive.