Law of Variable Proportions:

"in a given state of technology, when the units of  variable factor of production (L) are increased within the units of other fixed factors, the marginal productivity increases at increasing rate up to a point, after this point. it will become less and less"


The assumptions of the law of variable proportion are given as below:

  1. It is assumed that the technique of production should remain constant during production.
  2. It operates in the short-run because in the long run, fixed inputs become variable.
  3. Some inputs must be kept constant.
  4. The various factors are not to be used in rigidly fixed proportions but the law is based upon the possibility of varying proportions. It is also called the law of proportionality.
  5. It is assumed that all the units of variable factors of production are homogeneous in amount and quality.
  6. It is assumed that labor is a single variable factor.


The law of variable proportion is explained with the help of the following schedule:

Units of variable factor (L)   Marginal product (MPL)   Total product (TPL) Average product (APL) Stages
1   2   2 2 I
2   4   6 3
3   6   12 4
4   4   16 4 II
5   2   18 3.6
6   0   18 3 III
7   -2   16 2.28

In the above schedule, units of variable factor (labor) are employed with other fixed factors of production. The marginal productivity of labor goes on increasing up to the 3rd worker. This is so because the proportion of workers to other fixed factors was at first insufficient. After 3rd worker the marginal productivity goes on falling onwards till it drops down to zero at the 6th unit of labor. The 7th worker is only a cause of obstruction to the others and is responsible in making the marginal productivity negative. The marginal productivity (MPL) and the average productivity (APL) equalize at 4the worker. Then the MPL falls more sharply


Law of Variable Proportion

The number of workers are measured on X-axis while TPL, APL and MPL on Y-axis. The above diagram shows the three stages also obtained from the schedule.

Stage I:

At this stage MPL increases up to 3rd worker and its curve is higher than the average product, so that total product is increasing at increasing rate.

Stage II:

At this stage, MPL decreases up to 6th unit of labor where MPL curve intersects the X-axis. At 4the unit of labor MPL = APL after this, MPL curve is lower than the APL. TPL increases at decreasing rate.

Stage III:

At 6the unit of labor the MPL becomes negative, the APL continues falling but remains positive. After the 6th unit, TPL declines with the employment of more units of variable factor (L).

Relationship Among Total, Average and Marginal Product:

The relationship among total, average and marginal product of labor in the light of the law of variable proportion is explained as under:

  1. The marginal productivity of labor increases, the TPL also increases at increasing rate. It is shown in the schedule up till 3rd unit of labor. The MPL curve has positive slope and TPL curve has rising tendency towards Y-axis.
  2. When the MPL decreases onwards till it drops to zero, the TPL increases at decreasing rate as shown in the stage II and the TPL curve has positive slope but has rising tendency towards X-axis
  3. When the MPL is equal to zero, the TPL is maximum as shown on the 6th unit of labor.
  4. When the MPL becomes negative, the MPL curves falls below the X-axis, the TPL declines from its maximum position and its slope becomes negative as shown in the stage III in the above diagram.
  5. When the MPL increases, The APL also increases but at slow rate. The MPL curve becomes above the APL curve. Both have positive slopes.
  6. At some point, MPL = APL. At this point, MPL curve intersects the APL curve as shown at the 4th unit of labor in the above diagram.
  7. After intersecting point, MPL falls sharply. The MPL curve becomes below the APL curve. Both curves have negative slope.
  8. When MPL becomes negative, the APL never becomes negative because it is calculated from the TPL. So MPL curve is below the X-axis but APL curve is above the X-axis, having negative slope.