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.

CAUSES FOR OPERATION OF THE LAW

• Fixed of a factor.
• Scarcity of a factor.
• Existence of imperfect substitutes. There is no way capital can be substituted to labour.
• Optimum combination of the inputs.

LIMITATIONS OF LAW OF VARIABLE PROPORTIONAL

(DIMINISHING RETURNS)

• Operates only in the short run.
• It is restricted to land only yet in reality it can apply to other factors when they are fixed.
• It is not applicable in case of virgin land because the land becomes productive for a long period.
• Variable factors are not homogeneous, that is they differ in efficiency ability.
• It does not consider the influence of other factors such as health of a worker.

Thus the operation of law of returns to scale is mainly caused by two major means,which are;-economics of scale and diseconomics of scale.

1. Very short run.

Refers to the period of time which is very short to make all factors variable i.e. that is all factor are fixed.

1. Short run.

Refers to the period of time where at least one factor is fixed and the other is variable.

1. Long run.

Refers to the period of time that is long enough to make all factors variable.

1. Very long run.

Refer to the period of time which is able to not only change factors of production but also the technology.

The law of return to scale of low production operates in long run while the law of Diminishing returns operates in the short run production function.

ASSIGNMENTS

Consider the following table and then answer the question that follows;

 Labor (L) TP AP MP 1 4 4 4 2 14 7 10 3 27 9 13 4 40 10 13 5 60 12 20 6 72 12 12 7 77 11 5 8 80 10 3 9 80 9 0 10 75 7 -5

1. From the table draw the curve to depict the law of variable proportion.
2. Identify the number of labour at
3. MP=AP
4. Max=TP
5. MP=0
6. SOLUTION
1. MP=AP

The number of labour at MP=AP from the graph is 6

1. Max = TP

The number of labour of maximum is 9

1. MP = 0

The point at that level MP = 0 is 9. Because the maximum is 9.

Given the following TP =2L2-20L

1. Find the unit of labour which will maximize output.
2. Calculate the TP, MP, and AP.

SOLUTION

From TP = 2L2-20L
= 2 x 2L(2-1)-20L(1-1)
= 4L – 20

The about at maxim MP = 0
MP = TP
0=4L–20

20/20=4L/4

5 = L

The unit of labour which will maximize the output is 5

MP, TP, and AP

TP=2L2-20L

TP =2L2-2L

AP =  TP/L

= 2L2-20L

= L(2L-20)/L

= 2L – 20

= (2(25)-20(5))/5

= -50/5

AP= -10

The average product can’t be -10 is +10

TP = 2(25) – 20(5)

= 50 – 100