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Law of Variable Proportions

As equal increments of one input are added, the inputs of other productive services being held constant, beyond a certain point, the resulting increments of product will decrease, i.e., the marginal product will diminish.

Law of Variable Proportions

The law states that if all other factors are fixed and one input is varied in the short run, the total output will increase at an increasing rate at first instance, be constant at a point and then eventually decrease. Marginal product will become negative at last.

According to G.Stigler, “As equal increments of one input are added, the inputs of other productive services being held constant, beyond a certain point, the resulting increments of product will decrease, i.e., the marginal product will diminish”.

Assumptions

The Law of Variable Proportions is based on the following assumptions.

·           Only one factor is variable while others are held constant.

·           All units of the variable factor are homogeneous.

·           The product is measured in physical units.

·           There is no change in the state of technology.

·           There is no change in the price of the product.

Total Product (TP)

It refers to the total amount of commodity produced by the combination of all inputs in a given period of time.

Summation of marginal products, i.e.

TP = ∑MP

where, TP= Total Product, MP= Marginal Product

Average Product (AP)

It is the result of the total product divided by the total units of the input employed. In other words, it refers to the output per unit of the input.

Mathematically, AP = TP/N

Where,

AP= Average Product

TP= Total Product

N= Total units of inputs employed

Marginal Product (MP)

It is the addition or the increment made to the total product when one more unit of the variable input is employed. In other words, it is the ratio of the change in the total product to the change in the units of the input. It is expressed as

MP=  TP/ N

where,

MP = Marginal Product

ΔTP = Change in total product

ΔN = Change in units of input It

is also expressed as

MP = TP (n) – TP (n-1)

Where,

MP = Marginal Product

TP(n) = Total product of employing nth unit of a factor

TP(n-1) = Total product of employing the previous unit of a factor, that is, (n-1)th unit of a factor.

The Law of Variable Proportions is explained with the help of the following schedule and diagram:

In table 3.1, units of variable factor (labour) are employed along with other fixed factors of production.

The table illustrates that there are three stages of production. Though total product increases steadily at first instant, constant at the maximum point and then diminishes, it is always positive for ever. While total product increases, marginal product increases up to a point and then decreases. Total product increases up to the point where the marginal product is zero. When total product tends to diminish marginal product becomes negative.

In diagram 3.1, the number of workers is measured on X axis while TPL, APL and MPL are denoted on Y axis. The diagram explains the three stages of production as given in the above table.

Stage I

In the first stage MPL increases up to third labourer and it is higher than the average product, so that total product is increasing at an increasing rate. The tendency of total product to increase at an increasing rate stops at the point A and it begins to increase at a decreasing rate. This point is known as ‘Point of Inflexion’.

Stage II

In the second stage, MPL decreases up to sixth unit of labour where MPL curve intersects the X-axis. At fourth unit of labor MPL = APL. After this, MPL curve is lower than the APL. TPL increases at a decreasing rate.

Stage III

Third stage of production shows that the sixth unit of labour is marked by negative MPL, the APL continues to fall but remains positive. After the sixth unit, TPL declines with the employment of more units of variable factor, labour.

Relationship among Total, Average and Marginal Products

Tags : Production Analysis | Economics , 11th Economics : Chapter 3 : Production Analysis
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11th Economics : Chapter 3 : Production Analysis : Law of Variable Proportions | Production Analysis | Economics