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# Short-run production function - The law of variable proportions

The law examines the relationship between one variable factor and output, keeping the quantities of other factors fixed.

Short-run production function - The law of variable proportions

The law examines the relationship between one variable factor and output, keeping the quantities of other factors fixed.

## Definition

As the proportion of one factor in a combination of factors is increased, after a point, first the marginal and then the average product of that factor will diminish.

## Assumptions of the law

The law is based on the following assumptions

1.        Only one factor is made variable and other factors are kept constant.

2.        This law does not apply in case all factors are proportionately varied. i.e. where the factors must be used in rigidly fixed proportions to yield a product.

3.        The variable factor units are homogenous i.e. all the units of variable factors are of equal efficiency.

4.        Input prices remain unchanged

5.        The state of technology does not change or remains the same at a given point of time.

6.        The entire operation is only for short-run, as in the long-run all inputs are variable.

## Three stages of law

1.        The behaviour of the output when the varying quantity of one factor is combined with a fixed quantity of the other can be divided into three stages. They are Increasing returns stage

2.        Decreasing returns stage

3.        Negative returns stage

## Stage I: Stage of increasing returns

Stage I ends where the average product reaches its highest (maximum) point. During this stage, the total product, the average product and the marginal product are increasing. It is notable that the marginal product in this stage increases but in a later part it starts declining. Though marginal product starts declining, it is greater than the average product so that the average product continues to rise.

## Stage II: Stage of decreasing returns

Stage II ends at the point where the marginal product is zero. In the second stage, the total product continues to increase but at a diminishing rate. The marginal product and the average product are declining but are positive. At the end of the second stage, the total product is maximum and the marginal product is zero.

## Stage III: Stage of negative returns

In this stage the marginal product becomes negative. The total product and the average product are declining.

## The stage of Operation

In stage I the fixed factor is too much in relation to the variable factor. Therefore in stage I, marginal product of the fixed factor is negative. On the other hand, in stage III the marginal product of the variable factor is negative. Therefore a rational producer will not choose to produce in stages I and III. He will choose only the second stage to produce where the marginal product of both the fixed factor and variable factor are positive. At this stage the total product is maximum. The particular point at which the producer will decide to produce in this stage depends upon the prices of factors. The stage II represents the range of rational production decisions.

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