Law Of Variable Proportions m5r4u

LAW OF VARIABLE PROPORTIONS The law of variable proportions states that as the quantity of one factor is increased, keeping the other factors fixed, the marginal product of that factor will eventually decline. This means that upto the use of a certain amount of variable factor, marginal product of the factor may increase and after a certain stage it starts diminishing. When the variable factor becomes relatively abundant, the marginal product may become negative. Assumptions: The law of variable proportions holds well under the following conditions: 1. Constant State of Technology: First, the state of technology is assumed to be given and unchanged. If there is improvement in the technology, then the marginal product may rise instead of diminishing. 2. Fixed Amount of Other Factors: Secondly, there must be some inputs whose quantity is kept fixed. It is only in this way that we can alter the factor proportions and know its effects on output. The law does not apply if all factors are proportionately varied. 3. Possibility of Varying the Factor proportions: Thirdly, the law is based upon the possibility of varying the proportions in which the various factors can be combined to produce a product. The law does not apply if the factors must be used in fixed proportions to yield a product.

Illustration of the Law: The law of variable proportion is illustrated in the following table and figure. Suppose there is a given amount of land in which more and more labour (variable factor) is used to produce wheat. Units of Labour Total Product

Marginal Product

Average Product

1

2

2

2

2

6

4

3

3

12

6

4

4

16

4

4

5

18

2

3.6

6

18

0

3

7

14

-4

2

8

8

-6

1

It can be seen from the table that up to the use of 3 units of labour, total product increases at an increasing rate and beyond the third unit total product increases at a diminishing rate. This fact is shown by the marginal product which the addition is made to Total Product as a result of increasing the variable factor i.e. labour. It can be seen from the table that the marginal product of labour initially rises and beyond the use of three units of labour, it starts diminishing. The use of six units of labour does not add anything to the total production of wheat. Hence, the marginal product of labour has fallen to zero. Beyond the use of six units of labour, total product diminishes and therefore marginal product of labour becomes negative. Regarding the average product of labour, it rises up to the use of third unit of labour and beyond that it is falling throughout.

Three Stages of the Law of Variable Proportions: These stages are illustrated in the following figure where labour is measured on the X-axis and output on the Y-axis. Stage 1. Stage of Increasing Returns: In this stage, total product increases at an increasing rate up to a point. This is because the efficiency of the fixed factors increases as additional units of the variable factors are added to it. In the figure, from the origin to the point F, slope of the total product curve TP is increasing i.e. the curve TP is concave upwards upto the point F, which means that the marginal product MP of labour rises. The point F where the total product stops increasing at an increasing rate and starts increasing at a diminishing rate is called the point of inflection. Corresponding vertically to this point of inflection marginal product of labour is maximum, after which it diminishes. This stage is called the stage of increasing returns because the average product of the variable factor increases throughout this stage. This stage ends at the point where the average product curve reaches its highest point.

Stage 2. Stage of Diminishing Returns: In this stage, total product continues to increase but at a diminishing rate until it reaches its maximum point H where the second stage ends. In this stage both the marginal product and average product of labour are diminishing but are positive. This is because the fixed factor becomes inadequate relative to the quantity of the variable factor. At the end of the second stage, i.e., at point M marginal product of labour is zero which corresponds to the maximum point H of the

total product curve TP. This stage is important because the firm will seek to produce in this range. Stage 3. Stage of Negative Returns: In stage 3, total product declines and therefore the TP curve slopes downward. As a result, marginal product of labour is negative and the MP curve falls below the X-axis. In this stage the variable factor (labour) is too much relative to the fixed factor.

Importance and Applicability of the Law of Variable Proportion: The Law of Variable Proportion has universal applicability in any branch of production. It forms the basis of a number of doctrines in economics. The Malthusian theory of population stems from the fact that food supply does not increase faster than the growth in population because of the operation of the law of diminishing returns in agriculture. Ricardo also based his theory of rent on this principle. According to him rent arises because the operation of the law of diminishing return forces the application of additional doses of labour and capital on a piece of land. Similarly the law of diminishing marginal utility and that of diminishing marginal physical productivity in the theory of distribution are also based on this theory. The law is of fundamental importance for understanding the problems of underdeveloped countries. In such agricultural economies the pressure of population on land increases with the increase in population. This leads to declining or even zero or negative marginal productivity of workers. This explains the operation of the law of diminishing returns in LDCs in its intensive form. Ragnar Nurkse have suggested ways to make use of these disguisedly unemployed labour by withdrawing them and putting them in those occupations where the marginal productivity is positive.

LAW OF VARIABLE PROPORTIONS – CONCLUSION :

In short-period when the output of a production is sought to be increased by way of additional application of the variable factor to a given quantity of fixed factors, law of variable proportions comes into operation. The law of variable proportions is that law which predicts the consequences of varying the proportions in which the fixed and variable factors of production are used. When the number of one factor is increased while all other factors remain constant, then the proportion between the fixed and variable factors is altered. Supposing there are two factors of production i.e. Land and labour. Land is fixed factor and labour is a variable factor. Suppose you have a land measuring 2 hectares. You grow tomatoes on it with the help of a labourer. Accordingly the proportion between labour and land will be 1:2. If the number of labourers is increased to 2 then the new proportion between labour and land will be 2:2, in other words, if there were 2 hectares of land per labourer previously, now there will be 1 hectare of land per laborer. On of change in the proportion of factors there will also be a change in total output at different rates. In Economics, this tendency is called Law of Variable Proportions. The law of variable proportions stats that as the proportion of factors is changed, the total production at first increases more than proportionately, then equalproportionately and finally less than proportionately. The classical economists called it the Law of Diminishing Returns. They derived it by applying more and more labour to a fixed acreage of land, and thought of it as associated particularly with agriculture. But it is a general principle that can be applied to any production operation. It is now usually called the Law of Variable Proportions. It can also be called the Law of Diminishing Marginal product or Diminishing Marginal Returns or simply as Diminishing Returns. In production, returns to scale refer to changes in output subsequent to a proportional change in all inputs (where all inputs increase by a constant factor). If output increases by that same proportional change then there are constant returns to scale (CRTS). If output increases by less than that proportional change, there are decreasing returns to scale (DRS). If output increases by more than that proportion, there are increasing returns to scale (IRS)Short example: Where all inputs increase by a factor of 2, new values for output should be: Twice the previous output given = a constant return to scale (CRTS)Less than twice the previous output given = a decreased return to scale (DRS)More than twice the previous output given = an increased return to scale (IRS)Assuming that the factor costs are constant, a firm experiencing CRTS will have constant average costs, a firm experiencing DRS will have increasing average costs and a firm experiencing IRS will have decreasing average costs.

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ASSUMPTIONS 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 (i) Only one factor is made variable and other factors are kept constant. (ii) 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. (iii) The variable factor units are homogenous i.e. all the units of variable factors are of equal efficiency. (iv) Input prices remain unchanged (v) The state of technology does not change or remains the same at a given point of time. (vi) The entire operation is only for short-run, as in the long-run all inputs are variable.

Total Product (TP) – Total quality of output produced by a firm. Average Product (AP) – The total produced by a firm divided by the quantity of variable factors used to produce. AP = TP/Q AP – Average Product TP – Total Product Q – Number of Variable Factors Marginal Product (MP) – Change in TP caused as a result of additional unit of Variable factor employed to the combination of Fixed Factor. Law of variable proportion is also called Law of Diminishing Returns. It examines the production function when one factor varies keeping the quantities of other fixed factors constant. That is how the output varies when Variable Factors are employed to the fixed factors. The law states, when Variable factors are increased in equal doses keeping the Fixed Factor constant, the total product will increase. But after a certain point it will increase at a diminishing rate and finally the total product starts decreasing. Assumption: This law is subject to certain assumptions: 1. The state of technology is given 2. Only one factor of production must be variable. In the example illustrated below, we have taken it as labour 3. There are some inputs, which are kept constant of fixed

In the above table, first column shows fixed factor as the land, say 5 acres. Second column shows labour as variable factor. Third column shows Total Product which changes due to change in the variable factor. Fourth column shows AP which is derived by dividing TP with Q. Fifth column, is MP

which is derived by change in TP with change in Q. In the above table, at the fourth unit of variable factor, the total product reaches maximum and then starts has reached its maximum at third unit of variable factor. Marginal product starts falling first, average product follows it and total product falls last.

Behavior of TPP,MPP & APP during the three stages of production.