Law Of Variable Proportion

LAW OF VARIABLE PROPORTION

Q2. Explain the Law of Variable Proporation. Ans. In the short-run the level of production can be changed by changing the factor proportions. This law examines the production function with on factor variable, keeping the other factors quantities fixed. In other words this law explains the shortrun production function. When the quantity of one input is varied, keeping other inputs constant, the proportion between factors changes. When the proportion of variable factors increases, the total output does not always increase in the same proportion, but in varying proportion. This is why the law is named’ Law of Variable proportions’. The law of variable proportion is the new name given to the famous ‘Laws of Diminishing Returns. ‘The law of variable proportion’ or the law of diminishing returns has been defined by a number of economists. In the words of F. Benham. “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”. This law explains return to a factor.

Thus, the law states that if more and more units of a variable factor are applied to a given quantity of fixed factor, the total output may initially increase at an increasing rate but beyond a certain level the total output, the rate of increase in total output eventually diminishes in the use of additional units of the variable factor. The volume of goods produced can be looked at form three different angles viz. :

(i)

Total Product, (ii) Marginal Product and (iii) Average Product.

Total product refers to the total volume of goods produced during a specified period of time. Total product can be raised only by increasing the quantity of variable factors employed in production. For instance, more shirts will be produced when more labour and capital are used. Total product, generally goes on increasing with an increase in the quantity of the factor services employed. But there is a limit to which total product can increase with increase in the quantity of variable factors of production.

Marginal Product (MP). The rate at which total product increases is known as marginal product. We also define marginal product as the addition to the total product resulting from a unit increase in the quantity of the variable factor. Initially marginal product rises, but ultimately it begins to fall down, it becomes zero and at last becomes negative. It would be seen that the total product is maximum when the marginal product is zero.

Average Product (AP). Average product can be known by dividing total product by the total number of units of the variable factor.

AP=Total Product Units of variable factor

It can be easily seen that the average product also show almost the same tendency as does the marginal product. Initially, both the marginal product and the average product rise but ultimately both of these fall. However, marginal product may be zero. The output does not increase at a constant rate as more of any one input is added to the production process. For example on a small plot of land. We can improve the yield by increasing the fertilizer use to some extent. However, excessive use of fertilizer beyond the optimum quantity may lead to reduction in the output instead of any increase as per the law of Diminishing Returns (for instance, single application of fertilizers may increase the output by 50 per cent, a second application by another 30 per cent and the third by 20 per cent. However, if we apply fertilizer five to six times in a year, the output may drop to zero).

The principle of diminishing marginal productivity (returns) states that as additional units of a variable inputs are added to other inputs that are fixed in supply, the increment to output eventually decline (for a constant technology). This phenomenon has been widely observed and there is enough empirical evidence to support it. For business managers, managers, marginal productivity of an input plays an important part in determining how much of that input will be employed.

A hypothetical production function is presented in the following table with the total, average and marginal products of the variable factor labour. Needless to say that the amount of other inputs and the state of technology are fixed in this example.

TOTAL, AVERAGE AND MARGINAL PRODUCT

Fixed Input X Do Do

No. of Labour 0 1 2

Total Output 0 3 8

AP 3 4

MP 3 5

Do Do Do Do Do Do

3 4 5 6 7 8

12 15 17 17 16 13

4 3-3/4 3-2/5 3-5/6 2-2/7 1-5/8

4 3 2 0 -1 -3

The Law of Variable Proportions explains the relation between proportions of fixed and variable inputs, on the one hand, and output on the other. When a firm expands output by employing more units of avariable factor. It alters the proportions between the fixed and the variable factors. There is always an optimum combination of factors of production at which cost per unit is minimum. Too less or too much of the variable factors leads to cost increases. The law speaks about three stages of production. The first stage goes from origin to the point where the average output is maximum. When a firm expands output by increasing the quantity of variable factors in proportion to fixed it moves towards optimum combination of factors of production. In this stage the law of increaisn return may be said to operate and marginal product begins to fall i.e law of diminishing returns set in.

The second stage goes from the point where the average output is maximum to the point where the marginal output is zero. After having attained the optimum. Combination of the fixed inputs and the variable input, if the firm increases still further the quantity of the variable input, the per unit output of the variable input falls. In this stage, total output rises but only at a diminishing rate.

The third stage covers the range over which the marginal output is regative and total output naturally falls. No producer will operate at this stage, even if he can procure the variable input at zero price.

The first and the third stages are known as stages are known as stages of economic absurdity or economic non-sense. A producer will always seek to operate in the second stage. At which point the producer will operate in this stage will depend upon the prices of the factor inputs. In the following figures we have drawn TP and units of variable umputs in one figure and AP and MP and units of variable inputs in the other figure. In both the table and the graphic representation,w e see that both average and marginal products first increase reach the miximum and eventully decline.

Note that MP-AP a the maximum of average product function. This is always the case if MP>AP, the average will be pushed up by the incremental unit and if MP<AP, the average will be pulled down. It follows that the average product will reach its peak where MP=AP.

Assumptions. The application of the law is subject to the following assumptions: (i) (ii) (iii) (iv)

Technique of production remain unchanged. Prices of inputs is given and do not change. Units of the variable factors are homogeneous. Factor proportion can be altered.

The diminishing return stage of the law is almost universal. This, generally, applies to every productive activity.