# The Technical Substitution’ (Fig. 7.3). Employment of

The following are the important properties of the isoquants:

#### (a) Isoquants Slope Downward from Left to Right:

Isoquants have negative slope. This is so because, when the quantity of one factor (say, ‘X’) is increased, the quantity of other factor (say, ‘Y’) must be reduced, so that total product remains constant (Fig. 7.4). If, however, the marginal productivity of the factor becomes negative, the isoquant bends back and acquires positive slope, (segments AD and BF in Fig 7.4).

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#### (b) Isoquants Never Cut, Touch or Intersect Each Other:

Intersection of isoquants showing different levels of output is a logical contradiction. It would mean that isoquants representing different levels of output (‘A’ and ‘C’ in Fig. 7.5) are showing the same amount of output (‘B’ in Fig. 7.5) at the point of intersection, which is wrong. Thus, we rule out the following cases in case of isoquants.

#### (c) Isoquants are Convex to Origin:

This property of isoquants is based upon the ‘Principle of Diminishing Marginal Rate of Technical Substitution’ (Fig. 7.3). Employment of each successive unit of one factor (say, labour) will be required to compensate for smaller and smaller sacrifice of the other factor (say, capital) so as to maintain the same level of output. Concave shape of the isoquants would be against the above principle of ‘Diminishing Marginal Rate of Technical Substitution’.

The degree of convexity of isoquants depends upon the rate at which marginal rate of technical substitution changes. The greater the rate at which MRTS falls, the greater the convexity of the isoquants and vice-versa. In extreme situation, when the two factors are perfect substitutes of each other, then for all practical purposes, they can be regarded as the same factor.

Thus, MRTS between two perfect substitutes will be constant. (Fig. 7.6 (a)). Here, equal addition in one factor requires sacrifice of other factor by same amount every time addition is made. Hence, the technical coefficient of production is variable. Isoquant in this case will be a straight line with negative slope. This isoquant touches both the axes implying that a given output can be produced by using even any one input.

In another extreme situation, when the two factors are perfect complements (factors used in fixed proportions), isoquant will be right-angled (Fig. 7.6 (b)). Here, MRTS is undefined. This type of isoquant is known as input-output isoquant or Leontief isoquant (after the name of Wassily Leontief, who did pioneer work in the field of input-output analysis).

Here, there is zero substitutability between the inputs implying only one method of production for any commodity, i.e., technical coefficients are fixed. Here, the output can be increased by increasing the amount of both the factors by the required given proportions.

A change in the quantity of one factor without change in the quantity of other factor will leave the output unaffected. The marginal product of either labour or capital is zero, if its usage is expanded, while the amount of other factor is held constant. The additional factor will be redundant.

Leontief isoquant does not imply that increase in the quantities of the two factors of production (labour and capital) will always increase the output proportionately. It only implies that for producing any quantity of a commodity, the factors must be used in fixed proportions. The ray OE in Fig. 7.6 (b) shows the capital labour ratio that has to be maintained for ensuring efficiency in production.

In real life, there are various techniques of producing a given amount of output, each technique having a different fixed combination of factors to produce a given level of output. Kinked isoquant is an example of the production of a commodity for which few different fixed proportions processes are available.

This form is also called activity analysis isoquant or linear programming isoquant, because it is basically used in linear programming. The kinked or linear programming isoquant can be illustrated by using L-shaped isoquants (Fig. 7.7).

In Fig. 7.7, OA, OB, OC and OD are four process-rays, whose slopes represent different capital-labour ratios. By joining points ‘A’, ‘B’,’C’ and ‘D’, we get the kinked isoquant. Each of these four points on the kinked isoquant represents a factor combination, which can produce the same level of output.

However, it is different from ordinary isoquant in the sense that every point on the kinked isoquant is not a feasible factor combination capable of producing the given level of output. Only the kinks (four factor combinations corresponding to four available processes) show the technically feasible factor combinations.

The kinked isoquants are more realistic than smooth convex isoquants. Engineers, managers and production executives consider the production processes as discrete rather than continuous, since machinery, equipment, etc. are available in limited range.

Therefore, the possibilities of substitutability between capital and labour (and for other inputs also) are limited. The continuous isoquant is only an approximation to the more realistic form of kinked isoquant, particularly when the number of processes becomes too large. The smooth convex isoquants are considered because they are easy to handle in practice.