Isoquants do not intersect each other, because intersection of isoquants creates logical contradiction. Let us assume that there are two isoquants – isoquant I and isoquant II, which intersect at point C. Left to point C, isoquant I lies above isoquant II.

So, it is clear that left to point C, any point on isoquant I represents more output than that of isoquant II. Following this logic, it can be claimed that point A yields more output than point B. Hence, A>B… (i)

Again, points A and C lie on the same isoquant. So, in terms of output, both are equal. That is, A = C. Similarly, B = C, since the points B and C lie on the isoquant II.

Therefore, A = C, B = C

Or, A = B…………. (ii) [Following assumption of transitivity]

Conditions (i) and (ii) are contradictory, which proves that isoquants never intersect.

#### iii) Isoquants Are Convex to the Origin:

It has been already noted that isoquants are negatively sloped. But the negative slope does not necessarily indicate that a curve is convex to the origin; it may also be concave (figure 8.3) or convex to the origin (figure 8.4) or even a straight linear curve (figure 8.5). But if it is specified that Marginal Rate of Technical Substitution (MRTS) is diminishing for a curve, it automatically implies that the curve is convex to the origin.

MRTS can be defined as the rate at which one input can be substituted by another in a particular production process without any change in output. It is expressed as

MRTS = – ?K/?L

Here ?K indicates small change in capital and ?L indicates small change in labour. Though MRTS always assumes negative value for a normal isoquant (continuous and convex to the origin), it is expressed as the absolute value of ratio of two inputs, i.e.

MRTS = – ?K/?L

Normally, isoquants are downward sloping from left to right. As we move from left to right along an isoquant, value of MRTS diminishes. In other words, if quantity of output can be kept unaltered, the more of one input is withdrawn from the production process, the more and more of another input is required to be added to compensate for each one-unit reduction in the first input. Let us explain this point with the help of a diagram (see figure 8.6).

Suppose the initial position is point A, where ‘OL1‘ amount of labour and ‘Ok1‘ amount of capital are employed to produce a particular quantity of output. Now, assume that use of capital is reduced by ?K amount. To remain on the same isoquant (i.e, to maintain the previous level of output) ?L1 quantity of extra labour is employed in the production process.

This change in input combination leads to a shift from point A to point B. If the same quantity of capital (?K) is again withdrawn from production process, ?L2 (?L2 > ?L1) quantity of labour is to be added in order to maintain the same output level.

It will cause a movement from B to C along the isoquant. If the same process is repeated again, it will be observed that ?K quantity of capital will have to be substituted by ?L3 quantity of labour where ?L3 > ?L2 and this will cause a shift from point C to point D.

Hence, input substitution ratios are related as

#### (iv) Higher isoquants represent higher level of production:

Rightward movement of an isoquant implies higher level of production. Two isoquants IQ1 and IQ2 are shown in the figure 8.7. Isoquant IQ1 lies below IQ2

Let us compare point ‘b’ on IQ1 with point ‘c’ of IQ2. The former denotes employment of ‘bm’ quantity of capital along with ‘ab’ amount of labor. In the latter case, employment of capital and labour are ‘cp’ and ‘ac’ respectively. Clearly, for both the points, employment of capital is same (since cp = bm) whereas, employment of labour varies.

Since we are considering ‘smooth and convex to the origin’ isoquants point ‘c’ will represent more output than point ‘b’, because point ‘c’ denotes employment of same amount of capital but more amount of labour as compared to point ‘b’. Similarly, if comparison is made between points ‘y’ and ‘z’ of isoquant 1 and 2 respectively, it will be revealed that point ‘z’ yields more output than that of point ‘y’. Not only for these two sets of points on the isoquants; it is true for all such comparable points, which establishes the fact that IQ2 represents higher production than IQ1.