Law of variable Properties Iso-Quants

Law of Variable Proportions occupies an important place in economic theory. This law is also known as Law of Proportionality.

Keeping other factors fixed, the law explains the production function with one factor variable. In the short run when output of a commodity is sought to be increased, the law of variable proportions comes into operation.

Therefore, when the number of one factor is increased or decreased, while other factors are constant, the proportion between the factors is altered. For instance, there are two factors of production viz., land and labour.

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

Samuelson: “An increase in some inputs relative to other fixed inputs will in a given state of technology cause output to increase, but after a point the extra output resulting from the same additions of extra inputs will become less and less.”

Leftwitch: “The law of variable proportion states that if the inputs of one resource is increased by equal increment per unit of time while the inputs of other resources are held constant, total output will increase, but beyond some point the resulting output increases will become smaller and smaller.”

Iso-Quant Curve

The term Iso-quant or Iso-product is composed of two words, Iso = equal, quant = quantity or product = output.

Thus it means equal quantity or equal product. Different factors are needed to produce a good. These factors may be substituted for one another.

Bilas: “The Iso-product curves show the different combinations of two resources with which a firm can produce equal amount of product.”

Samuelson: “Iso-product curve shows the different input combinations that will produce a given output.”

Peterson: “An Iso-quant curve may be defined as a curve showing the possible combinations of two variable factors that can be used to produce the same total product.”

Ferguson: “An Iso-quant is a curve showing all possible combinations of inputs physically capable of producing a given level of output.”

Characteristics of Isoquant

• An isoquant slopes downward to the right.
• An isoquant is convex to origin.
• An isoquant is smooth and continuous.
• Two isoquants do not intersect.

Properties of Isoquants

Isoquants possess certain properties which are similar to those of indifference curves.

1. Isoquants are negatively inclined

If they do not have a negative slope, certain logical absurdities follow. If the isoquant slopes upward to the right, it implies that both capital and labour increase but they produce the same output. In Figure 24.2 (A), combination В on the IQ curve having a larger amount of both capital and labour (ОС₁ +OL₁ > ОС + OL) will yield more output than before. Therefore, point A and В on the IQ curve cannot be of equal product.

Suppose the isoquant is vertical as shown in Figure 24.2 (B), which implies a given amount of labour is combined with different units of capital. Since OL of labour and OC₁ of capital will produce a larger amount than produced by OL of labour and ОС of capital, the isoquant IQ cannot be a constant product curve.

Take Figure 24.2 (С) where the isoquant is horizontal which means combining more of labour with the same quantity of capital. Here ОС of capital and OL₁ of labour will produce a larger or smaller amount than produced by the combination ОС of capital and OL of labour. Therefore, a horizontal isoquant cannot be an equal product curve.

Thus it is clear that an isoquant must slope downward to the right as shown in Figure 24.2 (D) where points A and В on the IQ curve are of equal quantity. As the amount of capital decreases from ОС to OC₁ and that of labour increases from OL to OL₁ so that output remains constant.

2. An Isoquant lying above and to the right of another represents a higher output level. In Figure 24.3 combination В on IQ₁curve shows larger output than point A on the curve IQ. The combination of ОС of capital and OL of labour yields 100 units of product while OC₁ of capital and OL₁ of labour produce 200 units. Therefore, the isoquant IQ₁ which lies above and to the right of the isoquant IQ, represents a larger output level.

3. No two isoquants can intersect each other. The absurd conclusion that follows when two isoquants cut each other is explained with the aid of Figure 24.4. On the isoquant IQ, combination A =B. And on the isoquant IQ₁combination R=S. But combination S is preferred to combination B, being on the higher portion of isoquant IQ₁. On the other hand, combination A is preferred to R, the former being on the higher portion of the isoquant IQ. To put it algebraically, it means that S> В and R< A. But this is logically absurd because S combination is as productive as R and A combination produces as much as B. Therefore, the same combination cannot both be less and more productive at the same time. Hence two isoquants cannot intersect each other.

4. Isoquants need not be parallel because the rate of substitution between two factors is not necessarily the same in all the isoquant schedules.

5. In between two isoquants there can be a number of isoquants showing various levels of output which the combinations of the two factors can yield. In fact, in between the units of output 100, 200, 300, etc. represented on isoquants there can be innumerable isoquants showing 120, 150, 175,235, or any other higher or lower unit.

6. Units of output shown on isoquants are arbitrary. The various units of output such as 100, 200, 300, etc., shown in an isoquant map are arbitrary. Any units of output such as 5, 10, 15, 20 or 1000, 2000, 3000, or any other units can he taken.

7. No isoquant can touch either axis. If an isoquant touches X-axis, it would mean that the product is being produced with the help of labour alone without using capital at all. This is a logical absurdity for OL units of labour alone are incapable of producing anything. Similarly, ОС units of capital alone cannot produce anything without the use of labour. Therefore IQ and lQ₁cannot be isoquants, as shown in Figure 24.5.

8. Each isoquant is convex to the origin:

As more units of labour are employed to produce 100 units of the product, lesser and lesser units of capital are used. This is because the marginal rate of substitution between two factors diminishes. In Figure 24.6, in order to produce 100 units of the product, as the producer moves along the isoquant from combination A to В and to С and D, he gives up smaller and smaller units of capital for additional units of labour. To maintain the same output of 100 units, BR less of capital and relatively RC more of labour is used.

If he were producing this output with the combination D, he would be employing CT less of capital and relatively TD more of labour. Thus the isoquants are convex to the origin due to diminishing marginal rate of substitution. This fact becomes clear from successively smaller triangles below the IQ curve ∆ ASB > ∆BRC > ∆ CTD.

9. Each isoquant is oval-shaped

It is elliptical which means that at some point it begins to recede from each axis. This shape is a consequence Labour of fact that if a producer uses more of capital or more of labour or more Fig. 24.6 of both than is necessary, the total product will eventually decline.

The firm will produce only in those segments of the isoquants which are convex to the origin and lie between the ridge lines.

This is the economic region of production. In Figure 24.7, oval­-shaped isoquants are shown. Curves OA and OB are the ridge lines and in between them economically feasible units of capital and labour can be employed to produce 100, 200, 300 and 400 units of the product. For example, ОТ units of labour and ST units of the capital can produce 100 units of the product, but the same output can be obtained by using the same quantity of labour ОТ and less quantity of capital VT.

Thus only an unwise entrepreneur will produce in the dotted region of the isoquant 100. The dotted segments of an isoquant are the waste- bearing segments. They form the uneconomic regions of production. In the upper dotted portion, more capital and in the lower dotted portion more labour than necessary is employed. Hence GH, JK, LM, and NP segments of the elliptical curves are the iso- quants.