# Isoquants: Meaning, Assumptions and Properties

### Meaning

The term ‘isoquant’ is composed of two terms ‘iso’ and ‘quant’. Iso is a Greek word which means equal and quant is a Latin word which means quantity. Therefore, these words together refer to equal quantity or equal product.

An isoquant curve is the representation of a set of locus of different combinations of two inputs (labor and capital) which yield the same level of output. It is also known as or equal product curve or producer’s indifference curve.

It is a firm’s counterpart of the consumer’s indifference curve. Thus, an isoquant may also be defined as the graphical representation of different combinations of two inputs which give same level of output to the producer. Since all the combinations lying in an isoquant curve yield the same level of production, a producer is indifferent between the combinations.

### Few Definitions of Isoquant Curve

The isoproduct curves show the different combinations of two resources with which a firm can produce equal amount of product.

– Bilas

Isoproduct curve shows the different input combinations that will produce a given output.

– Samuelson

An isoquant 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.

– Peterson

An isoquant is a curve showing all possible combinations of inputs physically capable of producing a given level of output.

– Ferguson

### Example of Isoquant Schedule and Isoquant Curve

 Table 1: isoquant schedule Combinations Labor (L) Capital (K) Output (units) A 1 12 100 B 2 8 100 C 3 5 100 D 4 3 100 E 5 2 100

The given isoquant schedule represents various combinations of inputs (labor and capital).

From the table, we can see combination A consists of 1 unit of labor and 12 units of capital which together produce 100 units of output. In combination B, when 1 unit of labor was added in place of 4 units of capital, the production process still produced 100 units of output. In the same way, other combinations C (3L + 5K), D (4L + 3K) and E (5L + 2K) made the same level of output, i.e. 100 units.

Figure 1: graphical representation of isoquant schedule (isoquant curve)

### Assumptions of Isoquant Curve

The concept of isoquant is based on the following assumptions.

1. Only two inputs (labor and capital) are employed to produce a good.
2. There is technical possibility of substituting one input for another. It implies that the production function is of variable proportion type.
3. Labor and capital are divisible.
4. The producer must be rational, i.e. trying to maximize his profit.
5. State of technology is given and unchanged.
6. Marginal rate of technical substitution diminishes in production process.

### Marginal Rate of Technical Substitution

Marginal rate of technical substitution (MRTS) indicates the rate at which one factor (labor) can be substituted for the other input (capital) in the production process of a commodity without changing the level of output or production. The marginal rate of technical substitution of labor for capital (MRTSL,K) can be defined as the units of capital which can be replaced by one unit of labor, keeping constant the level of output. Mathematically, it is represented as

 Table 2: marginal rate of technical substitution (MRTS) Combination Capital (K) Labor (L) MRTSL,K Output A 12 1 100 B 8 2 4:1 100 C 5 3 3:1 100 D 3 4 2:1 100 E 2 5 1:1 100

Given table 2 represents various combinations of inputs, all of which yield the same level of output, i.e. 100 units, to the producer.

Comparing combination A with B, we see that 4 units of capital is replaced by 1 unit of labor, without altering the output. Therefore, 4:1 is the marginal rate of technical substitution in this case.

Similarly, if we compare combination B with C, we can find that the MRTS for this case is 3:1. Likewise, MRTS between C and D, and D and E is 2:1 and 1:1, respectively.

Figure 2: marginal rate of technical substitution

Figure 2 is a graphical representation of MRTS. In the figure, MRTS between any two points is given by the slope between those points.

For example, MRTS between the points A and B can be found as

In the same way, MRTS at any particular point on the isoquant curve can be calculated by finding the slope of the line that is tangent to that point on the curve.

### Properties of Isoquant Curve

The isoquant curve has almost the same properties as are possessed by the indifference curve of the theory of consumer behavior. They are explained below.

#### Isoquant is convex to the origin

The isoquant is convex to the origin because the marginal rate of technical substitution (MRTS) between the inputs is diminishing. As shown in the tabular example of MRTS, the ratio by which the input units of capital is substituted by labor units diminishes with more and more substitution of labor for capital. Thus, the isoquant curve is convex to the origin.

If the isoquant curve had been concave to the origin, it would imply that the MRTS increases as more and more of labor is substituted for capital. And this would be against the assumption that the isoquant curve is based on.

#### Isoquant is negatively sloped

The isoquant curve is neither upward sloping nor horizontal but always slopes downward from left to right. It is because the producer will have to give up some of the input units of capital to increase the input of labor when keeping the production amount unchanged.

Increasing input units of either of the factors without deducing the input of the other factor will result in increased production and it is beyond the principle of isoquant curve.

In the figure, when OK1 units of capital were employed, OL1 units of labor were employed too. When the input units of labor was increased to OL2, the input units of capital was reduced to OK2.

Therefore, the curve is downward sloping from to right. And slope of any downward sloping curve is always negative.

#### Higher isoquant represents higher production

The isoquant which is in higher stage has higher units of labor and capital combinations. Greater combination of labor and capital makes large scale of production. So, higher the isoquant curve, greater will be the production level.

In the figure, we can see that there are two isoquant curves (Iq1 and Iq2). We can also see that the combination A lies on Iq1 and combination B lies on Iq2.

Combination A consists of OL1 units of labor and OK1 units of capital which is visibly lesser than the OL2 units of labor and OK2 units of capital at point B. So we can say that production level at Iq2 is higher than the production level at Iq1.

#### Two isoquants never intersect each other

Each isoquant curve is a representation of particular level of production. The level of production or output of a production process is same throughout the curve.

In the above figure, Iq1 and Iq2 are two isoquant curves and R is the point where both the curves intersect.

According to the principle of isoquant curve, production level at point S = production level at point R = production level at point T

Also, production level at point P = production level at point R = production level at point Q

But, production level at point S and point T ≠ production level at point P and point Q

Therefore, two isoquant curves cannot intersect. Yet, two isoquant curves need not be parallel to each other.

The parallelism of isoquant curves depend upon the MRTS. The isoquant curves can be parallel only when the MRTS of both the curves are equal.