 # Indifference Curve – Definition, Schedule & Properties

The Indifference Curve Analysis approach was first introduced by Slutsky, a Russian Economist in 1915. Later it was developed by J.R. Hicks and R.G.D. Allen in the year 1928.

## What is Indifference Curve?

Koutsoyiannis (1985) defines the indifference curve as the locus of points particular combinations or bundles of goods which yield the same utility to the consumer, so that he is indifferent as to the particular combination he consumes.

Dwivedi (1997) on the other hand, defines it as the locus of points, each representing a different combination of two goods which yield the same utility or level of satisfaction to the consumer so that he is indifferent between any two combinations of goods when it comes to making a choice between them.

The indifference curve indicates the various combinations of two goods that yield equal satisfaction to the consumer. The theory of consumption is based on the scale of preference and the ordinal ranks or orders of one’s preferences.

The ordinal utility theory or the indifference curve analysis is based on the assumptions as discussed above. Other names for the indifference curve are the Iso-utility curve; Equal utility curve.

## What is the Indifference Curve Schedule?

The indifference curve schedule is the combination of two different commodities that yield exactly the same utility. In the table below there are four columns, the first shows the different combinations of the two commodities, while 2 and 3 showed the various quantities of rice and beans and column 4 shows that the various combinations yield exactly the same level of utility. Hence, the consumer is indifferent to any combination.

### Indifference Schedule

 Combination points Commodity Y (Rice) Commodity X (Beans) Utility A 04 16 U B 07 12 U C 09 11 U D 12 10 U E 17 04 U

#### The Construction of an Indifference Curve:

We can use the information in the table above to construct an indifference curve as shown below: The consumer’s preferences can be shown in a diagram with an indifference curve. The indifference curve is showing nothing about the absolute amounts of satisfaction obtained. It merely indicates a set of consumption bundles that the consumer views as being equally satisfactory. Fig above.

We measure the quantity of rice along the X-axis and beans along the Y-axis. It is shown in the diagram that a consumer may buy 7 kilograms of rice and 12 kilograms of beans or 9 kilograms of rice and 11 kilograms of beans. Both of these combinations are equally preferred by him and he is indifferent to these two combinations.

When the scale of preference of the consumer is graphed, by joining the points a, b, c, d, e, we obtain an Indifference Curve IC. Every point on the indifference curve represents a different combination of the two goods and the consumer is indifferent between any two points on the indifference curve. All the combinations are equally desirable to the consumer. The consumer is indifferent as to which combination he receives.

The Indifference Curve IC thus is a locus of different combinations of two goods that yield the same level of satisfaction.

NOTE:

Question: How is the indifference curve similar or different from the demand curve you learn in study session two?

Answer: The only similarity is that both curves are negatively sloped, while the following are the differences.

1. The demand curve shows the relationship between price and quantity purchased, while the indifference curve shows combinations of two products or services
2. The demand curve does not necessarily have to be convex to the origin, while the indifference curve must be convex to the origin.

III. Two demand curves can intersect each other, while two indifference curves cannot intersect each other.

### Indifference Map Fig above.

Shows a whole set of indifference curves which is called an indifference map. An indifference map shows all the indifference curves which rank the preference of the consumer. The further away from each successive indifference curve from the origin, the higher the level of utility it measures. In figure 5.2, four indifference curves IC1, IC2, IC3, and IC4 have been shown.

• The various combinations of commodities of beans and rice along with IC1 yield the same level of satisfaction to the consumer.
• The combinations of commodities along the higher indifference curve IC2 contain more of both commodities i.e. beans and rice.
• The indifference curve IC2 gives more satisfaction to the consumer than IC1. Similarly, the set of combinations of two goods on IC3 yield still higher satisfaction to the consumer than IC2.

In short, the further away a particular curve is from the origin, the higher the level of satisfaction it represents.

## Properties of Indifference Curve

The following are the main properties, attributes or features or characteristics of indifference curves:

### (1) They are Negatively Sloped:

The indifference curve must slope down from left to right. This means that an indifference curve is negatively sloped. It slopes downward because as the consumer increases the consumption of X commodity, he has to give up certain units of Y commodity in order to maintain the same level of satisfaction.

A negatively sloped Indifference curve Fig above.

The two combinations of commodity Rice and commodity beans are shown by the points (a) and (b) on the same indifference curve. The consumer is indifferent towards points (a) and (b) as they represent an equal level of satisfaction.

At point (a) on the indifference curve, the consumer is satisfied with OE units of rice and OD units of beans. He is equally satisfied with OF units of rice and OK units of beans shown by point b on the indifference curve.

It is only on the negatively sloped curve that different points representing different combinations of goods X and Y give the same level of satisfaction to make the consumer indifferent.

### (2) A Higher Indifference Curve Represents a Higher Level of Satisfaction:

A higher indifference curve that lies above and to the right of another indifference curve represents a higher level of satisfaction and combination on a lower indifference curve yields a lower satisfaction.

In other words, we can say that the combination of goods which lies on a higher indifference curve will be preferred by a consumer to the combination which lies on a lower indifference curve.

A higher “IC” depicts a higher level of satisfaction. Fig above.

There are three indifference curves, IC1, IC2 and IC3 which represent different levels of satisfaction. The indifference curve IC3 shows greater amount of satisfaction and it contains more of both goods than IC2 and IC1 (IC3 > IC2 > IC1).

### (3) Indifference Curves are Convex to the Origin:

This is an important property of indifference curves. They are convex to the origin (bowed inward). This is equivalent to saying that as the consumer substitutes commodity X for commodity Y, the marginal rate of substitution diminishes of X for Y along an indifference curve.

The marginal rate of substitution. Fig above.

As the consumer moves from A to B to C to D, the willingness to substitute rice (X) for beans (Y) diminishes. This means that as the amount of rice (X) is increased by equal amounts, that of beans (Y) diminishes to smaller amounts.

The marginal rate of substitution of rice (X) for beans (Y) is the number of beans (Y) that the consumer is willing to give up gaining marginal units of rice (X), indicating that the slope of IC is negative and it is convex to the origin.

### 4) The Indifference Curve cannot Intersect each other:

Given the definition of the indifference curve and the assumptions behind it, the indifference curves cannot intersect with each other. It is because, at the point of tangency, the higher curve will give as much as of the two commodities as is given by the lower indifference curve. This is absurd and impossible.

The intersection of two “IC”. Fig above.

Two indifference curves are cutting each other at point B. The combinations represented by points B and F gave equal satisfaction to the consumer because of both lies on the same indifference curve IC2.

Similarly, the combinations showed by points B and E on indifference curve IC1 give equal satisfaction to the consumer. If combination F is equal to combination B in terms of satisfaction and combination E is equal to combination B in satisfaction. It follows that the combination F will be equivalent to E in terms of satisfaction.

This conclusion looks quite absurd because combination F on IC2 contains more of good Y (beans) than combination which gives more satisfaction to the consumer. We, therefore, conclude that indifference curves cannot cut each other.

If indifference curves are allowed to intersect, it will break down the assumptions of transitivity and consistency.

### (5) The Indifference Curves do not Touch the Horizontal or Vertical Axis:

One of the basic assumptions of indifference curves is that the consumer purchases combinations of different commodities. He is not supposed to purchase only one commodity, in which case the indifference curve will touch one axis.

This violates the basic assumption of indifference curves. This again presupposes that rational consumers will prefer a variety of commodities combinations.

Note also that one of the ordinality analyses is that consumers have a minimum of two commodities hence opportunity for choice exists. In a single commodity situation, there will be no opportunity to choose between alternatives or the concept of indifference.

“IC” touching Y and X-axis. Fig above.

It is shown that the indifference IC touches the Y-axis at point C and the X-axis at point E.

At point C, the consumer purchases only OC of beans and no rice. Similarly, at point E, he buys the OE quantity of rice and no beans. Such indifference curves are against our basic assumption.

Our basic assumption is that the consumer compares such combinations of various quantities of the two commodities that make him indifferent among the combinations.