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# Theory of Ordinal Utility/Indifference Curve Analysis:

## Definition and Explanation:

The indifference curve indicates the various combinations of two goods which yield equal satisfaction to the consumer. By definition:

"An indifference curve shows all the various combinations of two goods that give an equal amount of satisfaction to a consumer".

The indifference curve analysis approach was first introduced by Slustsky, a Russian Economist in 1915. Later it was developed by J.R. Hicks and R.G.D. Allen in the year 1928.

These economist are the of view that it is wrong to base the theory of consumption on two assumptions:

(i) That there is only one commodity which a person will buy at one time.

(ii) The utility can be measured.

Their point of view is that utility is purely subjective and is immeasurable. Moreover an individual is interested in a combination of related goods and in the purchase of one commodity at one time. So they base the theory of consumption on the scale of preference and the ordinal ranks or orders his preferences.

## Assumptions:

The ordinal utility theory or the indifference curve analysis is based on four main assumptions.

(i) Rational behavior of the consumer: It is assumed that individuals are rational in making decisions from their expenditures on consumer goods.

(ii) Utility is ordinal: Utility cannot be measured cardinally. It can be, however, expressed ordinally. In other words, the consumer can rank the basket of goods according to the satisfaction or utility of each basket.

(iii) Diminishing marginal rate of substitution: In the indifference curve analysis, the principle of diminishing marginal rate of substitution is assumed.

(iv) Consistency in choice: The consumer, it is assumed, is consistent in his behavior during a period of time. For insistence, if the consumer prefers combinations of A of good to the combinations B of goods, he then remains consistent in his choice. His preference, during another period of time does not change. Symbolically, it can be expressed as:

If A > B, then B > A

(iv) Consumer’s preference not self contradictory: The consumer’s preferences are not self contradictory. It means that if combinations A is preferred over combination B is preferred over C, then combination A is preferred over combination A is preferred over C. Symbolically it can be expressed:

If A > B and B > C, then A > C

(v) Goods consumed are substitutable: The goods consumed by the consumer are substitutable. The utility can be maintained at the same level by consuming more of some goods and less of the other. There are many combinations of the two commodities which are equally preferred by a consumer and he is indifferent as to which of the two he receives.

## Example:

For example, a person has a limited amount of income which he wishes to spend on two commodities, rice and wheat. Let us suppose that the following commodities are equally valued by him:

Various Combinations:

a)      16 Kilograms of Rice          Plus          2 Kilograms of Wheat

b)      12 Kilograms of Rice          Plus          5 Kilograms of Wheat

c)      11 Kilograms of Rice          Plus          7 Kilograms of Wheat

d)      10 Kilograms of Rice          Plus          10 Kilograms of Wheat

e)      9   Kilograms of Rice          Plus          15 Kilograms of Wheat

It is matter of indifference for the consumer as to which combination he buys. He may buy 16 kilograms of rice and 2 kilograms of wheat or 9 kilograms of rice and 15 kilograms of wheat. All these combinations are equally preferred by him.

An indifference curve thus is composed of a set of consumption alternatives each of which yields the same total amount of satisfaction. These combinations can also be shown by an indifference curve.

## Figure/Diagram of Indifference Curve:

The consumer’s preferences can be shown in a diagram with an indifference curve. The indifference 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. In fig. 3.1 we measure the quantity of wheat along X-axis (in kilograms) and along Y-axis, the quantity of rice (in kilograms). IC is an indifference curve.

It is shown in the diagram that a consumer may buy 12 kilograms of rice and 5 kilograms of wheat or 9 kilograms of rice and 15 kilogram of wheat. Both 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 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 which yield the same level of satisfaction.

## An Indifference Map:

A graph showing a whole set of indifference curves is called an indifference map. An indifference map, in other words, is comprised of a set of indifference curves. Each successive curve further from the original curve indicates a higher level of total satisfaction. In the fig. 3.2 three indifference curves IC1, IC2 and IC3 have been shown. The various combinations of goods of wheat and rice lying on IC1 yield the same level of satisfaction to the consumer. The combinations of goods lying on higher indifference curve IC2 contain more both the goods wheat and rice. The indifference curve IC2 gives more satisfaction to the consumer than IC1. Similarly, the set of combinations of two goods on IC3 yields still higher satisfaction to the consumer than IC2. In short, the further away a particular curve is from the origin, the higher level of satisfaction it represents.

It may here be noted that while an indifference curve shows all those combinations of wheat and rice which provide equal satisfaction to the consumer but it does not indicate exactly how much satisfaction is derived by the consumer from these combinations. It is because of the fact that the concept of ordinal utility does not involve the qualitative measurement of utility.

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