Marshall’s demand analysis is based on the cardinal measurement of utility. The approach is criticised for two reasons.

(i) Utility is a psychological phenomenon and

(ii) It cannot be measured.

Hence, the indifference curve approach based on ordinal ranking preference was evolved. Vilfred Pareto, Wicksteed and Slutsky developed this approach. Two noted English economists Prof. J.R. Hicks and Prof. Allen provided a refined version of indifference curve approach. According to Hicks and Allen, utility cannot be measured. It can only be ranked or ordered. The consumer can rank his preference very easily and say which is better than the other.

The concept of scale of preference has been explained by indifference curve. An indifference curve shows different combinations of two commodities, which give the consumer an equal satisfaction.

Indifference Curve : It is a curve that represents all the combinations of goods that give the same satisfaction to the consumer. Since all the combinations give the same amount of satisfaction, the consumer prefers them equally. Hence the name Indifference Curve.

Assumptions of Indifference Curve Analysis

The indifference curve analysis retains some of the assumptions of the cardinal theory, rejects others and formulates its own. The assumptions of the ordinal theory are the following:

(1) The consumer acts rationally so as to maximise satisfaction.

(2) There are two goods X and Y.

(3) The consumer possesses complete information about the prices of the goods in the market.

(4) The prices of the two goods are given.

(5) The consumer’s tastes, habits and income remain the same throughout the analysis.

(6) He prefers more of X to less of У or more of Y to less of X.

(7) An indifference curve is negatively inclined sloping downward.

(8) An indifference curve is always convex to the origin.

(9) An indifference curve is smooth and continuous which means that the two goods are highly divisible and those levels of satisfaction also change in a continuous manner.

(10) The consumer arranges the two goods in a scale of preference which means that he has both ‘preference’ and ‘indifference’ for the goods. He is supposed to rank them in his order of preference and can state if he prefers one combination to the other or is indifferent between them.

(11) Both preference and indifference are transitive. It means that if combination A is preferable to В, and В to C, then A is preferable to C. Similarly, if the consumer is indifferent between combinations A and B, and В and C, then he is indifferent between A and C. This is an important assumption for making consistent choices among a large number of combinations.

(12) The consumer is in a position to order all possible combinations of the two goods.

Here is an example to understand the indifference curve better. Peter has 1 unit of food and 12 units of clothing. Now, we ask Peter how many units of clothing is he willing to give up in exchange for an additional unit of food so that his level of satisfaction remains unchanged.

Peter agrees to give up 6 units of clothing for an additional unit of food. Hence, we have two combinations of food and clothing giving equal satisfaction to Peter as follows:

• 1 unit of food and 12 units of clothing
• 2 units of food and 6 units of clothing

By asking him similar questions, we get various combinations as follows:

The diagram shows an Indifference curve (IC). Any combination lying on this curve gives the same level of consumer satisfaction. It is also known as Iso-Utility Curve.

Indifference Map

An Indifference Map is a set of Indifference Curves. It depicts the complete picture of a consumer’s preferences. The following diagram showing an indifference map consisting of three curves:

We know that a consumer is indifferent among the combinations lying on the same indifference curve. However, it is important to note that he prefers the combinations on the higher indifference curves to those on the lower ones.

This is because a higher indifference curve implies a higher level of satisfaction. Therefore, all combinations on IC1 offer the same satisfaction, but all combinations on IC2 give greater satisfaction than those on IC1.

Marginal Rate of Substitution

This is the rate at which a consumer is prepared to exchange a good X for Y. If we go back to Peter’s example above, we have the following table:

In this example, Peter initially gives up 6 units of clothing to get an extra unit of food. Hence, the MRS is 6. Similarly, for subsequent exchanges, the MRS is 2 and 1 respectively. Therefore, MRS of X for Y is the amount of Y whose loss can be compensated by a unit gain of X, keeping the satisfaction the same.

Interestingly, as Peter accumulates more units of food, the MRS starts falling – meaning he is prepared to give up fewer units of clothing for food. There are two reasons for this:

• As Peter gets more units of food, his intensity of desire for additional units of food decreases.
• Most of the goods are imperfect substitutes for one another. If they could substitute one another perfectly, then MRS would remain constant.

Properties of an Indifference Curve or IC

Here are the properties of an indifference curve:

(i) An IC slopes downwards to the right

This slope signifies that when the quantity of one commodity in combination is increased, the amount of the other commodity reduces. This is essential for the level of satisfaction to remain the same on an indifference curve.

(ii) An IC is always convex to the origin

From our discussion above, we understand that as Peter substitutes clothing for food, he is willing to part with less and less of clothing. This is the diminishing marginal rate of substitution. The rate gives a convex shape to the indifference curve. However, there are two extreme scenarios:

• Two commodities are perfect substitutes for each other – In this case, the indifference curve is a straight line, where MRS is constant.
• Two goods are perfect complementary goods – An example of such goods would be gasoline and water in a car. In such cases, the IC will be L-shaped and convex to the origin.

(iii) Indifference curves never intersect each other

Two ICs will never intersect each other. Also, they need not be parallel to each other either. Look at the following diagram:

Fig 3 shows tow ICs intersecting each other at point A. Since A and B lie on IC1, the give the same satisfaction level. Similarly, A and C give the same satisfaction level, as they lie on IC2. Therefore, we can imply that B and C offer the same level of satisfaction, which is logically absurd. Hence, no tow ICs can touch or intersect each other.

(iv) A higher IC indicates a higher level of satisfaction as compared to a lower IC

A higher IC means that a consumer prefers more goods than not.

(v) An IC does not touch the axis

This is not possible because of our assumption that a consumer considers different combinations of two commodities and wants both of them. If the curve touches either of the axes, then it means that he is satisfied with only one commodity and does not want the other, which is contrary to our assumption.