# Indifference Curve (full)

Pareto, an Italian economist, first invented the concept of indifference curve. Edge worth stated this device in his book ‘Mathematical Physics’. Later it was developed and applied to economic analysis by economists like

Hicks and Allen

Indifference curve is a geometrical identity that exhibits the various amounts of two or more commodities, which yield the same satisfaction to the consumer. Some of the important definitions are as under:

Edge worth

Indifference Curve is that path on which a substitution of a particular commodity by another in any manner or quantity gives the consumer the same satisfaction in any position.”

1. J. Boumol

“An Indifference curve as the locus of points each of which represents a collection of commodities such that the consumer is indifference among any of these combinations.”

Milton Friedman

“Indifference Curve is a boundary line separating two areas i.e. areas showing combinations of higher and lower levels of satisfaction. All points on an indifference curve represent the same level of satisfaction.”

The indifference curve is a graphical representation of an indifference schedule. Indifference Schedule lists all those different combinations of the goods, which give exactly the same satisfaction to the consumer, in other words the consumer is indifferent between these combinations. It is shown in the following table.

An Indifference Schedule

 Name of the combination Units of goods X Units of goods Y A 1 30 B 2 24 C 3 19 D 4 15 E 5 12 F 6 10 G 7 9

In the table the consumer is indifferent between seven combinations of goods X and Y. He gets same satisfaction when we consume 1 X and 30 Y. He gets the same level of satisfaction when consume 2X and 2Y or 4X and 15Y or 7X and 9Y. When these combinations are represented graphically and joined together with the help of a curve, we get an indifference curve. An indifference curve shows the one particular level of satisfaction. The family or group of indifference curves is known as Indifference map. In the indifference map a higher indifference curve shows the higher level of satisfaction. An indifference curve shown below shows various combinations A, B, C, D, etc. of goods X and Y which Yield the same satisfaction to the consumer. The indifference curve slopes downward from the left to right to indicate that less units of Yth commodity represented on axis-OY so that the total satisfaction may remain the same will accompany more unity of X represented on OX-axis. As more units of X are added, fewer units of Y need be given up, so as to maintain the same satisfaction. The second combination shows that even if the consumer has an extra unit of X the total utility can remain the same if he gives up 6Y. That is the consumer can substitute one unit of X by 6Y. In the third combination one unit of X substitute only 5 Y, in the fourth combination one cup substitutes only 4Y and so on. The rate of substitution can be defined as the rate at which a consumer can exchange very small amounts of another commodity for a very small amount of another commodity without affecting the total utility.

Assumptions of Indifference Curve Analysis

In indifference curve analyses the consumer behavior is based on some assumptions. Prof. W. J. Baumol and others have taken the following major assumptions.

1. Perfect Knowledge. A consumer is assumed to have complete knowledge regarding the type of goods available, their prices and their capacity to satisfy a want. He is also assumed to know his income during his consumption-planning period.
2. Non-satiety. The consumer consumes both the commodities; he is not oversupplied with either commodity. He prefers to have more of x and/or y. This assumption is very reasonable and realistic. The consumer has no special inclination towards one particular commodity. He always tries to move higher and higher level of satisfaction.
3. Consistencies and Transitivity. It is assumed that the consumer is consistent in his choice i.e. if in one period he chooses commodity A over B he will not choose B over A in another period if both the commodities are available in the same amount. This condition simply requires that the consumers tastes possess a conceptually simple type of consistency.

By transitivity we mean that if a consumer prefers A to B and B to C then he also prefers A to C. If he is indifferent between A and B between B and C, then he must be indifferent between A and C.

4. Tastes and preferences. Of the consumer are given. These do not change with the change in the period.

5. Diminishing Marginal Rate of Substitution. This assumption is technical in nature. According to this assumption as more and more units of X are substituted for Y, the consumer will be willing to give up lesser and lesser units of Y for each additional unit of X. When more and more units of Y are substituted for X which means our consumer will be willing to give up successively fewer and fewer units of X for each additional units of Y.

Properties of Indifference Curve

From the above discussion one gets that the indifference curves have four basic properties. Let us examine these properties in detail.

1. Each point in a commodity space is on an indifference curve. The point on indifference shows the combination of goods say X and Y. The indifference curve are plotted in a specific space is called commodity space.

In commodity space each point represents a bundle of goods and this in turn represents a particular level of satisfaction. Therefore this must be represented on indifference. Thus, there will be an indifference map where each point in X-Y spaces lies on an indifference curve.

2. Indifference curve are negatively sloped from left to right. To remain at the given level of satisfaction, if we increase the units of consumption of one good (say X), we need to decrease the consumption of the other goods (say y). In case this is not done, the bundle of goods will increase and hence the satisfaction level will also increase. It is therefore necessary that in order to remain at the same level of satisfaction, the increasing amount of one good must accompany the decreasing amount of the other goods. In this figure when we increase the consumption of one commodity without reducing the consumption of other commodity, then we move from P to Q. Q represents more units of X thereby consumer gets higher satisfaction. Hence it is not comparable to P. On the other hand if we move from P to R on a way that the satisfaction level of consumer remains the same. Thus the indifference curve will be downward sloping.

3. Generally convex to the origin of the axis. The third property of indifference curve is that they are generally convex to the origin of the axis. This property of the indifference curve is based on the assumption of diminishing marginal rate of substitution. In this Fig. The indifference curve is convex from the point of origin-of the axis-o. It shows that BC CU of X substitutes AB Y.

4. A higher indifference curve suggests higher level of satisfaction In the figure given below, points B and C have more of at least one goods (without having less of the other) compared to point A. point B and C therefore present higher utility levels and lie on a higher indifference curve. 5. Indifference curve will never intersect. Indifference curve will never intersect each other. It is because we assume that each IC represents a particular satisfaction to the consumer, it will necessarily be different from other indifference curves representing other satisfaction. This can be proved with the help of Fig. In this figure we are taking to combinations from IC1 and IC2 If two combinations on the same indifference curve represent equal satisfaction, then we have.

AB = (IC1) AC = (IC2)

BC = C

This is quite obscured. Hence two indifference curves each representing a different satisfaction, should not touch each other or intersect each other.

Thus the properties of indifference curves are as  follows:

1. Each point in commodity space is on an indifference curve.
2. They always downward from left to the right.
3. They are generally convex to the point of origin of the axis;
4. A higher indifference curve suggests higher level of satisfaction. And
5. They never intersect each other.

We can now define an indifference curve thus:

An indifference curve is the locus of various combinations of the two commodities, which yield the same total satisfaction to the consumer.

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