Indifference Curve Analysis



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 MICROECONOMICS
An indifference curve is a locus of combinations of goods which derive the same level of satisfaction, so that the consumer is indifferent to any of the combination he consumes.If a consumer equally prefers two product bundles, then the consumer is indifferent between the two bundles. The consumer gets the same level of satisfaction (utility) from either bundle. Graphically speaking, this is known as the indifference curve. An indifference curve shows combinations of goods between which a person is indifferent.

Symbolically,in the equation form,

An Indifference Curve =$$U = f (x_1,x_2,x_3,.....x_n)= k $$ ......where, k is a constant.

In indifference curve approach only ordination of preferences is needed.It overcomes the weakness of Cardinal measurement as the satisfaction cannot be measured objectively.

The cardinal approach provides the assumption of constant utility of money, which is unrealistic.In indifference curve approach, this assumption has been dropped.

Indifference curve approach is base for the measurement of 'consumer's surplus'.In a way it contributes to the Welfare economics.

Indifference curve is a better tool to classify substitutes and complementary goods.

The main attributes or properties or characteristics of indifference curves are as follows:

The indifference curves must slope downward from left to right. 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.

DIAGRAM:



In the above diagram, two combinations of commodity cooking oil and commodity wheat is shown by the points a and b on the same indifference curve. The consumer is indifferent towards points a and b as they represent equal level of satisfaction.

Indifference curve that lies above and to the right of another indifference curve represents a higher level of satisfaction. 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. Diagram:



In this diagram, there are three indifference curves, IC1, IC2 and IC3 which represents 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.

This is an important property of indifference curves. They are convex to the origin. As the consumer substitutes commodity X for commodity Y, the marginal rate of substitution diminishes as X for Y along an indifference curve. The Slope of the curve is referred as the Marginal Rate of Substitution. The Marginal Rate of Substitution is the rate at which the consumer must sacrifice units of one commodity to obtain one more unit of another commodity.

Diagram:



In the above diagram, as the consumer moves from A to B to C to D, the willingness to substitute good X for good Y diminishes. The slope of IC is negative.In the above diagram, diminishing MRSxy is depicted as the consumer is giving AF>BQ>CR units of Y for PB=QC=RD units of X. Thus indifference curve is steeper towards the Y axis and gradual towards the X axis. It is convex to the origin.

If the indifference curve is concave, MRSxy increases. It violets the fundamental feature of consumer behaviour.

If commodities are almost perfect substitutes then MRSxy remains constant. In such cases the indifference curve is a straight line at an angle of 45 degree with either axis.

If two commodities are perfect complements, the indifference curve will have a right angle.

In reality, commodities are not perfect substitutes or perfect complements to each other.Therefore MRSxy usually diminishes.

The indifference curves cannot intersect 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.

Diagram:



In the above diagram, two indifference curves are showing cutting each other at point B. The combinations represented by points B and F given equal satisfaction to the consumer because both lie on the same indifference curve IC2. Similarly the combinations shows by points B and E on indifference curve IC1 give equal satisfaction top 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 funny because combination F on IC2 contains more of good Y (wheat) than combination which gives more satisfaction to the consumer. We, therefore, conclude that indifference curves cannot cut each other.

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 that case indifference curve will touch one axis. This violates the basic assumption of indifference curves.

Diagram:



In the above diagram, it is shown that the in difference IC touches Y axis at point P and X axis at point S. At point C, the consumer purchase only OP commodity of Y good and no commodity of X good, similarly at point S, he buys OS quantity of X good and no amount of Y good. Such indifference curves are against our basic assumption. Our basic assumption is that the consumer buys two goods in combination.

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Consumer would derive equal satisfaction at any point along a given indifference curve, as each point brings the same level of satisfaction to the consumer. Hence consumer is indifferent about the various combinations of two goods along with the indifference curve.

Properties of Indifference Curves

1.	Indifference Curves are Negatively Sloped. Indifference curves are downward sloping. If the quantity of one goods is reduced, then you must have more of the other good to compensate for the loss.

2.	Higher Indifference Curve Represents Higher Level of satisfaction. Higher indifference curves are preferred to lower ones, since more is preferred to less (non-satiation).

3.	Indifference curves are convex to the origin (in most cases).The slope of the curve is referred as the Marginal Rate of Substitution. The Marginal Rate of Substitution is the rate at which the consumer must sacrifice units of one commodity to obtain one more unit of another commodity.

4.	Indifference curves do not intersect with each other.

J.R.Hicks, A Revision of Demand Theory Lipsey, Richard G. (1975). An introduction to positive economics (fourth ed.). Weidenfeld & Nicolson. pp. 214-7. ISBN 0297768999.

Bruce R. Beattie and Jeffrey T. LaFrance, "The Law of Demand versus Diminishing Marginal Utility" (2006). Review of Agricultural Economics. 28 (2), pp. 263-271. Volker Böhm and Hans Haller (1987). "demand theory," The New Palgrave: A Dictionary of Economics, v. 1, pp. 785-92. Silberberg and Suen (2000). The Structure of Economics A Mathematical Analysis, 3rd ed. McGraw-Hill.