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Indifference Curve Analysis: Assumptions, Indifference Schedule and the Meaning of Marginal Rate of Substitution

Introduction

Indifference curve analysis is basically an attempt to improve cardinal utility analysis (principle of marginal utility). The cardinal utility approach, though very useful in studying elementary consumer behavior, is criticized for its unrealistic assumptions vehemently. In particular, economists such as Edgeworth, Hicks, Allen and Slutsky opposed utility as a measurable entity. According to them, utility is a subjective phenomenon and can never be measured on an absolute scale. The disbelief on the measurement of utility forced them to explore an alternative approach to study consumer behavior. The exploration led them to come up with the ordinal utility approach or indifference curve analysis. Because of this reason, aforementioned economists are known as ordinalists. As per indifference curve analysis, utility is not a measurable entity. However, consumers can rank their preferences.

Indifference Curve Analysis Vs. Marginal Utility Approach

Let us look at a simple example. Suppose there are two commodities, namely apple and orange. The consumer has $10. If he spends entire money on buying apple, it means that apple gives him more satisfaction than orange. Thus, in indifference curve analysis, we conclude that the consumer prefers apple to orange. In other words, he ranks apple first and orange second. However, in cardinal or marginal utility approach, the utility derived from apple is measured (for example, 10 utils). Similarly, the utility derived from orange is measured (for example, 5 utils). Now the consumer compares both and prefers the commodity that gives higher amount of utility. Indifference curve analysis strictly says that utility is not a measurable entity. What we do here is that we observe what the consumer prefers and conclude that the preferred commodity (apple in our example) gives him more satisfaction. We never try to answer ‘how much satisfaction (utility)’ in indifference curve analysis.

Assumptions

Theories of economics cannot survive without assumptions and indifference curve analysis is no different. The following are the assumptions of indifference curve analysis:

Rationality

The theory of indifference curve studies consumer behavior. In order to derive a plausible conclusion, the consumer under consideration must be a rational human being. For example, there are two commodities called ‘A’ and ‘B’. Now the consumer must be able to say which commodity he prefers. The answer must be a definite. For instance – ‘I prefer A to B’ or ‘I prefer B to A’ or ‘I prefer both equally’. Technically, this assumption is known as completeness or trichotomy assumption.

Consistency

Another important assumption is consistency. It means that the consumer must be consistent in his preferences. For example, let us consider three different commodities called ‘A’, ‘B’ and ‘C’. If the consumer prefers A to B and B to C, obviously, he must prefer A to C. In this case, he must not be in a position to prefer C to A since this decision becomes self-contradictory.

Symbolically,

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

More Goods to Less

The indifference curve analysis assumes that consumer always prefers more goods to less. Suppose there are two bundles of commodities – ‘A’ and ‘B’. If bundle A has more goods than bundle B, then the consumer prefers bundle A to B.

Substitutes and Complements

In indifference curve analysis, there exist substitutes and complements for the goods preferred by the consumer. However, in marginal utility approach, we assume that goods under consideration do not have substitutes and complements.

Income and Market Prices

Finally, the consumer’s income and prices of commodities are fixed. In other words, with given income and market prices, the consumer tries to maximize utility.

Indifference Schedule

An indifference schedule is a list of various combinations of commodities that give equal satisfaction or utility to consumers. For simplicity, we have considered only two commodities, ‘X’ and ‘Y’, in our Table 1. Table 1 shows various combinations of X and Y; however, all these combinations give equal satisfaction (k) to the consumer.

Table 1: Indifference Schedule

Combinations
X (Oranges)
Y (Apples)
Satisfaction
A
2
15
k
B
5
9
k
C
7
6
k
D
17
2
k

You can construct an indifference curve from an indifference schedule in the same way you construct a demand curve from a demand schedule.

On the graph, the locus of all combinations of commodities (X and Y in our example) forms an indifference curve (figure 1). Movement along the indifference curve gives various combinations of commodities (X and Y); however, yields same level of satisfaction. An indifference curve is also known as iso utility curve (“iso” means same). A set of indifference curves is known as an indifference map.

Marginal Rate of Substitution

Marginal rate of substitution is an eminent concept in the indifference curve analysis. Marginal rate of substitution tells you the amount of one commodity the consumer is willing to give up for an additional unit of another commodity. In our example (table 1), we have considered commodity X and Y. Hence, the marginal rate of substitution of X for Y (MRSxy) is the maximum amount of Y the consumer is willing to give up for an additional unit of X. However, the consumer remains on the same indifference curve.

In other words, the marginal rate of substitution explains the tradeoff between two goods.

Diminishing marginal rate of substitution

From table 1 and figure 1, we can easily explain the concept of diminishing marginal rate of substitution. In our example, we substitute commodity X for commodity Y. Hence, the change in Y is negative (i.e., -ΔY) since Y decreases.

Thus, the equation is

MRSxy = -ΔY/ΔX and

MRSyx = -ΔX/ΔY

However, convention is to ignore the minus sign; hence,

MRSxy = ΔY/ΔX

In figure 1, X denotes oranges and Y denotes apples. Points A, B, C and D indicate various combinations of oranges and apples.

In this example, we have the following marginal rate of substitution:

MRSx for y between A and B: AA­­1/A1B = 6/3 = 2.0

MRSx for y between B and C: BB­­1/B1C = 3/2 = 1.5

MRSx for y between C and D: CC­­1/C1D = 4/10 = 0.4

Thus, MRSx for y diminishes for every additional units of X. This is the principle of diminishing marginal rate of substitution.

© 2013 sundaramponnusamy

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