Indifference Curve Analysis
This theory was propounded by Hicks and Allen. The ordinal approach assumes that utility is not measurable. The ordinal approach employs the device of indifference curves for the purpose of determination of the consumer's equilibrium. A prudent consumer seeks to maximize his satisfaction from the purchases he makes, i.e., reach an equilibrium position. For this, a consumer must build up a scale of preferences on which all objects of desire or pursuit find their place, and which registers the terms on which they would be preferred one to the other. He builds up his scale of preferences from the commodities he consumes.
A set of indifference curves plotted in an 'indifference map' determines the consumer's order of preferences.
According to Leftwich: “A single indifference curve shows the indifferent combination of X and
Y that yield equal satisfaction to the consumer.”
According to Hicks: “It is the locus of the points
representing parts of quantities between which the individual is indifferent and so it is termed as an
indifference curve.”
In other words, an indifference curve is a combination of goods, each of which yields the same level of satisfaction to which the consumer is indifferent.
Given the market prices of the commodities and the money income to be spent on them we can locate the attainable combinations of commodities. These can be plotted in the form of a straight line, called the budget line.
Consumers will get the equilibrium at the point where an indifference curve from the given indifference map is tangent to a given budget line.
Assumptions of the theory of indifference curve:
1. The consumer is rational in behavior and aims at maximizing his total satisfaction.
2. It is assumed that the customer has to make a choice between two goods.
3. Consumer's scale of preferences is so complete that he is able to choose any one of the two combinations of commodities presented to him.
4. If a consumer prefers Q than R and R then S, then he will prefer Q to S if this choice is open. It is called transitivity of choice.
5. If a consumer prefers A to B in one period, he will not prefer B to A in another period. It is called the consistency of choice.
6. The indifference curve is convex to the origin and shows the diminishing marginal rate of the substitution.
Indifference Curve Schedule:
An indifference curve represents the satisfaction of a consumer from two commodities.
An indifference curve schedule is the locus of points of particular combinations or baskets of two commodities that yield the same level of satisfaction to the consumer so that he is indifferent as to the particular combination he consumes.
In the above schedule, the consumer feels indifferent whether he gets the first combination [1 unit of good x and 12 unit of good y], the second combination [2 unit of good x and 8 unit of good y], the third combination [3 unit of good x and 5 unit of good y], the fourth combination [4 unit of good x and 3 unit of good y] or the fifth combination [5 unit of good x and 2 unit of good y] The total satisfaction is the same in all these combinations.
Indifference Map:
An Indifference Map is a set of Indifference Curves showing several combinations of different goods and giving an entire view of a consumer's choices. The below diagram shows an indifference map with four indifference curves.
We can not say how much more utility the higher indifference curve represents. That is, the aggregate utilities are rankable and not measurable. We can not say how much greater utility does IC2 represents than IC1 and IC3, than IC2, and so on.
Marginal Rate of Substitution:
When we move from one combination of two commodities to another, we substitute some units of one commodity for some units of another. It is called the marginal rate of substitution.
The marginal rate of substitution shows how much of one commodity is substituted for how much of another or the rate at which the individual must give up 'Good Y' in order to obtain one more unit of 'Good x' while keeping their overall satisfaction constant.
In the words of Hicks: “The marginal rate of substitution of X for Y measures the number of units of Y that must be sacrificed for a unit of X gained so as to maintain a constant level of satisfaction”.
The concept of the marginal rate of substitution is a tool of indifference curve technique and is parallel to the concept of marginal utility in the Marshallian analysis of demand.
In technical language, it will be said that the marginal rate of substitution of good X for good Y will fall as the consumer has more of X and less of Y. It is obvious that as a consumer has more and more of one good, he will be prepared to forego less and less of the other since his desire for the former becomes less and less intense with more and more of it.
symbolically,
Properties / Characteristics of Indifference Curve:
1. An indifference curve slopes downward from left to right: i.e., it has a negative slope. it denotes that if the quantity of one commodity [GoodY] decreases, the quantity of another commodity [Good X] must increase if the consumer is to stay on the same level of satisfaction. This is due to the non-satiety requirement.
a: The indifference curve cannot slope upward from left to right as we have to sacrifice a few units of good Y to get more one unit of Good X to get equal satisfaction. In this diagram, it is clear that the consumer is getting more quantity from both goods which is not satisfying the condition.
b: The indifference curve cannot be horizontal. In the below diagram, combination B has more of X and the same quantity of Y. So the indifference curve cannot be horizontal. This is again not satisfying the condition.
c: The indifference curve cannot be vertical. In the diagram, combination B is preferred to A as the consumer has more of Y and the same quantity of X. Therefore, the indifference curve cannot be vertical either.
Only in a downward sloping curve, the loss in one is compensated by the gain in another commodity so that the different points on the curve will give equal satisfaction to the consumer and he may be indifferent to the various combinations. So, a horizontal or vertical or sloping up curve is not possible.
2. Every Indifference Curve to the right represents a higher level of Satisfaction than that of Proceeding One: As the consumer move to the right he reaches to the higher indifference curve and it gives more and more satisfaction
In this diagram, at Q point at IC2, the consumer gets more units of good X in comparison to P point at IC1. Thus, it is clear that the indifference curve at a higher level shows greater satisfaction than an indifference curve at a lower level.
3. The indifference curve can not intersect each other: If they did, the point of their intersection would supply two different levels of satisfaction, which is not possible. This is due to the assumption of transitivity.
Suppose two indifferent curves cut each other at point A as shown in the diagram. This means that points A and C which are on the same indifference curve IC2 show equal satisfaction; similarly points A and B which are on the same indifference curve IC1 show equal satisfaction.
But this is contrary to our previous assumption that a higher indifference curve shows greater satisfaction than lower indifference curves. Therefore, to be consistent with this assumption, we can say that different indifference curves would not cut each other.
4. The indifference curve does not touch the axis: If the curve touches either of the axis, it means that he is satisfied with one commodity only and does not want the other, which is contrary to the assumption.
If IC1 touches Y-axis at A point, the consumer will be having OA quantity of good Y and none of good X. Similarly, if IC2 touches the X-axis at B, the consumer will have only OB of X good and no amount of Y. Such curves are contrary to the assumption.
5. Indifference curves are convex to the origin: Convexity of indifference curves is due to the assumption of the diminishing marginal rate of substitution. It means that as the amount X is increased by equal amounts that of Y diminish by smaller amounts. The slope of the curve becomes smaller as we move to the right.
6. Indifference curves are not necessarily parallel to each other: Though they are falling, negatively inclined to the right, even the rate of substitution between the two commodities need not be the same in all the indifference schedules. It is therefore not necessary that the Indifference Curve should be parallel to each other.
7. In reality, Indifference Curves are like Bangles: This is because of indifference curves have negative slop and convex to the origin.
Criticism of the Indifference Curve Approach: The main points of criticism are discussed below.
1. Old wine in a new bottle: professor D.H. Robertson is of the opinion that the indifference curve technique is merely " the old wine in a new bottle". this technique has substituted new concepts in place of the old ones such as the term, " preferences" has been used in place of the concept of "utility'. The ordinal number system of first, second, and third, etc have been used to indicate the scale of preferences in place of the cardinal number system of one, two, three, etc to measure the strength of a consumer's desire. The concept of marginal utility has been replaced by the marginal rate of substitution.
2. Marshallian base essential: Marshal's marginal utility is the base of Hicksian's marginal rate of the substitution. As the Indifference curve becomes convex to the origin because of the diminishing marginal rate of substitution. When consumer increases the stock of good X, the marginal utility of X in term of Y decreases. According to professor Armstrong," Hicks has not been able to derive the fundamental concept of diminishing marginal rate of substitution independently of the concept of utility."
3. Unrealistic: The indifference curve technique imagines a consumer who thinks of multitudinous possible combinations of two goods and his relative preferences. It is based on unrealistic assumptions also such as rationality, perfect market, divisibility of goods, etc. Consumer's purchases are much more affected by their habits, customs, and fashion.
4. Only two goods models: Another drawback of this theory is that it can analyze consumer behavior in respect of two goods only. In reality, the consumer consumes more than two goods, thus this theory can not be applicable.
5. Cannot explain Uncertainty: This technique ignores the risk or uncertainty of expectations as regards, the consequences of choice while studying the consumer's behavior.
6. Introspective: Samuelson has criticized this technique as been introspective and he has chosen a behavioral method for constructing the demand theory.
7. Constancy of Taste: This theory assumes that consumers' taste does not change and his preference remains unaltered over a period of time which is not correct.
8. Market behavior ignored: It does not take any notice of market changes in the prices of other goods and considers only the prices of two goods.
9. Ignores Demonstration Effect: The level of consumption of others often affects the level of consumption of an individual. Thus no notice of this is taken in the critique.
10. Transitivity: According to Professor Armstrong, the consumers' indifference arises from his inability to recognize the difference between the alternative combinations of goods and not because of the relation of transitivity involved in the indifference curve technique.
In spite of these weaknesses, this technique is considered superior to the marginal utility analysis of Dr. Marshall.
Comparison between Indifference curve analysis [Ordinal theory] and Marginal utility analysis[Cardinal theory]
The similarity between the two approaches: Both approaches assume the rational and utility-maximizing behavior of the consumer.
The marginal rate of substitution in ordinal theory is based on the diminishing marginal utility of the cardinal approach.
Both approaches contain the same proportionality rule for maximizing satisfaction. The equilibrium condition of the cardinal theory is that the total expenditure must not exceed the consumer's total income while the equilibrium condition of the ordinal theory is to reach at the highest possible indifference curve with the given price line. Both are similar.
both approaches are introspective.
The superiority of the Indifference Curve Approach- In spite of these similarities, Indifference curve analysis is superior in many respects-
1. More Realistic: Marshall’s utility analysis is based on the cardinal utility function which assumes that the utility is measurable and exact numbers can be assigned to it. Whereas utility is a purely subjective matter and cannot be exactly measured in numbers. It varies from person to person and from time to time.
The indifference approach is based on the ordinal utility function which is based on the preferences of the consumer and according to preferences, he provides the ranks to the commodity which is more realistic.
2. It studies the combination of two goods: Marshall's theory is based on a single commodity, but in reality, a consumer buys more than one commodity at a time. The indifference curve technique is a two-commodity model that studies consumer behavior in the case of substitutes, complementaries, and unrelated goods. Thus it is superior to utility analysis.
3. No assumption of constancy of marginal utility of money: the assumption of constant marginal utility of money is not compatible where the consumer has more than a single good to spend his income on. Thus, the cardinal theory ignored the "income effect' of a price change and failed to distinguish between the two components [income effect and substitution effect] of the "price-effect".
The indifference curve technique does not assume the constancy of the marginal utility of money and is able to distinguish between the income effect and the substitution effect of a price change.
4. Application of the marginal rate of substitution: The law of diminishing marginal utility has been replaced with the diminishing marginal rate of substitution which is applicable in the field of consumption, production, and distribution.
5. The more general theory of demand: The indifference curve technique gives us a more general theory of demand. Marshall could not provide and satisfactory explanation in the case of Giffen goods. It was the exception to the Marshallian law of demand.
Hicks' explanation of a Giffen case is that the negative income effect is so powerful that it outweighs the positive substitution effect and, hence the fall in the price of a Giffen good, its demand also falls.
Significance / Applications of Indifference curve Analysis
According to Boulding. " The Indifference Curve is a powerful weapon of economics analysis." It is not merely a tool of theoretical analysis but can also be put for practical use in several economics spheres.
1. In Consumption: Each consumer wants to get maximum satisfaction. With the given income and prices of the goods, a consumer must decide the quantity of each commodity that he should purchase to maximize his satisfaction. For it, he must select one of the many possible combinations of two goods lying on the indifference curve and he will try to reach the highest possible indifference curve touching the price line.
Indifference curve analysis can also be used to measure consumer's surplus in a more realistic manner without using the utility in cardinal numbers.
It is also used to study the price effect, the substitution effect, and income effect as well as the demand curve for Giffen goods.
2. In production: The indifference curve technique is also used in production. It is known as the Iso-product curve. The iso-product curve shows the various combinations of two factors of production showing the same amount of output.
A producer aims at maximization of output with the minimum cost. He is said to be in equilibrium at the point where the highest possible Iso-product curve is tangent to the factor price line.
3 In the field of Exchange: Prof. Edgeworth used the indifference curves technique to show the mutual benefits gained from the exchange of two goods between buyers and sellers. An exchange makes it possible for both to reach a higher level of satisfaction by building an Edgeworth Bowley box figure on the basis of their choice maps. The two goods are exchanged with each other until their marginal rate of substitution becomes equal for both of them.
4. In Rationing: This technique can be applied in the field of rationing. In rationing, a fixed quantity of goods is given to the consumers at a fixed price. It reduces the satisfaction of consumers because of not getting the desired quantity of the goods. The effect of rationing can be studied with the help of indifference curves. A consumer can save more money with rationing but it does not allow him to reach the highest possible indifference curve and his level of satisfaction decreases.
The diagram shows that before rationing the consumer was in equilibrium on IC2 at point E with OQ1 commodity X and he was saving OP1 money. But after rationing, he is at equilibrium on F point of IC1 with OQ of commodity X and he saves money OP. It means that he is able to save more money but getting less satisfaction.
5. Cost of living Index: The standard of living consists of the various combinations of goods giving equal satisfaction. The cost of living depends on the collection of goods and services consumed by the consumer. The standard of living has risen or fallen, it can be shown on the indifference curve. If the consumer is able to reach on the highest indifference curve touching the respective price line with the most preferable combination, then his standard of living must be high.
6. In taxation: The indifference curve can help us to find out whether a direct tax like income-tax will be better or not than indirect taxes like sales tax or excise duty.
In the above figure, the money income of the taxpayer is shown on OY axis. He has OA1 of money income and his original price-income line, before the tax is levied, is A1B1. He is in equilibrium at a point P on the indifference curve IC1.
For A1T quantity of X, he spends TP. When the excise duty on commodity X is levied, its price rises so that his price-income line shifts to A1B2 where he is in equilibrium at point Q on the IC2 curve. As a result of the tax, he buys A1S quantity of X and spends SQ on it. But at the original price, this quantity A1S would have cost him SU. Thus UQ is the amount of tax that he pays for it.
If an equal amount of tax is raised by the government through income tax instead, the taxpayer’s income would be reduced by A1A2 (=UQ). He moves to a lower budget line A2B3 on the indifference curve IC3, at point R. Since the indifference curve IC3 is higher than IC2 the income tax equivalent to an excise duty places the taxpayer in a favorable position.
7. A measurement of National Income: The indifference curves, showing the different combinations open to a consumer, can be used for measuring national income. National income is the aggregate value of the net output of an economy and it is produced by the members of the community and it is also consumed by them. In the system of purchases, the consumers combine the commodities in such a way as to maximize their satisfaction. The relative importance of the commodities in these combinations and the relative prices indicate the relative importance of these commodities to various members of the community.
8. In Distribution: It analyzes the supply curve of the labor in the case of poorly paid workers any rise in the wages will not lead to a reduction in working time, it will only result in larger income which will be utilized in purchasing more goods but behind a certain stage, the worker will work less and still enjoy more goods.
Thus, the indifference curve technique is an important tool in economic analysis.
Dr. Swati Gupta
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Very good explanation
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