# Indifference curve

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Updated: Aug 20, 2021

A curve showing a series of ‘bundles’ of two goods, between which a consumer is indifferent. For example, if a bundle of goods consisting of 5 lb. of sugar and 2 lb. of potatoes were regarded by a consumer as neither more nor less preferable than 4 lb. of sugar and 2½ lb. of potatoes, then these two pairs of values would lie on an indifference curve drawn between axes on which were measured quantities of potatoes and sugar respectively. The figure illustrates a typical indifference curve. In constructing it we assume we have confronted the consumer with a larger number of choices between pairs of alternative consumption bundles, and in each case he has indicated whether he prefers one bundle to the other or is indifferent between them. The properties we ascribe to the curve follow from specific assumptions we make about the psychology of the consumer. These properties, and the assumptions which give rise to them, are as follows:

(a) The set of bundles between which the consumer is indifferent lie along a line and not in an area or band. This follows from the assumption that the consumer will always prefer more of a good to less. For example, given point B in the figure, corresponding to 5 lb. sugar and 2 lb. of potatoes, the consumer would prefer any bundle with at least 5 lb. of sugar and more than 2 lb. of potatoes, or at least 2 lb. of potatoes and more than 5 lb. of sugar. Sirnilarly, B would be preferred to any bundle with less of one good and no more of the other. It follows that all points due north or due east of B, or in between, must be preferred to it, while B must be preferred to all points south and west of it or in between. If we apply that argument to every point on the indifference curve, it is clear that the graph of the set of bundles indifferent to each other cannot be ‘thicker’ than a line.

(b) It is continuous, having no gaps or breaks. This follows from an assumption which could be expressed as ‘a willingness by the consumer always to accept some quantity of one good in “exact compensation” for a reduction, however small or large, in the amount he has of the other’. At point B in the figure, if we were to make a reduction in the amount of sugar in the bundle by any amount, however small or large, we could always find a corresponding increase in potatoes which would bring the consumer back to the indifference curve (which is what we mean by ‘exact compensation’). This would not be so if, for example, the curve had a gap between points Band C – all points south-east of B and north-west of C either preferred or inferior to them. It would then follow that a reduction from B of, say, l lb. of sugar could not be exactly compensated – there would be no quantity of potatoes which, in conjunction with 4 lb. of sugar, yielded a bundle indifferent to Band C. Although this continuity assumption may seem esoteric, it plays an important part in ensuring that certain mathematical conditions are met which ensure an optimal choice of consumption bundle by the consumer, given his income and the prices of the goods.

(c) It is drawn sloping downwards from left to right. This expresses the idea that if we subtract some of one of the goods from his bundle, we would have to increase the quantity of the other to compensate and so leave him with a new bundle equivalent to the first. This again rests on the assumption that a consumer will always prefer to have a combination containing more of at least one good and no less of the other. This then rules out indifference curves which are horizontal, vertical or sloping upwards from left to right. If, on the other hand, one of the ‘goods’ was something like household waste, aircraft noise, work, then we would expect the indifference curve to slope upwards from left to right.

(d) It is drawn convex to the origin, i.e. it bulges outward when looked at from below. This curvature of the indifference curve expresses the idea that as one good becomes more plentiful relative to the other, further increases in it are worth less in terms of the other. This can be illustrated as follows: beginning at point B in the figure, we could imagine ‘moving’ the consumer along his indifference curve by reducing the amount of sugar in the bundle and increasing the amount of pptatoes. We substitute potatoes for sugar in such a way as to lea ve him always with bundles which he regards as equivalent to B. Now, at B, the consumer has a lot of sugar and not many potatoes. If we subtract 1 lb. of sugar from his bundle, we have to compensate by giving roughly ½ lb. of potatoes, leaving him with a new bundle which is equivalent to B. At C, on the other hand, he has a lot of potatoes and little sugar. If we now subtract 1 lb. of sugar from his bundle, we find we have to give him about 2 lb. of potatoes in order to give him a bundle which is equivalent to C. The quantity of potatoes required to compensate the individual for the loss of I lb. of sugar gets steadily greater as potatoes become plentiful and sugar scarce, and this is reflected in the shape of the curve.

The concept of the indifference curve is used extensively in the theory of consumer demand, in welfare economics and indeed in any area of economics concerned with problems of choice between alternative combinations of variables. It is away of representing the preferences of a decision-taker on the basis of information on rankings alone and no assumption of the measurability of utility is involved. Since the decision-taker can rank all possible bundles, there can be drawn a set of indifference curves which completely fill the space between the two axes, and this set is known as the indifference map. As a result of assumption (a) bundles on higher indifference curves are preferred to those on lower. Also, two indifference curves cannot intersect without logical contradiction. If, for example, X and Y are points on two intersecting indifference curves, with Xhaving more of both goods than Y, then because of assumption (a) X must be preferred to Y. But both K and Y are indifferent to the point Z at which the two indifference curves intersect, and so should be indifferent to each other. Since X cannot at the same time be both preferred to and indifferent to Y, avoidance of logical contradiction implies that indifference curves cannot intersect. The overall result of the theory of indifference curves is that the decision-taker’s preferences over alternatives can be represented by a set of continuous, non-intersecting, convex-to-the-origin indifference curves which the forms the basis fo further analysis of choice.

Reference: The Penguin Business Dictionary, 3rd edt.

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