Substitutes and Complements in Indifference Curve Analysis

In this article we will discuss about Substitutes and Complements in Indifference Curve Analysis.

The indifference curve analysis is based on the assumption that there are two related goods which may be substitutes or complements. Pareto explained the relation between substitute and complementary goods as reversible which means that if X is a substitute of Y, Y is a substitute of X, and if X is a complement to Y then Y is complement to X.

In this sense, the shape of an indifference curve depends on whether the two related goods are perfect or imperfect substitutes or complements.

The shape of an indifference curve is convex to the origin and this is based on the principle of diminishing marginal rate of substitution. This principle makes it possible to substitute one good for another in order to achieve any particular level of satisfaction or utility. Thus when two goods X and Y are imperfect substitutes; the indifference curve has its usual negatively sloping shape, as in Figure 1.

If two goods X and Y are perfect substitutes, the indifference curve is a straight line with negative slope, as shown in Figure 41 because the MRS_XY is constant. The value of this slope is throughout minus 1, and MRS_XY = 1.

In the figure, ab of Y = bc of X, and cd of Y = de of X. In this case, the consumer does not distinguish between these two goods and regards them as the same commodity, such as two brands of tea. The consumer is obsessed with the purchase of only one good. This is called monomania for that good.

If the two goods are close substitutes, such as coarse rice and wheat, there is the high degree of substitutability of the two goods.

The slope of the indifference curve:

I₁ in Figure 42 is almost constant between the ranges AB that is MRS_XY is almost identical at all points in this range.

If the two goods are perfect complements the indifference curve is right-angled or L shaped, as shown in Figure 43 (A). The vertical portion of the I₁, curve reveals that no amount of reduction in good Y will lead even to a slight increase in good X. For example, point’s A, M and В are all on the curve I_t but point В involves the same amount of Y but more of X than point M.

Thus MRS_XY is zero. The two goods X and Y are consumed in the desired ratio, as indicated by the slope of the ray OR at point M. Such complementary goods are left and right shoes which are used in the 1:1 fixed ratio.

In the case of highly or close complementary goods, the indifference curve has a sharp curvature near the bend. The consumer substitute X for Y at and near the bend of the curve. In Figure 43 (В), X and Y will be substituted for each other within the narrow range A and В of the indifference curve I₁ .Such close complements are tyres and tubes, electricity and electric appliances, etc..