The elasticity of goods substitution (es) is the ratio of the proportionate change in the combination in which the two goods are to a given proportionate change in their marginal rate of substitution. Thus,
X/Y is the original proportion between the quantities of goods ‘X’ and ‘Y.’
?(X/Y) is the small change in the proportion between the quantities of goods ‘X’ and ‘Y’.
(?X/?Y) is the original marginal rate of substitution of good ‘Y’ for good ‘X’.
? (?X/?Y) is the small change in the marginal rate of substitution of good ‘Y’ for good ‘X.’
Here, it should be remembered that elasticity of substitution is always negative. For the sake of simplicity, we have ignored the sign.
The elasticity of substitution can be infinite, zero or somewhere between infinity and zero, depending upon the extent of substitutability of the two goods. The two goods can be perfect substitutes of each other.
That is, their indifference curve is a straight line. If the two goods are perfect substitutes of each other, then their proportion (X/Y) can be increased infinitely without affecting the marginal rate of substitution (?X/?Y) at all. Thus, in the case of perfect substitute goods, marginal rate of substitution remains constant.
From this, it follows that there is no change in the marginal rate of substitution. In other words, marginal significance of good ‘Y’ in term of ‘X’ does not change at all. Thus, ? (AX/AY) is equal to zero, making the denominator of the formula for elasticity of substitution zero. We know that any number divided by zero is infinity.
Therefore, elasticity of substitution between perfect substitute goods is infinite. However, it is not possible to find the examples of such goods, which ate perfect substitutes. For if, the two goods are perfect substitutes, economically they are the same good.
In practical life, we can find numerous examples of goods, which are not perfect, but, close substitutes of each other. Tea and coffee, air travel and rail travel are some examples of close substitutes. The elasticity of substitution between these goods is not infinite, but, it is very large, as the rate of substitution falls gradually. On the other hand, if the rate of substitution falls rapidly, the elasticity of substitution will be low.
There are goods between which no substitution is possible. These are perfect complements to each other. These can be used in a fixed proportion. As no substitution between them is possible, the marginal rate of substitution between them is zero. In this case, the elasticity of substitution between the goods is zero.
But, it is unlikely to find such a combination of goods which are perfect complements. For example, elasticity of substitution between shirts and pants may not be very high. One may not like to have more than 2 or 3 shirts with each pant. One may not be willing to give up shirts for trousers and vice-versa. Though their elasticity of substitution is not zero, it is very low.