Cross Elasticity of Demand

Cross Elasticity of Demand:

The idea of elasticity of demand can also be applied in a situation where two commodities are related to each other in some ways. The relationship between the two commodities X and Y can be either substitutive or complementary or even of neutrality. In other words, the two goods can either be substitutes of each other or complimentary to each other, or completely independent of each other. Let us take the first two types of relationships, namely substitutive and complimentary relationships. In the context of these relationships, the term cross elasticity of demand may be defined as the ratio of proportionate change in the quantity demanded of commodity X to a given proportionate change in the price of the related commodity Y. The cross elasticity of demand can be calculated with the help of the following formula:

Let us assume that the two commodities X and Y are substitutes of each other. Now, if the price of Y rises, assuming that the price of X remains constant, the quantity demanded of X will increase, because the consumers will now substitute X for Y (Y having become costlier than before). On the contrary, if the price of Y falls, assuming that the price of X remains constant, the quantity demanded of X will decrease because the consumers will now substitute Y for X (Y having become cheaper than before). Now, if X and Y are perfect substitutes for each other, the cross elasticity of demand will be infinity. It means that the slightest change in the price of Y will cause a substantial change in the quantity demanded of X. A slight rise in the price of Y will reduce the demand for Y to almost zero. If, on the contrary, the two goods are no substitutes at all (or are not related to each other), the cross elasticity of demand will be zero. A change in the price of one commodity will not affect the quantity demanded of the other. In the case of substitute goods, thus, the cross elasticity of demand varies between two extremes- infinity and zero, depending upon the degree of substitutability existing between them. If the substitutability is perfect, cross elasticity is infinity; if, on the other hand, substitutability does not exist, cross elasticity is zero.

Now, let us assume that the commodities X and Y are complements instead of being substitutes. What shall be the nature of cross elasticity in such a case? Obviously, the cross elasticity in such a case will be negative. A rise in the price of Y will mean not only a decrease in the quantity demanded of Y, but also a decrease in the quantity demanded of X, because both are demanded together. It is a case of joint demand. The cross-elasticity in the case of jointly-demanded commodities is negative.

Thus, cross elasticity can be positive, zero, or negative. The price elasticity is. normally speaking, negative in value. The cross elasticity is positive when X and Y are good substitutes (and infinity when X and Y are perfect substitutes); it is zero when X and Y are not related to each other or are perfectly independent of each other; it is negative when X and Y are complements. In the first case, a rise in the price of Y, assuming that the price of X remains constant, will cause an increase in the quantity demanded of X. In the second case, a rise or fall in the price of Y does not affect the quantity demanded of X at all. In the third case, a rise in the price of Y, assuming that the price of X remains constant, will cause a decrease in the quantity demanded of X.

The positive, zero, and negative cross elasticities can be illustrated diagrammatically.