In this article we will discuss about the formula for calculating the cross-elasticity of demand. Also learn about the use and application of the concept of cross-elasticity of demand.

The responsiveness of the demand for a good Y in response to a change in the price of another good X is called the cross-elasticity of demand for good Y with respect to the price of good X.

The formula for cross-elasticity of demand is given by:

Remember the following points about EC:

(i) The sign of EC, i.e., whether EC would be positive or negative, depends upon the relation­ship of substitutability or complementarity between the two goods (here X and Y). For exam­ple, if X and Y are substitutes (like tea and coffee), then the sign of EC would be positive.

For, in this case, if the price of X increases (decreases), then the consumers would buy less (more) of X and more of Y (less of y), i.e., if the (p.c.) change in the price of X is positive (negative), the (p.c.) change in the demand for Y would also be positive (negative). Consequently, EC would be positive.

On the other hand, if the goods X and Y are complements, then the sign of EC would be negative. For, in this case, if the price of X increases (decreases), the consumers would buy less (more) of X and also less (more) of Y, i.e., if the p.c. change in the price of X be positive (negative), the p.c. change in the demand for Y would be negative (positive). Consequently, here, EC would be negative.

(ii) If, in response to a change in the price of good X, demand for good Y does not change at all, then the value of EC would be zero (EC = 0). Here, to conclude that there is no relation between the two goods.

#### Use and Application of the Concept of Cross-Elasticity of Demand:

The concept of cross-elasticity of demand may be used to classify the relation between different goods.

It is already known:

(i) If the coefficient of cross-elasticity of demand (EC) between two goods be positive (EC > 0), then to understand that there is a relationship of substitution between the two goods.

(ii) If EC between any two goods is negative (EC < 0), then to understand that the two goods are complements to each other.

(iii) If EC between two goods is zero (EC = 0), then to conclude that the two goods are not related to each other, i.e., they are neither substitutes, nor are they complements.

The concept of cross-elasticity of demand may also be used in the process of decision-­making of business concerns. There are large business concerns that produce goods which are substitutes of, or complements to each other. For example, Gillette produces both razors and razor blades. These two goods are complements. Again, Ford produces motor cars of different brands that are (close) substitutes of each other.

When a business concern produces related goods, the pricing of one of the goods may influence the demand for some other good. For example, if Gillette reduces the price of its razor, then, along with an increase in the demand for razor, demand for razor blades would also increase, since these two goods are complements to each other.

Again, if Ford reduces the price of one of its brands of motor car, then the demand for that brand will increase, but the demand for some other Ford brand(s) may decrease, since the different brands are (close) substitutes of each other. In view of this, it may be said that while setting or changing the prices of its goods, a business firm should have a clear idea of the cross-elasticity of demand be­tween its goods.

The concept of cross-elasticity of demand may also help us to determine the borderline between different industries. Sometimes, it seems to be very difficult to determine what goods belong to which industries. However, the concept of cross-elasticity may help us to solve such a problem.

The goods for which the cross-elasticity of demand is obtained to be very high and positive should be classified as close substitute products belonging to a particular industry. On the other hand, there may be some goods for which the value of Ec is obtained to be negative or it is obtained to be positive and small. These goods cannot be considered to be the products of the same industry.