# CROSS-PRICE ELASTICITY

The sales volume of one product may be influenced by the price of either substitute or complementary products. Cross-price elasticity of demand provides a means to quantify that type of influence. It is defined as the ratio of the percentage change in sales of one product to the percentage change in price of another product. The relevant arc (Ec) and point (ec) cross-price elasticities are determined as follows:

where the alphabetic subscripts differentiate between the two products involved. A negative coefficient of cross-price elasticity implies that a decrease in the price of product A results in an increase in sales of product B, or vice versa, we can conclude that the products are complementary to one another (such as DVD players and DVDs). Thus, when the coefficient of cross-price elasticity for two products is negative, the products are classified as complements.

A similar line of reasoning leads to the conclusion that if the cross-price elasticity is positive, the products are substitutes. For example, an increase in the price of sugar would cause less sugar to be purchased, but would increase the sale of sugar substitutes. When we calculate the cross-price elasticity for this case, both the numerator and the denominator (% change in Q of sugar substitutes and % change in P of sugar, respectively) would have the same sign, and the coefficient would be positive.

If two goods are unrelated, a change in the price of one will not affect the sales of the other. The numerator of the cross-price elasticity ratio would be 0, and thus the coefficient of cross-price elasticity would be 0. In this case, the two commodities would be defined as independent. For example, consider the expected effect that a 10% increase in the price of eggs would have on the quantity of electronic calculator sales.

These relationships can be summarized as follows:

If ec or Ec > 0, goods are substitutes

If ec or Ec < 0, goods are complementary

If ec or Ec = 0, goods are independent

Cross price elasticities may not always be symmetrical. For example, consider two dailies, Times of India and the Hindustan Times competing in the Delhi market. Most analysts will agree that the two products are substitutes i.e. the cross price elasticity is positive. However, there is no reason to believe that the change in demand for the Times of India following a one percent change in the price of Hindustan times will be equal to the change in demand for Hindustan Times following a one per cent change in the price of the Times of India.

Many large corporations produce several related products. Maruti produces many varieties of automobiles, Hindustan Lever produces many brands of soap and Gillette produces much type of razors. If Maruti reduces the price of it’s Alto model, sales of its old warhorse the Maruti 800 may decline. When a company sells related products, knowledge of cross elasticities can aid decision makers in assessing such impacts.

THE EFFECT OF ADVERTISING ON DEMAND

Advertising influences our attitudes towards the product or service being promoted. In most cases, the intent of a firm’s advertising is to stimulate sales of a particular product or product line. When Pepsi Cola Corporation decides to sponsor a television show or cricket match it hopes that doing so will increase the sales of its products. Such product promotions have their impact on consumers through tastes and preferences.

In addition to shifting the demand function to the right, advertising may have the effect of making it somewhat more steep. The reason for this is that advertisements can create stronger consumer brand preferences, thus making consumers less sensitive to price changes for that product. This means that one effect of advertising can be to make the demand for a firm’s product more price inelastic. To the extent that this is true, management has an increased ability to raise price without losing as many sales as would have been lost otherwise. We have seen that raising the product’s price will increase total revenue for the firm if demand is inelastic.