Cross elasticity of demand

Cross elasticity of demand (XED) is the responsiveness of demand for one product to a change in the price of another product. Many products are related, and XED indicates just how they are related.

The following equation enables XED to be calculated.


% change in (∆) quantity demanded of good A  % change in (∆) price of good B  


When XED is positive, the related goods are substitutes. For example, if the price of Coca Cola increases from 50p to 60p per can, and the demand for Pepsi Cola increases from 1m to 2m per year, the XED between the two products is:

+100/+20 = (+) 5 

The positive sign means that the two goods are substitutes, and because the coefficient is greater than one, they are regarded as close substitutes.


When XED is negative, the goods are complementary products. The equation is the same as for substitutes.

For example, if the price of Cinema Tickets increases from £5.00 to £7.50, and the demand for Popcorn decreases from 1000 tubs to 700, the XED between the two products will be:

-30/+50  = (-) 0.6 

The negative sign means that the two goods are complements, and the coefficient is less than one, indicating that they are not particularly complementary.

Why does a firm want to know XED?

  1. Knowing the XED of its own and other related products enables the firm to map out its market. Mapping allows a firm to calculate how many rivals it has, and how close they are. It also allows the firm to measure how important its complementary products are to its own products.

  2. This knowledge allows the firm to develop strategies to reduce its exposure to the risks associated with price changes by other firms, such as a rise in the price of a complement or a fall in the price of a substitute.

  3. Risks can be reduced in a number of ways, including adopting the following strategies:

    Horizontal integration

    Horizontal integration usually means merging with a rival, such as the merger of brewing giants Anheuser-Busch InBev and SABMiller  in 2015. Horizontal integration occurs when two or more firms producing similar products merge with each other, or where one takes over the other.

    Vertical integration

    Vertical integration means merging with a complement producer, such as a record producer merging with or taking over a record store, or radio station.

    Alliances and collusion

    Joint alliances with competitors can also take place, such as Sony-Ericsson combining resources to create mobile phones.

    Collusion is also a possibility. For example, firms may enter into price fixing agreements so that they avoid having to fight a price war. This is more likely to occur in oligopolostic markets, where there are only a few competitors.