What it means
When the price of one product moves, customers often change what they buy of other products. If coffee becomes more expensive, some drinkers may switch to tea, so demand for tea rises.
Cross elasticity captures that relationship in a single number. For substitutes, such as tea and coffee, the cross elasticity is positive: a price rise in one increases demand for the other.
For complements, such as printers and ink cartridges, it is negative: when the printer price rises, fewer printers are sold and demand for ink falls. A value near zero means the products are largely unrelated.
The size of the number matters too. A high positive figure means the products are close substitutes and customers switch easily, which gives a business little room to raise prices without losing sales.
A low figure suggests the products are not close competitors, so a price change has little effect on the other. Managers use the measure for pricing, product planning and competitor analysis.
A company that sells both a premium and a budget version of a product can test whether a price change in one pulls customers from the other, a problem known as cannibalisation. It is also useful when defining a market for competition or merger analysis.
If two products have a high cross elasticity, regulators are likely to treat them as competing in the same market. Estimates depend on data and conditions, and the figure can change with income, tastes and time horizon.
Treat it as a guide to relationships rather than a precise law.
In practice
Real-world examples.
Example
A supermarket raises the price of its own-brand butter by 8%, and sales of margarine increase by 6%. The cross elasticity of 0.75 suggests the products are reasonably close substitutes. The supermarket uses the figure to decide whether a butter promotion would hurt its margarine sales.
Example
A games console maker cuts the console price by 15%, and sales of its games rise by 9%. The cross elasticity is negative at -0.6 because the price fall of the console increases demand for the complementary games. The maker concludes that a lower console price is worthwhile because the extra game sales are very profitable.
Example
A car manufacturer considers raising the price of its mid-range model. It models the effect on its compact car and finds a strong positive link, so it prepares for some customers to switch down in size. Management plans an advertising push for the compact car to retain those customers within the brand.
Formula
Calculation
Cross elasticity of demand = % change in quantity demanded of Product A / % change in price of Product B
Worked example: the price of coffee beans (Product B) rises by 10%. As a result, sales of tea (Product A) rise from 20,000 to 20,800 boxes per month.
% change in quantity of tea = (20,800 - 20,000) / 20,000 x 100 = 4%.
Cross elasticity = 4% / 10% = 0.4.
The positive value of 0.4 shows that tea and coffee are substitutes, although the relationship is fairly weak because a 10% price rise in coffee shifts only 4% more demand to tea.Case study
Seen in the real world.
Sunvale Beverages is a fictional drinks company, and this story is illustrative only. It sold both a premium sparkling water and a cheaper still water, and wanted to raise the price of the premium product by 10%.
The analyst estimated cross elasticity between the two at about 0.5, meaning a 10% rise in the premium price would increase sales of still water by roughly 5%. Because still water had a lower profit margin, the company worried that the shift would reduce overall profit.
After testing several pricing scenarios, management raised the premium price by only 5% and ran a promotion on the premium product to keep customers loyal. The analyst said the cross elasticity estimate prevented a pricing decision that would have looked good on one product but poorly across the range. Six months later, sales of both waters held steady and the company recorded a higher total profit than either of the original proposals would have delivered.
Watch out
Common mistakes.
- Mixing up the signs, when a positive figure means substitutes and a negative figure means complements. A quick memory aid is that complements move in opposite directions, like printers and ink.
- Treating a single estimate as permanent, when customer behaviour changes with income, fashion and competition. Re-estimate the figure whenever competitors launch new products or prices change significantly.
- Confusing cross elasticity with price elasticity, which measures the response of a product's own demand to its own price. Own-price elasticity looks at one product, while cross elasticity looks across two.
Questions
People also ask.
What does a value of zero mean?
The products are essentially unrelated, so a price change in one has no meaningful effect on demand for the other. Many pairs of everyday products, such as bread and bicycles, would show a cross elasticity near zero.
How is it used in pricing?
Managers use it to predict how a price change will shift demand between their own products and competitors' products. This avoids setting a price that wins customers from a rival but only by taking them from your own other products.
Why do regulators care?
A high cross elasticity suggests the products compete, which helps define the market in a merger or competition review. Close substitutes are treated as part of the same market, so a merger between them draws more scrutiny.
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