Cross elasticity of demand
Cross elasticity of demand (also called cross-price elasticity of demand or XED) is an economic measure that quantifies how the quantity demanded of one good responds to price changes in another good. The concept extends Alfred Marshall's foundational work on price elasticity, which he introduced in his 1890 treatise Principles of Economics[1]. Cross elasticity reveals whether products are substitutes, complements, or unrelated to each other in consumer purchasing decisions.
Formula and calculation
The cross elasticity of demand is calculated by dividing the percentage change in quantity demanded of Good A by the percentage change in price of Good B:
XED = (% change in quantity demanded of Good A) / (% change in price of Good B)
To compute the percentage changes:
- Percentage change in quantity = (new quantity - old quantity) / old quantity
- Percentage change in price = (new price - old price) / old price
The calculation assumes all other factors remain constant (ceteris paribus). This isolates the relationship between the two specific goods being analyzed.
Interpreting the coefficient
The sign and magnitude of the cross elasticity coefficient reveal the relationship between goods:
Positive cross elasticity indicates substitute goods. When the price of Good B rises and consumers buy more of Good A, these goods serve similar purposes. Higher positive values indicate closer substitution. For example, if tea prices increase by 10% and coffee demand rises by 2%, the cross elasticity equals +0.2, confirming these beverages substitute for each other.
Negative cross elasticity indicates complementary goods. When the price of Good B rises and consumers buy less of Good A, these goods are used together. A study found that when chip prices increased by 10% and salsa demand fell by 15%, the cross elasticity of -1.5 revealed their complementary relationship[2].
Zero cross elasticity indicates unrelated goods. Price changes in one product have no effect on demand for the other. Tennis racket prices have no bearing on bread consumption, for instance.
Historical development
Alfred Marshall introduced the concept of price elasticity of demand in Principles of Economics (1890). Marshall, who taught at Cambridge University from 1885 to 1908, developed elasticity to quantify how sensitive buyers are to price changes. His work integrated ideas about supply, demand, marginal utility, and production costs into a coherent framework[3].
Marshall also applied elasticity concepts to supply. Later economists extended the framework to examine relationships between different goods, leading to cross-price elasticity. The concept of income elasticity of demand similarly emerged from Marshall's foundational approach.
The Marshallian cross diagram, showing supply and demand curves intersecting at equilibrium, became a fundamental tool in economic analysis. While predecessors had used similar diagrams, Marshall's persuasive presentation made him the technique's most influential advocate.
Examples of substitute goods
Coca-Cola and Pepsi demonstrate positive cross elasticity. When Coca-Cola raises prices, some consumers switch to Pepsi. The products serve the same basic consumer need for cola-flavored soft drinks. Brand loyalty limits but does not eliminate substitution.
Butter and margarine show similar substitution patterns. Generic medications exhibit high cross elasticity with branded equivalents. Different airline carriers on the same route compete as close substitutes.
The magnitude of positive cross elasticity reflects substitutability degree. Perfect substitutes would have very high positive values. Weak substitutes show lower positive coefficients.
Examples of complementary goods
Hamburger buns and hamburger patties are classic complements. When patty prices rise, bun demand falls because consumers prepare fewer hamburgers overall. Printers and ink cartridges exhibit similar complementarity.
Automobiles and gasoline demonstrate complementary relationships. Higher fuel prices reduce demand for fuel-inefficient vehicles. Video game consoles and compatible games are purchased together, making them complements.
Stronger complementarity produces larger negative coefficients. Essential complements with no alternatives show more pronounced negative cross elasticity than goods with partial substitutes.
Business applications
Firms use cross elasticity analysis to develop pricing strategies. Products without close substitutes can command higher prices because consumers lack alternatives. Products facing many substitutes require competitive pricing to maintain market share.
Cross elasticity helps identify competitors. High positive coefficients between products indicate direct competition, even across different product categories. A streaming service might discover its main competitor is not another streaming platform but cable television.
Bundle pricing for complements reflects cross elasticity understanding. Companies selling printers often price ink cartridges as a profit center, knowing customers must purchase both products together.
Limitations of the measure
Cross elasticity assumes other factors remain constant. In practice, multiple prices and incomes change simultaneously. Isolating the effect of a single price change requires careful analysis.
Consumer preferences shift over time. Historical cross elasticity data may not predict future relationships accurately. New products can disrupt established substitution and complementarity patterns.
Measurement requires substantial sales data. Small firms may lack sufficient transaction records to calculate reliable coefficients. Market research can supplement internal data but adds cost.
| Infobox5 — recommended articles |
| Template:Infobox list5 wrap |
References
- Lipsey, R.G. & Chrystal, K.A. (2015). Economics. 13th ed. Oxford University Press.
- Marshall, A. (1890). Principles of Economics. Macmillan.
- Nicholson, W. & Snyder, C. (2012). Microeconomic Theory: Basic Principles and Extensions. 11th ed. South-Western.
- Pindyck, R.S. & Rubinfeld, D.L. (2018). Microeconomics. 9th ed. Pearson.
Footnotes
<references> <ref name="fn1">[1] Marshall, A. (1890). Principles of Economics introduced the concept of price elasticity of demand</ref> <ref name="fn2">[2] Complementary goods show negative cross elasticity as price increases in one reduce demand for the other</ref> <ref name="fn3">[3] Marshall taught economics at Cambridge University and systematized supply and demand analysis</ref> </references>