Cross-Price Elasticity of Demand Calculator: Are Two Goods Substitutes or Complements?
Find the cross-price elasticity of demand with the midpoint or simple % method, see if two goods are substitutes or complements, and forecast demand.
How it works
Cross-price elasticity (E) = % change in quantity demanded of X ÷ % change in price of Y · Midpoint: E = [(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)] ÷ [(P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2)] · Simple: E = [(Q₂ − Q₁) ÷ Q₁] ÷ [(P₂ − P₁) ÷ P₁] · E > 0 substitutes, E < 0 complements, E ≈ 0 unrelated
Cross-price elasticity measures how demand for one good (X) reacts when the price of a different good (Y) changes. Divide the percentage change in the quantity of X by the percentage change in the price of Y. The sign tells you how the two goods are related. A positive value means they are substitutes: when Y gets dearer, people switch to X (coffee and tea, two cola brands). A negative value means they are complements used together: when Y gets dearer, people buy less of both (printers and ink, cars and gasoline). A value near zero means the goods are unrelated. The size tells you how strong the link is: above 1 in absolute terms, demand for X moves proportionally more than the price of Y. The midpoint (arc) method divides each change by the average of the before and after values, so you get the same answer whether the price rose or fell. The simple method divides by the “before” values; it is easier to explain but gives a different number for the same two observations, and this calculator shows both side by side. If you already know the percentage changes, for example from a market report, choose “I know the % changes”. Under More options you can enter the price of X to see the revenue effect, and a planned price change of Y to forecast demand for X. This differs from the own-price elasticity calculator, which measures how demand for a good responds to its own price. The result is only meaningful when other demand drivers stayed the same between the two periods.
Worked example
Coffee (Y) goes from $4.00 to $4.50 and weekly tea sales (X) rise from 1,000 to 1,100 cups. With the midpoint method, the quantity change is 100 ÷ 1,050 = +9.5238% and the price change is $0.50 ÷ $4.25 = +11.7647%, so E = 9.5238 ÷ 11.7647 = 0.810. The value is positive, so coffee and tea are substitutes, and below 1, so the link is weak (inelastic). The simple % method on the same data gives 10% ÷ 12.5% = 0.800. If coffee rises another 5%, tea demand is forecast to rise about 0.810 × 5% = +4.05%, to roughly 1,145 cups.
Sources: OpenStax Principles of Economics 3e, 5.4 Elasticity in areas other than price · Omni Calculator: Cross price elasticity (Coca-Cola and Pepsi example) · WallStreetMojo: Cross price elasticity of demand (midpoint formula and examples)
Frequently asked questions
What does a positive cross-price elasticity mean?
The goods are substitutes. When the price of one rises, buyers switch to the other, so its demand rises. Butter and margarine, or two brands of soda, are typical examples. The larger the value, the closer the substitutes.
What does a negative cross-price elasticity mean?
The goods are complements that are used together. A higher price for one reduces demand for both, as with game consoles and games or cars and gasoline. For example, if gasoline rises 50% and car purchases fall 10%, E = −10 ÷ 50 = −0.2.
Should I use the midpoint or the simple percentage formula?
Use the midpoint (arc) formula for two observed points, because it gives the same answer whether the price went up or down. The simple formula is fine for small changes or when your textbook asks for it. For large changes the two can differ noticeably.
What is the difference between cross-price elasticity and price elasticity of demand?
Own-price elasticity compares a good’s demand with its own price and is almost always negative. Cross-price elasticity compares a good’s demand with the price of another good, and its sign can be positive or negative depending on whether they are substitutes or complements.
How do businesses use cross-price elasticity?
To spot competing products, plan prices across a product range, and predict how a competitor’s price cut will affect sales. Competition authorities also use it to decide which products belong to the same market.
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This calculator is for educational purposes. Double-check important results before acting on them.