Cross-Price Elasticity Calculator
Using the midpoint method, compute how the demand for X responds to a price change of Y — substitutes or complements.
Input Data
Results
At a glance:Cross-price elasticity Exy (midpoint) = (ΔQx / avg Qx) / (ΔPy / avg Py). Exy > 0 → substitutes (Y dearer, X demand up); Exy < 0 → complements (Y dearer, X demand down); ≈0 → unrelated. Larger |Exy| = stronger link. WARNING: arc elasticity over the range; sign matters more than size; other factors may move demand. Education, not advice.
Formula
Exy = (% change in Qx) / (% change in Py), each % computed by the midpoint method: ΔQ/avg(Q), ΔP/avg(P).
$$E_{xy} = \dfrac{\Delta Q_x / \bar{Q_x}}{\Delta P_y / \bar{P_y}}$$How to Use
- Enter X's quantity before and after Y's price change.
- Enter Y's price before and after.
- View Exy — positive = substitutes, negative = complements.
FAQ
What does the sign of cross elasticity mean?
Positive = substitutes: Y dearer pushes consumers to X (coffee & tea). Negative = complements: Y dearer cuts X demand too (cars & petrol). Near zero = unrelated. For judging the relationship, the sign matters more than the number.
What does the magnitude tell us?
Larger absolute value = stronger linkage. A strong substitute (similar brands) has high Exy — a rival's small price cut steals many of your customers; weak substitutes/complements sit near zero. Firms use it to gauge competitor pricing impact and bundle pricing.
What is it used for?
Competition analysis (how much a rival's cut steals), bundle pricing (use a low-margin lead item to drive high-margin accessories), and antitrust/market definition (high cross elasticity = same relevant market). It reveals demand linkages between goods.
Why the midpoint method instead of start-value percentages?
The midpoint method gives direction-symmetric, unique results. Traditional 'change / start' percentages are asymmetric: 20→25 is +25%, but 25→20 is -20% — same move, different numbers, so elasticity differs by direction. Midpoint uses the average of start and end as denominator, so 20↔25 both give 5/22.5 ≈ 22.22%, symmetric and unique. This suits arc elasticity over a range. This tool applies midpoint to both quantity and price, so swapping initial/final yields the same absolute value.
How does it differ from own-price elasticity?
Both measure responsiveness to price, but own-price elasticity looks at a good's OWN price effect on its OWN demand (usually negative, for pricing/ revenue); cross-price elasticity looks at good Y's price effect on good X's demand, revealing the relationship between two goods. The sign of cross elasticity is economically meaningful (positive = substitutes, negative = complements), whereas own-price mainly uses the absolute value. Own answers 'if this good's price rises, does it still sell'; cross answers 'if another good's price rises, how does this good's sales move — friend or foe'. Use both for competition and portfolio decisions.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.