Cross Price Elasticity Calculator

What is Cross Price Elasticity of Demand?

The Cross Price Elasticity of Demand ($E_{xy}$) measures how responsive the quantity demanded of one good (Good Y) is to a change in the price of another good (Good X). It helps economists and businesses evaluate whether two products are substitutes, complements, or completely independent.

Formula for Cross Price Elasticity

The fundamental formula for cross price elasticity is:

$$E_{xy} = \frac{\% \text{ Change in Quantity Demanded of Good Y}}{\% \text{ Change in Price of Good X}}$$

When calculating elasticity from initial and final prices and quantities ($P_{x1}, P_{x2}, Q_{y1}, Q_{y2}$), the Midpoint (Arc) Formula is recommended because it provides consistent results regardless of whether price increases or decreases:

$$E_{xy} = \frac{(Q_{y2} - Q_{y1}) / \left(\frac{Q_{y1} + Q_{y2}}{2}\right)}{(P_{x2} - P_{x1}) / \left(\frac{P_{x1} + P_{x2}}{2}\right)}$$

Interpreting the Results

• Positive Cross Elasticity ($E_{xy} > 0$): Good X and Good Y are substitute goods. For example, if the price of coffee increases, the demand for tea increases as consumers switch to the cheaper alternative.
• Negative Cross Elasticity ($E_{xy} < 0$): Good X and Good Y are complementary goods. For instance, if the price of printers goes up, the demand for printer ink cartridges decreases because fewer printers are purchased.
• Zero Cross Elasticity ($E_{xy} = 0$): Good X and Good Y are unrelated (independent) goods. A change in the price of shoes has no measurable effect on the demand for apples.