Price Elasticity of Demand Calculator

What price elasticity measures

Price elasticity of demand measures how strongly the quantity sold responds to a change in price. It is defined as the percentage change in quantity divided by the percentage change in price:

ε = (ΔQ / Q) ÷ (ΔP / P)

Because demand usually falls when price rises, elasticity is normally negative. An elasticity of −2 means that a 1% price increase reduces volume by about 2%; an elasticity of −0.5 means volume falls by only 0.5%.

• Elastic demand (|ε| > 1): volume reacts more than proportionally. Price increases reduce revenue, price cuts increase it.
• Inelastic demand (|ε| < 1): volume reacts less than proportionally. Price increases raise revenue.
• Unit elastic (|ε| = 1): revenue does not change with small price changes; this is where revenue is maximised.

The cross-price elasticity measures how a product’s demand responds to a competitor’s or another product’s price. A positive value means the products are substitutes (when the competitor raises its price, your sales rise); a negative value means they are complements.

Estimating elasticity with a log-log model

The standard way to estimate elasticity from sales data is a log-log regression:

ln(Q) = a + ε ln(P) + γ ln(P_competitor) + δ₁ promo + … + error

In this constant-elasticity model, the coefficient on log price is the elasticity, and the coefficient on log competitor price is the cross-price elasticity. Controls such as promotions, seasonality, distribution or advertising enter linearly so that their influence is not mistaken for a price effect. The tool reports each coefficient with its standard error, t-test, p-value and 95% confidence interval, so you can see how precisely the elasticity is estimated.

The alternative linear model (Q = a + bP + …) has a slope rather than an elasticity; the tool converts it to an elasticity at the mean price and mean quantity, ε = b × P̄ / Q̄. In a linear model elasticity changes along the curve, becoming more elastic at higher prices, which is sometimes more realistic over wide price ranges.

From elasticity to pricing decisions

With a constant elasticity, a price change of Δ (for example +10%) changes quantity by (1 + Δ)^ε − 1 and revenue by (1 + Δ)^1+ε − 1. The table of price changes shows these effects for ±5%, ±10% and ±20%, and, if you enter a unit cost, the change in gross profit as well.

When demand is elastic and you know the unit cost c, the profit-maximising price in the constant-elasticity model follows the Lerner rule: P* = c × ε / (1 + ε). With ε = −2, for example, the optimal price is twice the unit cost (a 100% markup); with ε = −4 it is 1.33 times cost. When demand is inelastic (|ε| ≤ 1), the constant-elasticity model implies that raising the price always increases profit, so there is no finite optimum within the model: in reality elasticity rises at higher prices, which is why you should not extrapolate far beyond the observed range. In the linear model, the tool also gives the revenue-maximising price and, with a cost, the profit-maximising price.

Worked example with the built-in data

The example contains 156 weeks of unit sales with the product’s price, a competitor’s price and a promotion indicator. The log-log model (R² = .82) estimates an own-price elasticity of −1.74 (95% CI −1.89 to −1.59): demand is elastic, so price cuts raise revenue. A 10% price increase would cut volume by about 15% and revenue by about 7%. The cross-price elasticity with the competitor’s price is +0.67, so the two products are substitutes: a 10% competitor price increase lifts sales by about 7%. Promotion weeks sell about 23% more (e^0.21 − 1). With a unit cost of 2.20, the Lerner rule gives a profit-maximising price of about 5.19, slightly above the average observed price of 4.57.

Data for elasticity estimation

• One row per period (week or month), store-week, or product-period, with price and quantity.
• Price must vary. If price never changed, elasticity cannot be estimated; promotions, regional price differences or planned price tests provide the variation.
• Use the price customers actually paid (net of discounts), not list price.
• For the log-log model, prices and quantities must be positive; drop periods with zero sales or use the linear model.
• About 50 or more observations give reasonably precise estimates; 2–3 years of weekly data is common.

Pitfalls: endogeneity and omitted variables

The biggest risk in estimating elasticity from historical data is endogeneity: prices are often set in response to demand. If a retailer raises prices in peak season when demand is high anyway, the data show high prices together with high sales, and the estimated elasticity is biased towards zero or even positive. Solutions include controlling for seasonality and demand drivers, using price variation that is unrelated to demand (cost changes, planned experiments), or instrumental variables, available in this site’s 2SLS tool, for example with input costs as instruments.

Omitted variables such as advertising, distribution changes, out-of-stocks or competitor promotions also bias elasticity if they move together with price. Include them as controls when you have them.

Finally, distinguish short-run from long-run effects: a temporary promotion causes stockpiling and brand switching, so promotional elasticities are usually larger than the response to a permanent price change.

Typical elasticity values

Meta-analyses of consumer goods find an average price elasticity of about −2.6 (Bijmolt, Van Heerde and Pieters, 2005), with large variation across categories, brands and countries. Necessities and products without close substitutes are inelastic; discretionary items, products with many substitutes and brands in competitive categories are elastic. Elasticity is also higher in the long run, as consumers find alternatives.

Reporting

Report the model form, the sample, the elasticity with its 95% confidence interval, model fit, controls and any cross-price elasticity. Example: “A log-log demand model (n = 156 weeks, R² = .816), controlling for promotions and competitor price, estimated an own-price elasticity of −1.74, 95% CI [−1.89, −1.59], and a cross-price elasticity of 0.67.”

Glossary of pricing terms

• Own-price elasticity: the % change in a product’s quantity for a 1% change in its own price.
• Cross-price elasticity: the % change in quantity for a 1% change in another product’s price.
• Arc elasticity: elasticity measured between two price points using their averages.
• Point elasticity: elasticity at a single point on the demand curve, for example at the mean price.
• Lerner index: (P − c) / P, the markup as a share of price; at the profit optimum it equals −1/ε.
• Endogeneity: correlation between price and unobserved demand shocks, which biases simple estimates.
• Instrumental variable: a variable that shifts price but not demand directly, such as an input cost, used to remove endogeneity bias.
• Promotional elasticity: the short-run response to temporary price cuts, usually larger than the response to permanent changes.

Key references: Bijmolt, Van Heerde and Pieters (2005), Journal of Marketing Research; Tellis (1988), Journal of Marketing Research; Nagle and Müller (2018), The Strategy and Tactics of Pricing.