Price Elasticity Calculator
This calculator computes price elasticity of demand using three established methods: arc (midpoint) elasticity, initial-base percent change elasticity, and point elasticity (requires dQ/dP). Elasticity is unitless and reports the proportional change in quantity demanded per proportional change in price.
Use the arc (midpoint) method for comparisons between two observations to avoid base-dependent biases. Use initial-base when the starting observation is your policy baseline. Use point elasticity when you have a continuous demand function or a measured derivative.
Recommended when comparing two distinct price/quantity observations to reduce bias from base selection; uses midpoint averages for percentage changes.
Inputs
Results
Arc Elasticity (midpoint)
-0.8182
| Output | Value | Unit |
|---|---|---|
| Arc Elasticity (midpoint) | -0.8182 | — |
Visualization
Methodology
Arc (midpoint) elasticity: ((Q2 - Q1) / ((Q2 + Q1)/2)) ÷ ((P2 - P1) / ((P2 + P1)/2)). This reduces sensitivity to which observation is chosen as the base.
Initial-base elasticity: ((Q2 - Q1) / Q1) ÷ ((P2 - P1) / P1). This is straightforward but dependent on the initial reference point.
Point elasticity: (dQ/dP) × (P / Q). Use when you can estimate or compute the instantaneous slope of the demand curve at a specific price and quantity.
Interpretation conventions: elasticity bigger than 1 (in absolute value) indicates elastic demand (quantity responds proportionally more than price); elasticity less than 1 indicates inelastic demand; negative sign reflects the usual inverse relationship between price and quantity for normal goods. Always report the sign and magnitude.
Calibration and data quality: ensure prices and quantities are comparable (same units, same time periods). For small sample changes or noisy data, prefer the arc method and complement the point estimate with confidence intervals from regression-based elasticity estimates.
Worked examples
Example — Arc method: P1 = 100, P2 = 80, Q1 = 1000, Q2 = 1200. Arc elasticity = [((1200-1000)/1100) ÷ ((80-100)/90)] ≈ [0.1818 ÷ (-0.2222)] ≈ -0.82 (inelastic).
Example — Point method: if dQ/dP = -15 at P = 80 and Q = 1200, point elasticity = -15 x (80 / 1200) = -1.0 (unit elastic at that point).
Further resources
External guidance
Expert Q&A
Which method should I use?
Use the arc (midpoint) method when comparing two discrete observations to avoid base-selection bias. Use initial-base if the first observation is the policy baseline you care about. Use point elasticity only when you have an estimated derivative (dQ/dP) or a demand function.
What does a negative elasticity mean?
A negative price elasticity is typical for ordinary (normal) goods: price rises lead to lower quantity demanded. Report both sign and magnitude; absolute value indicates responsiveness.
How precise are these estimates?
Point estimates are sensitive to data quality, measurement noise, and the time horizon. For rigorous analysis, estimate elasticity via regression with standard errors and report confidence intervals. Short-run elasticities tend to be smaller in magnitude than long-run estimates.
Can I use this for cross-price elasticity or income elasticity?
This tool focuses on own-price elasticity. For cross-price elasticity, replace quantity change in the numerator with change in demand for good A and price change with price of good B, and interpret sign (positive for substitutes, negative for complements). For income elasticity, substitute income for price in the denominator.
What are common pitfalls?
Mixing nominal and real prices, misaligned time periods, small sample percentage changes, and failure to account for confounding factors (promotions, seasonality) are common. Always check units and consider econometric controls where possible.
Are there regulatory or policy considerations to be aware of?
Yes. When using elasticity to model tax incidence, welfare changes, or price-cap regulation, document data sources and assumptions. Where available, cross-check estimates against published government statistics and peer-reviewed literature before using results for compliance or policy decisions.
Sources & citations
- MIT OpenCourseWare — Principles of Microeconomics (elasticity overview) — https://ocw.mit.edu
- National Institute of Standards and Technology (NIST) — https://www.nist.gov
- U.S. Bureau of Labor Statistics (data for prices and quantities) — https://www.bls.gov
- National Bureau of Economic Research (elasticity research) — https://www.nber.org