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Elasticity Midpoint Formula Calculator

Calculates elasticity using the average of start and end points.

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Midpoint Elast.

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Overview

The Elasticity Midpoint Formula, also known as Arc Elasticity, calculates the responsiveness of quantity demanded to changes in price by using the average values of both variables as the base. This method resolves the directionality problem where calculating percentage changes from a starting point vs. an ending point yields different results.

Symbols

Variables

E = Midpoint Elast., P_1 = Price 1, P_2 = Price 2, Q_1 = Quantity 1, Q_2 = Quantity 2

Midpoint Elast.
Price 1
Price 2
Quantity 1
Quantity 2

Apply it well

When To Use

When to use: This formula should be applied when measuring elasticity over a specific segment of the demand or supply curve rather than at a single point. It is the preferred method in economics textbooks for calculating price elasticity between two price-quantity pairs to ensure consistency regardless of whether the price is increasing or decreasing.

Why it matters: It allows businesses to accurately predict how pricing adjustments will impact total revenue and consumer behavior without the bias of the initial starting value. For policymakers, it provides a stable metric to evaluate the likely effects of taxes or subsidies on market equilibrium.

Avoid these traps

Common Mistakes

  • Using only the starting point as the denominator.

One free problem

Practice Problem

A specialty coffee shop increases the price of a coffee bean bag from 12.00. Consequently, the quantity demanded by local customers drops from 100 bags to 80 bags per week. Calculate the price elasticity of demand using the midpoint formula.

Price 110 £
Price 212 £
Quantity 1100
Quantity 280

Solve for:

Hint: First find the average quantity (90) and average price (11) before calculating the percentage changes.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Principles of Economics by N. Gregory Mankiw
  2. Economics by Campbell R. McConnell, Stanley L. Brue, and Sean M. Flynn
  3. Wikipedia: Price elasticity of demand
  4. Mankiw, N. Gregory. Principles of Economics. 9th ed. Cengage Learning, 2021.
  5. McConnell, Campbell R., Stanley L. Brue, and Sean M. Flynn. Economics: Principles, Problems, and Policies. 22nd ed.
  6. Samuelson, Paul A., and William D. Nordhaus. Economics. 19th ed. McGraw-Hill Education, 2010.
  7. N. Gregory Mankiw, Principles of Economics