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1 Price Elasticity of Demand

Learn how price elasticity measures buyers’ percentage response to price changes, how to calculate it with the midpoint method, and how to interpret the result.

Meaning and classification

measures the percentage responsiveness of quantity demanded to a change in price. It is calculated as:

Ed=% change in quantity demanded% change in priceE_d = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}

By the law of demand, price and quantity demanded usually move in opposite directions, so signed elasticity is usually negative. Economists commonly use its absolute value, ∣Ed∣|E_d|, to classify responsiveness as a positive number.

Calculating with the

A basic percentage change uses the initial value as its base:

% change=new value−initial valueinitial value×100\%\text{ change} = \frac{\text{new value} - \text{initial value}}{\text{initial value}} \times 100

This base can produce different elasticity results depending on whether the change is measured forward or backward. The avoids this by using the average of the two values as the base:

% change in quantity demanded=Q2−Q1(Q1+Q2)/2×100\%\text{ change in quantity demanded} = \frac{Q_2-Q_1}{(Q_1+Q_2)/2} \times 100
% change in price=P2−P1(P1+P2)/2×100\%\text{ change in price} = \frac{P_2-P_1}{(P_1+P_2)/2} \times 100

Divide the percentage change in quantity demanded by the percentage change in price. Since both changes use midpoint values, the result is the same when moving between the same two points in either direction.

Worked example

Suppose price rises from $10 to $12, while quantity demanded falls from 100100 to 8080 units. The midpoint percentage changes are:

%ΔQd=80−100(80+100)/2×100=−2090×100≈−22.2%\%\Delta Q_d = \frac{80-100}{(80+100)/2} \times 100 = \frac{-20}{90} \times 100 \approx -22.2\%
%ΔP=12−10(12+10)/2×100=211×100≈18.2%\%\Delta P = \frac{12-10}{(12+10)/2} \times 100 = \frac{2}{11} \times 100 \approx 18.2\%

Therefore:

Ed=−22.2%18.2%≈−1.22E_d = \frac{-22.2\%}{18.2\%} \approx -1.22

The signed result is about −1.22-1.22, and its absolute value is 1.221.22, which is greater than 11. Demand is elastic over this price range: quantity demanded changed by a greater percentage than price, indicating that buyers were relatively responsive.

Interpreting the measure

Elasticity compares percentage changes, not changes in units or dollars. A change of 1010 units can be a large or small percentage depending on the starting quantity; similarly, the significance of a dollar change in price depends on the starting price. Elasticity is therefore distinct from the slope of a demand curve, which relates changes in quantity and price in their original units.

An elasticity is calculated for a particular point or range of a demand relationship. It describes the response over that point or range, but does not by itself explain why buyers respond as they do.