Calculating price elasticity of demand and its variation along a demand curve

Price elasticity of demand (PED) measures how much the quantity demanded of a good changes in response to a change in its price. For a straight-line demand curve, PED does not stay the same but changes constantly as you move along the curve.

Formula for price elasticity of demand

$\text{PED}=\frac{\mathrm{\Delta }\text{Q}}{\mathrm{\Delta }\text{P}}\times \frac{{\text{P}}_1}{{\text{Q}}_1}$

Where:

• ΔQ = Change in quantity demanded
• ΔP = Change in price
• P₁ = Original price
• Q₁ = Original quantity demanded

This formula combines the inverse of the demand curve's slope (ΔQ/ΔP) with the ratio of the original price to quantity (P₁/Q₁). While the slope of a straight-line demand curve remains constant, the P₁/Q₁ ratio changes at different points, causing PED to vary.

PED is not the same as the slope of the demand curve. Even though the slope is fixed for a linear curve, PED adjusts based on the specific price and quantity levels.

Reasons why price elasticity of demand varies along a straight-line demand curve

On a negatively sloped straight-line demand curve, PED changes because the ratio of price to quantity (P/Q) alters as you move along it. At higher prices and lower quantities, this ratio is larger, making PED higher. At lower prices and higher quantities, the ratio is smaller, resulting in lower PED.

Factors causing variation in price elasticity of demand

• Higher prices and lower quantities - Demand tends to be more elastic here because consumers react more strongly to price changes when costs are already high.
• Lower prices and higher quantities - Demand is more inelastic in this area since buyers are less sensitive to changes when prices are already low.
• Consumer responsiveness - People are more likely to adjust their buying habits significantly if an expensive item changes in price, compared to a cheap one.

This variation happens even though the demand curve's slope is constant, as PED depends on both the slope and the changing P/Q ratio.

The range of price elasticity of demand values on a demand curve

Along a straight-line demand curve with a negative slope, PED takes on a wide range of values, from very high to zero, depending on the position on the curve.

Key price elasticity of demand values at different points

• At the y-axis intercept (highest price, zero quantity) - PED approaches infinity, meaning demand is perfectly elastic.
• At the x-axis intercept (zero price, highest quantity) - PED equals zero, indicating perfectly inelastic demand.
• At the midpoint of the curve - PED equals 1, showing unitary elasticity where percentage changes in price and quantity are equal.

These values show how PED decreases steadily from the top-left to the bottom-right of the demand curve.

Elastic and inelastic regions on the demand curve

A straight-line demand curve can be divided into regions based on PED values, which help explain how responsive demand is in different parts.

Regions of elasticity on a linear demand curve

• Upper half (above the midpoint) - Demand is price elastic (PED > 1), where quantity demanded changes by a larger percentage than the price change.
• Lower half (below the midpoint) - Demand is price inelastic (0 < PED < 1), where quantity demanded changes by a smaller percentage than the price change.