2.16:
Elasticity of a Linear Demand Curve
The price elasticity of demand for any good can be expressed as the change in quantity demanded associated with a change in price multiplied by the ratio of price to quantity.
Consider a linear demand curve with a constant slope, which means that the delta P over delta Q ratio remains constant.
At the vertical intercept, the quantity demanded is zero. This indicates an infinite elasticity, showing a perfectly elastic demand.
Moving down the curve, the price decreases, and the quantity demanded increases. This reduces the P by Q ratio, leading to a decrease in the magnitude of elasticity.
Between points A and B, the percentage change in price is less than the percentage change in quantity demanded. This results in an elasticity greater than one, indicating a region of elastic demand.
At point B, the midpoint, the elasticity is exactly one. This indicates a unitary elastic demand.
Beyond the midpoint, the percentage change in price is more than the percentage change in quantity demanded. This leads to reduced elasticity, indicating a region of inelastic demand.
At the horizontal intercept, where price equals zero, the elasticity is zero, indicating perfectly inelastic demand.
2.16 Elasticity of a Linear Demand Curve
A linear demand curve, which plots the relationship between price and quantity demanded, is a straight line, but the elasticity along this line is not constant. This means that the responsiveness of consumers to price changes varies at different points on the line.
Vertical Intercept: Quantity demanded is zero; elasticity theoretically approaches infinity due to division by zero, making it not directly calculable.
Elastic Demand Zone: Between the vertical intercept and the midpoint, demand is elastic (PED > 1), indicating high sensitivity to price changes. Consumers readily adjust their consumption based on price, especially for goods with substitutes.
Midpoint (Unitary Elastic Demand): At the midpoint, elasticity is exactly 1, showing a balanced, proportionate change in price and quantity demanded. This represents equal responsiveness to price changes.
Inelastic Demand Zone: Beyond the midpoint towards the horizontal intercept, demand becomes inelastic (PED < 1). Consumers show less sensitivity to price changes, typical for necessities or goods with fewer substitutes.
Horizontal Intercept: Approaching zero price, the curve suggests a maximum quantity demanded. Elasticity is very low or approaches zero, indicating minimal increases in demand despite further price reductions, representing a theoretical boundary condition.