Define price elasticity of demand with its types. [5]

Price Elasticity of Demand

The price elasticity of demand (PED) measures the responsiveness of the quantity demanded of a good to a change in its price.
It is defined as the ratio of the percentage change in quantity demanded to the percentage change in price:

$$E_d=\frac{\%\Delta Q_d}{\%\Delta P}=\frac{\frac{Q_2-Q_1}{Q_1}}{\frac{P_2-P_1}{P_1}}$$

Because of the law of demand, $E_d$ is normally negative. Economists usually report its absolute value and classify the demand as elastic, inelastic, or unitary.

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Types of Price Elasticity of Demand

Numerical Illustration

Suppose the price of a commodity falls from Rs 10 to Rs 8 and the quantity demanded rises from 50 units to 60 units.

1. Compute percentage changes
   $$\%\Delta P=\frac{8-10}{10}\times 100=-20\%$$ $$\%\Delta Q_d=\frac{60-50}{50}\times 100=20\%$$

2. Compute elasticity
   $$E_d=\frac{20\%}{-20\%}=-1.0$$

3. Take absolute value for classification
   $$|E_d|=1.0$$

Result: The demand is unit‑elastic.

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Graphical Representation

The slope of the demand curve determines the elasticity at any point. Where the curve is flatter, elasticity is greater than one (elastic); where it is steeper, elasticity is less than one (inelastic). The point where the slope yields an elasticity of exactly one is the unit‑elastic point.

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Summary of Key Points

• Definition: $E_d=\frac{\%\Delta Q_d}{\%\Delta P}$.
• Sign: Negative due to inverse relationship between price and quantity demanded.
• Classification: Elastic (>1), Inelastic (<1), Unit‑elastic (=1), Perfectly elastic (∞), Perfectly inelastic (0).
• Economic Implication:
  • Elastic demand → price changes significantly affect revenue.
  • Inelastic demand → price changes have limited impact on revenue.
  • Unit‑elastic demand → revenue remains unchanged when price changes.

These concepts are essential for pricing decisions, tax incidence analysis, and understanding consumer behavior in the market.