Economics · Ch 8 — Theory of Consumer Behaviour

Elasticity of Demand

8.6

Elasticity of Demand

The Concept of Price Elasticity of Demand

The law of demand tells us that price and quantity demanded move in opposite directions. But it does not tell us how much quantity changes when price changes. For some goods, a small price rise causes a huge drop in demand. For others, even a large price change barely affects how much people buy. This difference in responsiveness is captured by price elasticity of demand.

Price elasticity of demand ( $e_D$ ) is defined as the percentage change in quantity demanded divided by the percentage change in the price of the good.

e_D = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}

In algebraic terms, if $\Delta Q$ is the change in quantity demanded and $\Delta P$ is the change in price, we can write:

e_D = \frac{\frac{\Delta Q}{Q} \times 100}{\frac{\Delta P}{P} \times 100} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}

Here, $P$ and $Q$ are the original price and quantity, $\Delta P$ is the change in price, and $\Delta Q$ is the corresponding change in quantity demanded.

Watch out

Since demand curves slope downward, $\Delta Q$ and $\Delta P$ have opposite signs. This makes $e_D$ a negative number. For simplicity, economists usually refer to the absolute value of elasticity. When we say "elasticity is 0.5", we mean $|e_D| = 0.5$ .

A Worked Example: Elasticity of Demand for Bananas

Note

Example 2.2

An individual buys 15 bananas when the price is Rs 5 per banana. When the price rises to Rs 7 per banana, she reduces her purchase to 12 bananas. So the old price is $P_1 = 5$ with old quantity $Q_1 = 15$ , and the new price is $P_2 = 7$ with new quantity $Q_2 = 12$ .

Step 1 — percentage change in quantity demanded:

$\frac{Q_2 - Q_1}{Q_1}\times 100 = \frac{12 - 15}{15}\times 100 = -20\%$

Step 2 — percentage change in price:

$\frac{P_2 - P_1}{P_1}\times 100 = \frac{7 - 5}{5}\times 100 = 40\%$

Step 3 — price elasticity of demand:

$e_D = \frac{-20\%}{40\%} = -0.5, \qquad |e_D| = 0.5$

The percentage change in quantity (20%) is less than the percentage change in price (40%), so $|e_D| < 1$ — demand for bananas in this price range is not very responsive to price.

Classifying Elasticity: Elastic, Inelastic, and Unitary Elastic

The numerical value of $e_D$ tells us how responsive demand is. The textbook classifies three broad categories.

1. Inelastic Demand ( $|e_D| < 1$ )

When the percentage change in quantity demanded is less than the percentage change in price, elasticity is less than one. Demand is said to be inelastic at that price. Essential goods — things people need regardless of price — typically show inelastic demand. For example, demand for basic food items, medicines, or electricity often falls in this category.

2. Elastic Demand ( $|e_D| > 1$ )

When the percentage change in quantity demanded is greater than the percentage change in price, elasticity exceeds one. Demand is said to be elastic at that price. Luxury goods — items people can easily postpone or forgo — tend to have elastic demand. A small price drop for a luxury car or designer clothing can lead to a large increase in quantity demanded.

3. Unitary Elastic Demand ( $|e_D| = 1$ ) …

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