Price elasticity of demand and its calculation

Price elasticity of demand (PED) measures the responsiveness of the quantity demanded for a product to a change in its price.

Formula for price elasticity of demand

$\text{PED}=\frac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}$

Where:

• Percentage change in quantity demanded = $\frac{\text{new quantity}-\text{old quantity}}{\text{old quantity}}\times 100$
• Percentage change in price = $\frac{\text{new price}-\text{old price}}{\text{old price}}\times 100$

PED values are typically negative because quantity demanded usually falls as price rises. However, the absolute value is often used to classify elasticity, and PED is expressed as a number, not a percentage.

Worked example - Calculating price elasticity of demand

The price of a game subscription rises from £12 to £15, and the number of subscribers drops from 80 to 60. Calculate the PED.

Step 1: Identify the values

• Old price = £12
• New price = £15
• Old quantity = 80
• New quantity = 60

Step 2: Calculate percentage change in quantity demanded

$\text{Percentage change in quantity demanded}=\frac{60-80}{80}\times 100=-25\%$

Step 3: Calculate percentage change in price

$\text{Percentage change in price}=\frac{15-12}{12}\times 100=25\%$

Step 4: Calculate PED

$\text{PED}=\frac{-25\%}{25\%}=-1.0$

Types of price elasticity of demand

PED can range from perfectly inelastic to perfectly elastic, depending on how much demand changes with price.

Categories of price elasticity of demand

• Elastic demand - PED greater than 1 in absolute value (e.g., -1.5). A percentage change in price leads to a larger percentage change in quantity demanded.
• Inelastic demand - PED between 0 and 1 in absolute value (e.g., -0.4). A percentage change in price causes a smaller percentage change in quantity demanded.
• Unit elastic demand - PED equal to 1 in absolute value (e.g., -1). The percentage change in price equals the percentage change in quantity demanded.
• Perfectly elastic demand - PED is infinite. Any price increase causes demand to drop to zero.
• Perfectly inelastic demand - PED is 0. Demand remains unchanged regardless of price.

Income elasticity of demand and its calculation

Income elasticity of demand (YED) assesses how the quantity demanded for a good changes in response to variations in consumers' real income levels.

Formula for income elasticity of demand

$\text{YED}=\frac{\text{percentage change in quantity demanded}}{\text{percentage change in real income}}$

Where:

• Percentage change in quantity demanded = $\frac{\text{new quantity}-\text{old quantity}}{\text{old quantity}}\times 100$
• Percentage change in real income = $\frac{\text{new income}-\text{old income}}{\text{old income}}\times 100$

YED can be positive or negative.

Worked example - Calculating income elasticity of demand

Real income rises by 5%, and demand for high-end headphones increases by 15%. Calculate the YED.

Step 1: Identify the values

• Percentage change in real income = 5%
• Percentage change in quantity demanded = 15%

Step 2: Apply the YED formula

$\text{YED}=\frac{15\%}{5\%}=3.0$

Step 3: Interpretation

A YED of 3.0 indicates the good is income elastic.

Types of income elasticity of demand

YED classifications reveal how income changes affect demand.

Categories of income elasticity of demand

• Income elastic demand - YED greater than 1. Demand increases by a larger percentage than income.
• Income inelastic demand - YED between 0 and 1. Demand increases by a smaller percentage than income.
• Perfectly income inelastic demand - YED equal to 0. Demand stays constant regardless of income changes.

Cross elasticity of demand and its calculation

Cross elasticity of demand (XED) evaluates how the quantity demanded for one good is affected by a price change in another good.

Formula for cross elasticity of demand

$\text{XED}=\frac{\text{percentage change in quantity demanded of good A}}{\text{percentage change in price of good B}}$

Where:

• Percentage change in quantity demanded of good A = $\frac{\text{new quantity of A}-\text{old quantity of A}}{\text{old quantity of A}}\times 100$
• Percentage change in price of good B = $\frac{\text{new price of B}-\text{old price of B}}{\text{old price of B}}\times 100$

Positive XED indicates substitutes, while negative XED shows complements.

Worked example - Calculating cross elasticity of demand

The price of a brand of soda rises by 15%, causing demand for a competitor's soda to increase by 9%. Calculate the XED.

Step 1: Identify the values

• Percentage change in price of brand B soda = 15%
• Percentage change in quantity demanded of brand A soda = 9%

Step 2: Apply the XED formula

$\text{XED}=\frac{9\%}{15\%}=0.6$

Step 3: Interpretation

An XED of 0.6 (positive) suggests the two brands of soda are substitutes.

Types of cross elasticity of demand

XED helps businesses understand relationships between products.

Categories based on relationships between goods

• Substitutes - Positive XED. A price rise in one good increases demand for the other.
• Complements - Negative XED. A price rise in one good decreases demand for the other.