The concept of elasticity of demand

Elasticity of demand measures how much the demand for a good changes with a change in one of the key influences on demand, which include the price of the good itself, the level of real income, and the price of another good.

Price elasticity of demand and its types

Price elasticity of demand (PED) shows how much the quantity demanded of a good changes in response to a shift in its price. It is usually negative because demand decreases as price rises for most goods.

Formula for calculating PED

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

Where:

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

Categories of PED

• Elastic demand - PED greater than 1. A percentage change in price leads to a larger percentage change in quantity demanded.
• Inelastic demand - PED between 0 and 1. A percentage change in price leads to a smaller percentage change in quantity demanded.
• Unit elastic demand - PED equal to 1. The percentage change in price matches the percentage change in quantity demanded exactly.
• Perfectly elastic demand - PED equals infinity. Any price increase causes demand to drop to zero, while consumers will buy unlimited quantities at the current price.
• Perfectly inelastic demand - PED equals 0. Quantity demanded remains unchanged regardless of price fluctuations.

Worked example - Calculating price elasticity of demand

A business increases the price of its product from £10 to £11, causing quantity demanded to fall from 500 units to 425 units. Calculate the PED.

Step 1: Identify the values

• Original price = £10
• New price = £11
• Original quantity demanded = 500 units
• New quantity demanded = 425 units

Step 2: Calculate percentage changes

Percentage change in price = $\frac{\pounds 11-\pounds 10}{\pounds 10}\times 100=10\%$

Percentage change in quantity demanded = $\frac{425-500}{500}\times 100=-15\%$

Step 3: Apply the PED formula

$\text{PED}=\frac{-15\%}{10\%}=-1.5$

Step 4: Interpretation

The PED of -1.5 indicates elastic demand, meaning the percentage change in quantity demanded is larger than the percentage change in price.

Income elasticity of demand and its categories

Income elasticity of demand (YED) indicates how the quantity demanded of a good responds to changes in consumers' real income.

Formula for calculating YED

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

Where:

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

Categories of YED

• Income elastic - YED greater than 1. An income increase leads to a proportionately larger increase in demand.
• Income inelastic - YED less than 1. An income increase leads to a proportionately smaller increase in demand.
• Perfectly inelastic - YED equals 0. Demand stays constant regardless of income changes.
• Negative YED - YED less than 0. Demand decreases as income rises.

Worked example - Calculating income elasticity of demand

When average real income rises from £20,000 to £24,000, demand for a luxury item increases from 200 units to 280 units. Calculate the YED.

Step 1: Identify the values

• Original real income = £20,000
• New real income = £24,000
• Original quantity demanded = 200 units
• New quantity demanded = 280 units

Step 2: Calculate percentage changes

Percentage change in real income = $\frac{\pounds \mathrm{24,000}-\pounds \mathrm{20,000}}{\pounds \mathrm{20,000}}\times 100=20\%$

Percentage change in quantity demanded = $\frac{280-200}{200}\times 100=40\%$

Step 3: Apply the YED formula

$\text{YED}=\frac{40\%}{20\%}=2$

Step 4: Interpretation

The YED of 2 shows income elastic demand, meaning demand rises more than proportionally with income, typical for luxury goods.

Cross elasticity of demand for substitutes and complements

Cross elasticity of demand (XED) measures how the quantity demanded of one good changes when the price of another good alters.

Formula for calculating XED

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

Where:

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

Categories of XED based on product relationships

• Substitutes - Positive XED. A price rise in one good increases demand for the other, as consumers switch.
• Complements - Negative XED. A price rise in one good decreases demand for the other, as they are used together.
• Unrelated goods - XED close to 0. Price changes in one have little to no effect on the other's demand.

Worked example - Calculating cross elasticity of demand

The price of brand A smartphones rises from £300 to £360, causing demand for brand B smartphones to increase from 1,000 units to 1,200 units. Calculate the XED.

Step 1: Identify the values

• Original price of brand A = £300
• New price of brand A = £360
• Original quantity demanded of brand B = 1,000 units
• New quantity demanded of brand B = 1,200 units

Step 2: Calculate percentage changes

Percentage change in price of brand A = $\frac{\pounds 360-\pounds 300}{\pounds 300}\times 100=20\%$

Percentage change in quantity demanded of brand B = $\frac{\mathrm{1,200}-\mathrm{1,000}}{\mathrm{1,000}}\times 100=20\%$

Step 3: Apply the XED formula

$\text{XED}=\frac{20\%}{20\%}=1$

Step 4: Interpretation

The XED of 1 indicates the goods are substitutes, with demand for brand B rising proportionally to the price increase of brand A.