The meaning and calculation of income elasticity of demand

Income elasticity of demand (YED) measures how much the quantity demanded of a good or service changes in response to a change in consumers' income. It indicates both the direction of the change in demand and the extent to which the demand curve shifts when income levels vary.

Formula for calculating YED

$\text{YED}=\frac{\%\mathrm{\Delta }\text{Qd}}{\%\mathrm{\Delta }\text{Y}}$

Where:

• %∆Qd = Percentage change in quantity demanded
• %∆Y = Percentage change in income

This can also be expressed as:

$\text{YED}=\frac{\mathrm{\Delta }\text{Q}}{\mathrm{\Delta }\text{Y}}\times \frac{\text{Y1}}{\text{Q1}}$

Where:

• ∆Q = Change in quantity demanded (Q2 - Q1)
• ∆Y = Change in income (Y2 - Y1)
• Y1 = Initial income
• Q1 = Initial quantity demanded

YED is positive if both the change in demand and the change in income are in the same direction (both positive or both negative). It is negative if they move in opposite directions.

Worked example - Calculating YED for public transport usage

In an economy, national income rises by 3.5%, leading to a 7.7% decrease in the use of public transport. Calculate the YED and interpret what this means for public transport.

Step 1: Identify the values

• %∆Y = +3.5%
• %∆Qd = -7.7%

Step 2: Apply the YED formula

$\text{YED}=\frac{-7.7\%}{+3.5\%}=-2.2$

Step 3: Interpretation

A YED of -2.2 indicates that public transport is an inferior good, as demand falls when income rises, and the response is elastic since the absolute value exceeds 1.

Worked example - Calculating YED for premium subscriptions

Income levels in a region increase from $50,000 to $56,000, causing subscriptions to a luxury streaming service to rise from 300,000 to 364,800. Calculate the YED and interpret the result.

Step 1: Identify the values

• Y1 = $50,000
• Y2 = $56,000
• Q1 = 300,000
• Q2 = 364,800

Step 2: Calculate changes and apply the formula

$\mathrm{\Delta }\text{Y}=\$\mathrm{56,000}-\$\mathrm{50,000}=\$\mathrm{6,000}$

$\mathrm{\Delta }\text{Q}=\mathrm{364,800}-\mathrm{300,000}=\mathrm{64,800}$

$\text{YED}=\frac{\mathrm{64,800}}{\mathrm{6,000}}\times \frac{\mathrm{50,000}}{\mathrm{300,000}}=1.8$

Step 3: Interpretation

A YED of 1.8 shows that the streaming service is a normal good with income elastic demand, meaning demand increases more than proportionately with income.

Normal and inferior goods based on YED values

Goods can be classified as normal or inferior depending on their YED value, which shows how demand responds to income changes.

Classification of goods by YED

• Normal goods (YED > 0) - Demand changes in the same direction as income. For example, if income rises, demand increases.
• Inferior goods (YED < 0) - Demand changes in the opposite direction to income. For example, if income rises, demand decreases.

For normal goods, further distinctions can be made:

• Income elastic (YED > 1) - Demand changes by a greater percentage than the income change, often seen in luxuries.
• Income inelastic (0 < YED < 1) - Demand changes by a smaller percentage than the income change, common for necessities.
• YED = 1 - Demand changes by exactly the same percentage as income.
• YED = 0 - Demand remains unchanged regardless of income variations.

Examples of income elastic and inelastic goods

Different types of goods exhibit varying YED values, influencing how businesses and economies respond to income fluctuations.

Income elastic goods (YED > 1)

These are often luxuries or services where demand grows significantly with rising income:

• International holidays
• Fine dining experiences
• Premium electronics
• Luxury cars
• Designer fashion

Income inelastic goods (0 < YED < 1)

These are typically essentials where demand increases modestly with income:

• Agricultural produce
• Basic foodstuffs
• Everyday necessities like soap or toothpaste
• Simple grooming services like standard haircuts
• Household staples such as cooking oil or basic cereals

Inferior goods (YED < 0)

These are lower-quality options that consumers abandon as income rises, opting for better alternatives:

• Second-hand cars
• Budget clothing
• Low-grade food products

Graphical representation using Engel curves

An Engel curve illustrates the relationship between income and the quantity demanded of a good, providing a visual representation of YED.

Features of Engel curves

• Positive slope - Indicates a normal good (YED > 0), as quantity demanded rises with income.
• Negative slope - Indicates an inferior good (YED < 0), as quantity demanded falls with rising income.
• Vertical curve - Shows YED = 0, where quantity demanded does not change with income.

Special cases of Engel curves

• Income elastic demand (YED > 1) - A straight-line curve that intersects the vertical axis, showing demand accelerates with income.
• Income inelastic demand (0 < YED < 1) - A straight-line curve that intersects the horizontal axis, indicating slower demand growth relative to income.
• YED = 1 - A straight-line curve passing through the origin, where demand grows proportionally with income.

How YED can vary at different income levels

A single good can shift between YED categories depending on consumers' income brackets, reflecting changes in preferences as wealth increases.

Changes in YED across income levels

• Low income levels - Demand may rise with income (YED > 0), as the good meets basic needs. For example, budget instant meals might see increased consumption as income allows more purchases.
• Middle income levels - Demand could stabilise (YED = 0), as consumers reach a saturation point without switching alternatives.
• High income levels - The good may become inferior (YED < 0), with consumers opting for superior options, like choosing fresh, nutritious meals over instant varieties.