2.15 - Income Elasticity of Demand (YED)
Meaning and calculation of YED
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
Where:
- %∆Qd = Percentage change in quantity demanded
- %∆Y = Percentage change in income
This can also be expressed as:
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 - YED for public transport
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
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 - 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
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.
| Category | YED value | Demand as income rises | Typical examples |
|---|---|---|---|
| Income elastic goods | YED > 1 | Grows significantly; these are often luxuries or services | International holidays, fine dining experiences, premium electronics, luxury cars, designer fashion |
| Income inelastic goods | 0 < YED < 1 | Increases only modestly; these are typically essentials | 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 | Falls, because consumers abandon these lower-quality options 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. It is drawn with income (Y) on the vertical axis and quantity demanded (Qd) on the horizontal axis.
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
For a normal good, where the straight-line Engel curve meets the axes tells you which side of 1 the YED value falls on.
Income elastic demand (YED > 1) - The curve intersects the vertical axis, so quantity demanded rises more than proportionately with income, as the diagram below shows.
Income inelastic demand (0 < YED < 1) - The curve intersects the horizontal axis, so quantity demanded grows more slowly than income.
YED = 1 - The curve passes through the origin, so quantity demanded grows in exact proportion to 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.
One Engel curve can therefore hold all three cases at once, as the diagram below shows, with income (Y) on the vertical axis and quantity demanded (Qd) on the horizontal axis. Up to income Y1 the curve has a positive slope, so YED > 0 and the good behaves as a normal good. Between Y1 and Y2 the curve is vertical, giving YED = 0: income rises but Qd stays the same. Above Y2 the curve has a negative slope, YED < 0, and the good has become an inferior good for that consumer.
