Chapter 3 · Elasticities
Engel curve · income elasticity
Compare Engel curves for necessities, luxuries and inferior goods. Explain how quantity demanded changes with income and interpret income elasticity.
The economic idea
Income elasticity of demand measures the responsiveness of quantity demanded to a change in consumer income, ceteris paribus. YED is calculated as the percentage change in quantity demanded divided by the percentage change in income.
An Engel curve shows the relationship between consumer income and the quantity demanded of a particular good, holding the good’s price and other influences on demand constant. Income is measured on the vertical axis and quantity demanded on the horizontal axis in this IB presentation.
A positive YED identifies a normal good because quantity demanded rises as income rises. A normal good is a luxury over a range where YED is greater than one and a necessity over a range where YED lies between zero and one.
A zero YED means quantity demanded is unchanged as income rises. A negative YED identifies an inferior good because quantity demanded falls as income rises; “inferior” describes the income response and does not imply poor quality.
The classification belongs to the observed income range, not permanently to the product. Changing income moves the consumer along the Engel curve; a change in price, preferences, household composition or another held-constant determinant can shift the relationship.
Following A to E along the Engel curve
“Quantity demanded” is measured on the horizontal axis. Movement to the right means the household demands more of the good.
“Income per week” is measured on the vertical axis. Movement upward means household income is higher.
“Engel curve” joins observations of income and quantity demanded for the same good while its price, preferences and other influences are held constant.
A to B: a luxury response
Between “A” and “B”, income rises while quantity demanded rises. Quantity demanded changes proportionately more than income. YED is positive and greater than one, so the good behaves as a normal luxury over this interval.
B to C: a necessity response
Between “B” and “C”, income rises while quantity demanded rises. Quantity demanded changes proportionately less than income. YED is positive but below one, so the good behaves as a normal necessity over this interval.
C to D: saturation
Between “C” and “D”, income rises while quantity demanded is unchanged. YED is equal to zero: the change in income produces no change in quantity demanded. This is zero income responsiveness, not perfectly inelastic demand with respect to price.
D to E: an inferior-good response
Between “D” and “E”, income rises while quantity demanded falls. YED is negative because income and quantity demanded move in opposite directions. The good behaves as inferior over this interval; this does not mean that its quality is poor.
Turn a classification into a useful conclusion
Both a luxury and a necessity are normal goods: demand rises as income rises. The distinction is how large that response is in percentage terms. A necessity can still sell more as households become richer; its demand does not have to be fixed.
Use the income range and household described in the question. An inferior-good response predicts falling demand as income rises, not that everyone will stop buying the product. A YED coefficient does not by itself give a sales-revenue figure: that requires price and quantity. Nor does it measure consumers’ well-being.
How to read the income journey
Read the actual position of each labelled observation: “Income per week”, not price, measures income. Do not infer its location from its name.
For each pair, compare the direction and proportionate change in “Quantity demanded” with the change in income, using the first observation as the percentage base.
Use the sign and magnitude of YED to classify the response: luxury, necessity, zero response or inferior good.
Keep the classification tied to that segment of “Engel curve”; do not assign one label to the good at every possible income.
What the current state establishes
The current observations from “A” to “E” show the responses described above. Moving observations can change an interval’s classification; the letters do not fix its elasticity.
The diagram does not show several different goods or several demand curves. It shows changing demand for the same good as the same household’s income changes, ceteris paribus.
Common mistakes to avoid
- “Engel curve” is not a demand curve: its vertical axis measures income rather than the good’s price.
- The labelled points “A” to “E” are income–quantity observations, not market equilibria.
- “Inferior good” means demand decreases as income rises. It does not mean the product is defective or objectively low quality.
- A vertical portion of an Engel curve shows zero income responsiveness when income changes and quantity remains fixed. Coincident observations do not establish zero YED because there is no income change to measure.
How to draw this diagram
- Title the diagram “Engel curve · income elasticity”. Label the horizontal axis “Quantity demanded” and the vertical axis “Income per week”.
- Draw Engel curve first and label it clearly.
- Mark each relevant intersection and distinguish the initial, market and socially optimum or policy outcomes where applicable.
- Project important intersections to the axes with dashed guide lines and label the outcomes.
- Check that every symbol used in the explanation appears on the diagram and add arrows showing the direction of change.
Assumptions and limitations
- The curve holds the good’s price, prices of related goods, preferences, expectations and household characteristics constant.
- The shape is illustrative. Different goods and households can have different turning points, and some goods never become inferior.
- Observed household data may combine income effects with changes in household size, age, location or tastes unless those influences are controlled.
- YED describes responsiveness and classification; it does not by itself establish welfare, product quality or whether consumption is socially desirable.
- The interval comparisons use original-value percentage changes with the first observation as their base. They are not claims of constant point elasticity over the whole interval; another specified method, such as midpoint arc elasticity, should be applied when a question requires it.