Income and Cross Elasticity of Demand
In one line. Income elasticity of demand (YED) is the percentage change in quantity demanded divided by the percentage change in income: positive for normal goods (zero to one for necessities, above one for luxuries) and negative for inferior goods. Cross elasticity of demand (XED) is the percentage change in quantity demanded of one good divided by the percentage change in the price of another: positive for substitutes, negative for complements, near zero for unrelated goods.
Exam relevance: a core A Level Economics topic, on ETG analysis of the last ten years. Taught the way an economics tutor who wrote the answer keys teaches it.
01What income elasticity of demand is
Income elasticity of demand measures how strongly demand for a good reacts to a change in income, and its sign tells you what kind of good you are looking at.
Income elasticity of demand (YED) is the percentage change in quantity demanded divided by the percentage change in income. The sign and magnitude classify the good as inferior, a normal necessity or a normal luxury.
This page is H2 content. H1 students cover price elasticity of demand and supply, but income and cross elasticity are studied only at H2.
02Calculating and interpreting YED
As with PED, two skills are assessed: computing YED from case figures and reading a quoted value to classify the good.
- The figures. Suppose a 10 percent rise in income raises quantity demanded for a good by 18 percent.
- The calculation. YED = (plus 18 percent) divided by (plus 10 percent) = plus 1.8.
- The interpretation. The value is positive, so the good is normal, and because it exceeds one it is income elastic, meaning a luxury: demand grows faster than income.
Read the sign first, then the magnitude. A higher positive YED means demand is more income responsive, so the good is more luxury like; a higher income level is usually what turns a good from a luxury into a necessity, which is the link a strong answer makes explicit.
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03Normal, necessity, luxury and inferior goods
The three ranges of YED map onto a clear set of categories, and keeping them in order is where most marks are lost or won.
- Normal luxury: YED above one. Demand rises more than proportionately with income, for example luxury cars or designer handbags.
- Normal necessity: YED between zero and one. Demand rises with income but less than proportionately, for example staple groceries.
- Inferior good: YED below zero. Demand falls as income rises, because consumers switch to better alternatives, for example the cheapest cuts or budget staples.
A low positive YED is a necessity, not an inferior good. Inferior means the sign is negative, so demand actually falls when income rises. Mixing the two up is the most common YED error in the exam.
04Cross elasticity of demand
Cross elasticity of demand measures how the demand for one good responds to a change in the price of another, capturing the relationship between the two goods.
Cross elasticity of demand (XED) is the percentage change in quantity demanded of good A divided by the percentage change in the price of good B. The sign reveals the relationship and the magnitude reveals how close it is.
Like YED, XED is interpreted rather than drawn. Most case questions give you co-movement in the data and ask you to deduce the sign, so reading the direction carefully matters.
05Substitutes, complements and unrelated goods
The sign of XED classifies the pair, and the size of the value shows how strong the relationship is.
- Substitutes: XED positive. A rise in the price of one good raises demand for the other, because buyers switch to it. Close substitutes have a larger positive value.
- Complements: XED negative. A rise in the price of one good lowers demand for the other, because the two are consumed together.
- Unrelated goods: XED near zero. A price change in one has little effect on demand for the other.
When data is given as co-movement rather than a clean price then quantity change, work out the direction carefully. If one good's consumption falls as another's price falls, the two move together, which signals substitutes, a positive XED.
06Applications
YED and XED are useful because they forecast how demand, expenditure and firm strategy change, not just because they classify goods.
- Firm planning and the structure of the economy. As incomes rise, demand for high YED luxuries and services grows faster than for low YED necessities, while demand for inferior goods falls. Firms use this to decide which product lines to expand, and it predicts how an economy's output mix shifts as it develops.
- Related good pricing. XED guides pricing of related goods. Complements support bundling or loss leader pricing, while close substitutes with a high positive XED constrain a firm's pricing because buyers will switch.
These applications turn a classification into a decision, which is the step that separates a definition from analysis.
07Test yourself
- A 5 percent rise in income lowers quantity demanded for a good by 2 percent. Calculate YED, state its sign, and classify the good.
- Explain why a good with a low positive YED is a necessity rather than an inferior good.
- Two goods have a cross elasticity of demand of minus 0.8. State the relationship and explain how a firm might use it in pricing.
08Questions students ask
Income elasticity of demand (YED) measures how responsive demand for a good is to a change in income. It is the percentage change in quantity demanded divided by the percentage change in income. Its sign and magnitude classify the good: a positive value is a normal good, a negative value is an inferior good, and within normal goods a value between zero and one is a necessity while a value above one is a luxury.
A normal good has positive YED, so demand rises as income rises: people buy more of it when they can afford to. An inferior good has negative YED, so demand falls as income rises, because consumers switch to better alternatives as they grow richer. A common error is to call a good with low positive YED inferior; a low positive value is a necessity, not an inferior good.
Cross elasticity of demand (XED) measures how responsive demand for one good is to a change in the price of another. It is the percentage change in quantity demanded of good A divided by the percentage change in the price of good B. A positive value means the two are substitutes, a negative value means they are complements, and a value near zero means they are unrelated.
Income and cross elasticity of demand are H2 content; H1 students study price elasticity of demand and supply but not YED or XED. Knowing the boundary keeps H1 students from spending time on material that cannot be examined at their level, while H2 students should be able to interpret both from case data and apply them.