Calculating and interpreting YED (normal, inferior, luxury, necessity) and XED (substitutes and complements), and why firms care.
As prices rose much faster than wages in 2022, households’ real incomes fell. Shoppers switched to discount supermarkets and own-brand ranges. In September 2022 the market research firm Kantar reported that Aldi had overtaken Morrisons to become Britain’s fourth-largest supermarket.
Which goods do people buy more of when they are worse off? Income elasticity of demand measures it.
Source: Kantar grocery market share (September 2022).
Income elasticity of demand (YED) measures how responsive demand is to a change in income.
YED = % change in quantity demanded ÷ % change in income
Cross elasticity of demand (XED) measures how responsive demand for good X is to a change in the price of good Y.
XED = % change in quantity demanded of X ÷ % change in price of Y
Unlike PED, the sign matters: it tells you what kind of good it is. Both assume everything else stays the same (ceteris paribus), and both shift the demand curve.
Average real incomes fall during a cost-of-living crisis.
What happens to demand for own-brand value food at discount supermarkets?
For some goods, demand rises when incomes fall, because shoppers switch from dearer alternatives. These are inferior goods, with a negative income elasticity of demand. In 2022 Aldi overtook Morrisons to become the UK’s fourth-biggest supermarket.
YED first. If income rises and demand increases, from D1 to D2, YED is positive: a normal good. If demand decreases, to D3, YED is negative: an inferior good, such as value-range food or, for some, bus travel.
The size matters too. YED greater than 1: income elastic, a luxury, such as holidays abroad: demand rises proportionately more than income. YED between 0 and 1: income inelastic, a necessity, such as bread: demand rises, but proportionately less than income.
Check: Incomes rise by 4% and demand for foreign holidays rises by 10%. What is the YED and what kind of good is it?
10 ÷ 4 = +2.5. Positive: normal. Greater than 1: income elastic, a luxury.
Now XED. If the price of tea rises and demand for coffee increases, XED is positive: they are substitutes. If the price of printers rises and demand for ink falls, XED is negative: complements. If XED is close to zero, the goods are unrelated.
The size of XED shows how close the relationship is. +3 means very close substitutes, such as two brands of petrol. +0.2 means weak substitutes. −2 means strong complements, such as games consoles and their games.
Check: The price of good Y rises by 10% and demand for good X falls by 5%. What is the XED, and how are the goods related?
−5 ÷ 10 = −0.5. Negative: when Y gets dearer, less X is wanted, so they are bought together.
Now think about what these figures mean for a business.
Check: A recession cuts incomes across the country. Which business is most likely to see its sales rise?
Value-range food is an inferior good with negative YED, so demand for it rises when incomes fall.
Why firms care. YED tells a firm how its sales will change in a boom or a recession: luxury sellers suffer most in a recession, discounters may gain. XED tells a firm how much a rival’s price cut will hurt, and how to price complements, such as cheap printers with dear ink.
A negative YED means demand falls as income rises: an inferior good, not a normal one. With YED, unlike PED, the sign tells you the type of good.
Explain what a YED of −0.6 and an XED of +2 tell a supermarket about two of its products.
Income elasticity of demand measures how responsive demand is to a change in income. A YED of −0.6 means a 1% rise in income causes a 0.6% fall in quantity demanded. The negative sign shows it is an inferior good, such as a value-range product, and because 0.6 is less than 1, demand responds proportionately less than income. The supermarket can expect sales to rise in a recession and fall in a boom.
Cross elasticity of demand measures how responsive demand for one good is to a change in the price of another. An XED of +2 means a 1% rise in the price of the other good raises demand for this one by 2%. The positive sign shows they are substitutes, and the size shows they are close substitutes, such as two brands of the same product. The supermarket should watch rivals’ prices closely: a small price cut by a rival would take a large share of its sales.
However, both figures are estimates from past data and assume other things stay the same. If tastes change or a new rival opens nearby, the true values could be different, so the supermarket should treat them as a guide rather than a forecast.
Supermarket shares: Kantar (2022). Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed. Your answers are saved only on this device.