When incomes rise, what do people buy?
Imagine that every family in a town earns 20% more this year. What happens to what they buy?
They will probably eat out more, and many more of them will take a holiday. They will buy a little more food, but not 20% more, because there is a limit to how much anyone eats. And some things they will buy less of: the cheapest instant noodles, perhaps, or the longest, cheapest bus route, as they switch to something they like better.
In the lecture on what shifts the demand curve, you saw that a rise in income shifts demand to the right for normal goods and to the left for inferior goods. That gave the direction. This lecture gives the size, using a second kind of elasticity.
Income elasticity of demand
It measures how strongly demand responds to a change in buyers' incomes, other things being equal.
The letter Y is the usual economics symbol for income. Like PED, YED compares two percentage changes, so it has no units. But there is one big difference. PED is negative for almost every good, so we often look only at its size. For YED, the sign is the most important thing, because it can be positive or negative, and the sign tells you what kind of good it is.
- YED above 0: a normal good. Demand rises when income rises. Most goods are normal.
- YED below 0: an inferior good. Demand falls when income rises, because buyers switch to something they prefer once they can afford it.
Normal goods divide again, by size:
- YED between 0 and 1: a necessity. Demand rises with income, but by a smaller percentage. Examples: basic food, electricity for a home, water.
- YED above 1: a luxury. Demand rises by a larger percentage than income. As people get richer, they spend a growing share of their income on it. Examples: foreign holidays, meals in restaurants, jewellery.
That is it. That is the whole idea. The sign tells you the direction, and the size tells you whether the good's share of the budget grows or shrinks as income grows. A luxury takes a bigger share as people get richer. A necessity takes a smaller share, even though people still buy more of it. An inferior good is bought less in total.
Incomes fall by 10%, and demand for a good falls by 25%. Is the good inferior, because its demand fell?
Show the answer
No. Both changes are negative, so YED = −25% ÷ −10% = +2.5. A positive YED means a normal good, and 2.5 is above 1, so it is a luxury. Demand fell because income fell. An inferior good is one whose demand moves in the opposite direction to income. When income falls, demand for an inferior good rises. Always divide the signed percentages, and read the sign of the answer.
Watch a budget change shape
The model below follows one invented household. It spends money on food (YED 0.5), holidays (YED 1.8) and the cheapest instant noodles (YED −0.6), and the rest on everything else. Change the household's income and watch the share of the budget each one takes.
Move the monthly income. At $2000, the household spends $800 on food, $100 on holidays and $40 on the cheapest noodles. Watch what happens to each amount and to its share of income.
The invented household's spending at three incomes, with each amount's share of income below it. Each amount changes in line with its YED (food 0.5, holidays 1.8, noodles −0.6).
| Income | Food | Holidays | Noodles |
|---|---|---|---|
| $1000 | $566 56.6% | $29 2.9% | $61 6.1% |
| $2000 | $800 40.0% | $100 5.0% | $40 2.0% |
| $4000 | $1131 28.3% | $348 8.7% | $26 0.7% |
As income rises, the household spends more on food but a smaller share of its income; more on holidays and a larger share; and less on the cheapest noodles altogether.
Did you see food's share fall as income rose, even though the household spent more on food? That pattern has a name. In 1857, the statistician Ernst Engel noticed that richer families spend a smaller share of their income on food than poorer families. It is called Engel's law, and in the language of this lecture it says simply: food is a necessity, with a YED between 0 and 1.
One note on the numbers. YED describes the response to a small change. Over large changes, the model's percentages differ slightly from "YED × the change in income". For example, a 20% rise in income raises food spending by about 9.5%, not exactly .
Why businesses and governments care
Incomes do not grow steadily. They rise faster in booms and fall in recessions. YED tells you who feels those swings most.
- Sellers of luxuries grow fastest in good years, but they suffer most in a recession, because luxuries are the first spending families cut.
- Sellers of necessities see steadier demand. People keep buying food and electricity when times are hard.
- Sellers of inferior goods can do relatively well in a recession, as families switch down to cheaper choices. In good years, the same switch works against them.
The same idea works across a whole economy. As a country grows richer, the share of spending on food falls, and the share on services, travel and manufactured goods rises. That is one reason why farming becomes a smaller part of an economy as it develops, even when farms produce more than before.
Test the categories below. Some cards show falling incomes, so read the signs carefully.
Each card gives a change in income and the change in demand that followed. Work out the YED, then place the card.
Each case, its YED and its type:
| Case | YED | Type |
|---|---|---|
| Income +10%, meals out +18% | 1.8 | luxury |
| Income +5%, bread +1% | 0.2 | necessity |
| Income +20%, cheapest rice −8% | −0.4 | inferior |
| Income −10%, foreign holidays −25% | 2.5 | luxury |
| Income −4%, long-distance bus trips +2% | −0.5 | inferior |
| Income +8%, household electricity +2% | 0.25 | necessity |
| Income +15%, new cars +30% | 2 | luxury |
| Income −6%, second-hand clothes +3% | −0.5 | inferior |
| Income +10%, salt +0.5% | 0.05 | necessity |
Worked examples
A family's income rises from $30 000 to $36 000 a year. Its restaurant meals rise from 4 to 5 a month. Find the YED.
Income: . Meals: .
YED = 25 ÷ 20 = +1.25. Positive, so a normal good; above 1, so a luxury. Eating out grows faster than income.
With the same 20% rise in income, the family now buys 7 packs of the cheapest instant noodles a month instead of 10. It also uses 420 kWh of electricity a month instead of 400. Find each YED.
Noodles: , so YED = −30 ÷ 20 = −1.5. Negative: an inferior good.
Electricity: , so YED = 5 ÷ 20 = +0.25. Between 0 and 1: a necessity.
The question. Between 2011–12 and 2022–23, spending per person in India rose strongly. Engel's law predicts that, if food is a necessity, its share of household spending should fall.
What the survey found. India's Household Consumption Expenditure Survey (Ministry of Statistics and Programme Implementation, results published February 2024) reported the following. In rural areas, average monthly spending per person rose from ₹1430 in 2011–12 to ₹3773 in 2022–23, and the share spent on food fell from 52.9% to 46.4%. In urban areas, spending rose from ₹2630 to ₹6459, and the food share fell from 42.6% to 39.2%. Rural households' non-food spending passed half of the total for the first time.
A rough elasticity. In rural areas, total spending rose by about 164%, while spending on food rose by about 131% (from about ₹756 to about ₹1750 a month). Food spending grew, but more slowly than total spending: a ratio of about 0.8. In urban areas, the ratio is about 0.86.
The verdict. The pattern is exactly Engel's law. Families spent more on food, so it is a normal good, but its share fell, so it behaves as a necessity. Treat the numbers with care. They compare spending, not income, in prices of each year, and prices of food and other goods did not rise at the same rate. The survey method was also revised between the two rounds. The direction is clear; the exact elasticity is not.
Three classic mistakes
For PED, people often drop the minus sign. For YED, the sign is the main result: it separates normal goods from inferior goods. Always keep it.
When income falls, demand for a normal good falls too, and YED is still positive. A good is inferior only if its demand moves in the opposite direction to income.
"Inferior" is a technical word here. It describes how demand responds to income, not how good the product is. The same good can be inferior for one group of buyers and normal for another, such as bus travel for families who are buying their first car.
Work each one on paper first. Open a hint only when you are stuck.
-
Average incomes in a city rise by 6%. Demand for gym memberships rises by 9%, and demand for the cheapest brand of bread falls by 3%. Find each YED and classify each good.
Hint 1
YED = % change in demand ÷ % change in income, keeping the signs.
Hint 2
9 ÷ 6, and −3 ÷ 6.
Full answer
Gym memberships: YED = 1.5, a luxury. Cheapest bread: YED = −0.5, an inferior good.
-
The YED for cinema tickets in a country is 1.4 (an invented figure). Incomes fall by 5% in a recession. What change in demand should cinemas expect?
Hint 1
% change in demand = YED × % change in income.
Hint 2
The change in income is −5%.
Full answer
. Demand falls by about 7%, more than incomes fell, because cinema tickets are a luxury in this example.
-
A shop sells three goods with YEDs of 2.0, 0.3 and −0.8. A recession is coming. Which good's sales should hold up best, and which should fall most? Explain.
Hint 1
Incomes will fall. For each good, what sign will the change in demand have?
Hint 2
A negative YED times a negative change in income gives a positive change in demand.
Full answer
The good with YED −0.8 is inferior, so its sales should actually rise as incomes fall. The necessity (0.3) falls a little. The luxury (2.0) falls most, by twice the percentage fall in income.
-
In a country, a family's food spending is $600 a month out of an income of $1500. Ten years later, its income is $3000 and its food spending is $900, with prices unchanged (an invented example). Find the food share at both times, estimate the YED for food, and say whether this fits Engel's law.
Hint 1
Share = food ÷ income. Then find the percentage changes in income and in food spending.
Hint 2
Income +100%; food +50%.
Full answer
Shares: , then . YED ≈ 50 ÷ 100 = 0.5. Food is a normal good (spending rose) and a necessity (YED below 1), so its share fell from 40% to 30%. This is exactly Engel's law. (For a change as large as doubling, the simple percentage method gives only an estimate.)
PED looks at a single moment: what happens when a price changes. YED looks across years: what happens as people grow richer or poorer. That makes it a tool for long-run thinking. A firm selling luxuries is betting on rising incomes. A country whose people are getting richer can expect its spending, and so its jobs, to move away from food and towards services.
Engel noticed the food pattern in the 1850s, and survey after survey has found it since, including India's most recent one. The next lecture asks a related question: how does the demand for one good respond to the price of a different good?
- Income elasticity of demand is the percentage change in quantity demanded divided by the percentage change in income.
- The sign of YED shows the type of good: positive for a normal good and negative for an inferior good.
- A necessity has a YED between 0 and 1, so its share of spending falls as income rises, while a luxury has a YED above 1, so its share rises.
- Engel's law, that food takes a smaller share of spending as incomes rise, is the necessity pattern, and recent Indian survey data follow it.
- Sellers of luxuries feel booms and recessions most strongly, sellers of necessities least, and sellers of inferior goods can gain in a recession.