Income Elasticity of Demand: Formula, Midpoint Method, Examples

Income elasticity of demand (YED) measures how much the quantity demanded of a good responds to a change in consumer income: YED = (% change in quantity demanded) ÷ (% change in income). A positive YED means the good is normal, a negative YED means it is inferior, and the size splits normal goods into necessities (between 0 and 1) and luxuries (above 1).

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Supply and demand at equilibrium, drawn by the interactive graph. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

This guide covers the formula, the midpoint method AP courses use, how to read the sign and the size, a worked example with three goods, and the mistakes that cost points in AP Microeconomics Topic 2.5 (Other Elasticities). For the broader idea of elasticity, start with the elasticity guide; for the short definition, see the glossary entry on income elasticity of demand.

The formula

YED = (% change in quantity demanded) ÷ (% change in income)

Income sits in the denominator. That one detail separates YED from its two siblings: price elasticity of demand puts the good's own price in the denominator, and cross-price elasticity puts a different good's price there. The numerator is always the quantity demanded of the good you are studying.

The simplest way to compute each percentage change is new minus old, divided by old, times 100. If income rises from $40,000 to $44,000, that is a 10% rise. If a household's coffee shop visits rise from 100 to 115 a year over the same period, that is a 15% rise, so YED = 15% ÷ 10% = 1.5.

The midpoint method

The simple formula has a flaw: it gives a different answer depending on which way you move. The midpoint method fixes this by dividing each change by the average of the old and new values instead of the old value alone:

% change in quantity = (Q2 - Q1) ÷ [(Q1 + Q2) ÷ 2]

% change in income = (I2 - I1) ÷ [(I1 + I2) ÷ 2]

Here is why it matters. Suppose income rises from $50,000 to $70,000 and concert tickets bought rise from 4 to 8 a year.

• Simple method, income rising: quantity +100% (4 to 8), income +40% (20,000 ÷ 50,000), so YED = 100 ÷ 40 = 2.5.
• Simple method, income falling back: quantity -50% (8 to 4), income -28.57% (20,000 ÷ 70,000), so YED = 50 ÷ 28.57 = 1.75.
• Midpoint method, either direction: quantity 4 ÷ 6 = 66.67%, income 20,000 ÷ 60,000 = 33.33%, so YED = 66.67 ÷ 33.33 = 2.0.

Same two points, three different answers, and only the midpoint answer is the same both ways. When a question gives you two data points and says "use the midpoint method," this is the calculation it wants. The midpoint method entry and the midpoint method calculator walk through the percentage step on its own.

Reading the sign and the size

The sign tells you the type of good. The size tells you how strongly income drives demand.

Two points to keep straight. First, necessities and luxuries are both normal goods; a necessity is not inferior just because people buy only a little more of it. Second, these labels depend on the buyer and the income range. Bus trips can be inferior for a student who buys a car after a raise and normal for a lower-income worker whose raise means they can now afford to ride the bus instead of walking. The normal vs inferior goods guide covers the full list of examples, how the same good can switch categories, and why an inferior good is not the same thing as a Giffen good, so this guide will not repeat that material.

Worked example: one raise, three goods

A household's annual income rises from $50,000 to $70,000. Using the midpoint method, the percentage change in income is:

(70,000 - 50,000) ÷ 60,000 = 20,000 ÷ 60,000 = 33.33%

The household's yearly purchases of three goods change as follows.

Concert tickets: 4 to 8. Change = 4, average = 6, so the percentage change is 4 ÷ 6 = 66.67%. YED = 66.67 ÷ 33.33 = 2.0. Positive and above 1, so concert tickets are a luxury for this household.

Gallons of milk: 50 to 55. Change = 5, average = 52.5, so the percentage change is 5 ÷ 52.5 = 9.52%. YED = 9.52 ÷ 33.33 = 0.29. Positive but below 1, so milk is a necessity: the household buys more, but far less than proportionally.

Packs of instant noodles: 60 to 40. Change = -20, average = 50, so the percentage change is -20 ÷ 50 = -40%. YED = -40 ÷ 33.33 = -1.2. Negative, so instant noodles are an inferior good for this household. The size, 1.2, says demand falls sharply as income rises, which fits a good that people drop as soon as they can afford something they prefer.

You can check each line with the income elasticity of demand calculator by entering the midpoint percentage changes from the table.

Using YED to predict changes

Once you know a YED, you can run the formula backward: % change in quantity demanded ≈ YED × % change in income. If incomes in a region fall 5% during a recession:

• A luxury with YED = 2.0 sees quantity demanded fall by about 2.0 × 5% = 10%.
• A necessity with YED = 0.3 sees quantity demanded fall by about 0.3 × 5% = 1.5%.
• An inferior good with YED = -1.2 sees quantity demanded rise by about 1.2 × 5% = 6%.

This is why firms that sell luxuries watch the business cycle closely, while discount grocers often hold up in a downturn. It also tells you how to draw the graph. A change in income is a determinant of demand, so it shifts the whole demand curve rather than moving along it. Higher income shifts a normal good's demand right and an inferior good's demand left. You can try both shifts in the supply and demand sandbox: shift demand, then watch the new equilibrium price and quantity.

How YED compares with the other elasticities

All three demand elasticities have the same shape, a percentage change in quantity over a percentage change in a driver. Only the driver changes.

The cross-price elasticity guide covers the middle row in full, and the comparison page on price elasticity vs income elasticity of demand sets the first and third side by side.

How it shows up on the AP exam

Income elasticity questions usually ask you to do one of three things:

• Calculate YED from data. You get two income levels and two quantities, sometimes with a direction to use the midpoint method, and you compute the coefficient.
• Classify the good from a given YED. A value such as -0.4 should lead you straight to "inferior," and a value such as 1.8 to "normal good, luxury."
• Apply it to a graph or a scenario. Given that incomes rise and the good is inferior, you shift demand left and state that equilibrium price and quantity both fall.

Common mistakes:

• Dropping the sign. With price elasticity of demand, you often report the absolute value. With YED you must keep the sign, because the sign is the classification.
• Calling a necessity inferior. A YED of 0.3 is a normal good. Only a negative YED means inferior.
• Flipping the ratio. Quantity goes on top and income goes on the bottom. Writing it the other way gives the reciprocal.
• Mixing up the drivers. A negative cross-price elasticity means complements; a negative income elasticity means an inferior good. Same sign, different meaning.
• Moving along the curve. An income change shifts the demand curve. It is not a movement along a fixed curve.

The topic page for AP Micro 2.5, Other Elasticities lists the related terms and calculators for the whole topic.

Summary

Income elasticity of demand divides the percentage change in quantity demanded by the percentage change in income. Use the midpoint method when you have two data points so the answer is the same in both directions. Keep the sign: positive means normal, negative means inferior. Among normal goods, a YED between 0 and 1 marks a necessity and a YED above 1 marks a luxury. Then use the number to predict how demand moves when incomes rise or fall, and show that change as a shift of the demand curve.