Price Elasticity of Demand vs Income Elasticity of Demand
Price Elasticity of Demand and Income Elasticity of Demand are two Elasticity concepts in AP Economics that students often mix up. Price elasticity of demand measures how responsive quantity demanded is to a change in the good's price. Income elasticity of demand measures how responsive the quantity demanded is to a change in consumers' income. Here is how they compare side by side.
It is the percentage change in quantity demanded divided by the percentage change in price. Demand is elastic when the absolute value is greater than 1 and inelastic when it is less than 1. Goods with many substitutes, that take a large share of income, or judged over a longer time horizon tend to be more elastic.
It is calculated as the percentage change in quantity demanded divided by the percentage change in income. Demand is considered a normal good if the ratio is positive, meaning demand increases as income increases. Demand is considered an inferior good if the ratio is negative.
Price vs Income Elasticity: Same Good, Two Different Verdicts
| Price Elasticity of Demand | Income Elasticity of Demand | |
|---|---|---|
| What sits in the denominator | The good's own price, with income held constant | The buyer's income, with every price held constant |
| What the sign tells you | Nothing, since the value is negative for any ordinary demand curve, so the absolute value is reported | Everything, since positive means a normal good and negative means an inferior good |
| What the value 1 marks | The border between elastic and inelastic, where a small price change leaves total revenue unmoved | The border between a normal necessity and a normal luxury, with revenue playing no part |
| What happens on the demand diagram | A movement along one fixed demand curve | A shift of the whole curve to a new position |
| Where the data comes from | Two price and quantity pairs from one market | One quantity pair from that market plus an income figure from outside it |
| What it predicts | Which way total revenue moves after a price change, and how a per-unit tax burden splits | Which firms grow in a boom and which grow in a downturn |
One bus fare can be price elastic and an inferior good at the same time
Take a household's weekly bus trips. When the fare falls from $3.00 to $2.40, trips rise from 40 to 52. Using the midpoint method, quantity changes by 12 over an average of 46, about 26.1 percent, while price changes by 0.60 over an average of 2.70, about 22.2 percent downward. Price elasticity is about 1.17 in absolute value, so bus rides are price elastic. Now hold the fare at $2.40 and raise weekly household income from $500 to $700. Trips fall from 52 to 44, so quantity changes by 8 over an average of 48, about 16.7 percent downward, against an income change of 200 over an average of 600, or 33.3 percent. Income elasticity is negative 0.50. The same good, in the same week, is price elastic and an inferior good. Neither label predicts the other, because the two calculations are driven by different variables. The first divides by a change in the fare, the second by a change in income. Students who assume an inferior good must also be price inelastic are importing a relationship that appears nowhere in either definition.
Dropping the negative sign is harmless for one formula and fatal for the other
Both formulas can produce a negative number, and the two negatives are treated in opposite ways. Price elasticity is negative for every ordinary demand curve, so the sign is predictable, carries no information, and convention reports the absolute value. Saying a bakery's bread has a price elasticity of 0.30 is a complete answer, because nobody doubted the direction. Income elasticity is different, because the sign is the classification. Negative 0.50 says inferior good. A value of 0.40 says normal necessity, positive but proportionally smaller than the income change that caused it. A value of 2.10 says normal luxury. Answering a free-response prompt with the words income elasticity is 0.50 when the calculated figure was negative throws away the only part a grader is scanning for. Build the difference into how you write the two answers. State price elasticity as a magnitude plus one word, elastic or inelastic. State income elasticity as a sign first, then the category that sign implies, then the magnitude and the necessity or luxury reading that follows from it. Two sentences, in that order, and the classification never gets lost.
One elasticity slides you along the curve, the other moves the curve leftward for an inferior good
Price elasticity and income elasticity live in different places on the same diagram. A price change is a movement along a fixed demand curve, so both the price and the quantity in that calculation are read off one curve. An income change shifts the curve, so the quantity in an income elasticity calculation comes from a second curve at the original price. An income elasticity question therefore cannot be answered from a single demand curve: you need a before curve and an after curve. The distinction fixes the vocabulary too. A price change alters quantity demanded. An income change alters demand. Multiple-choice items exploit this constantly by describing a rise in consumer income and offering quantity demanded rises as a tempting answer. For an inferior good the same item can catch you twice, because the shift runs leftward rather than rightward. In the bus example above, income rising from $500 to $700 pushes the demand curve for bus trips to the left, and a student who has corrected the vocabulary error still loses the point by sketching the arrow the other way. Read the sign of your income elasticity before you draw anything.
Frequently asked questions
Can a good be price inelastic and income elastic at the same time?
Price elasticity and income elasticity are independent properties, so one good can easily have both. A specialty coffee might have a price elasticity near 0.4, because buyers keep buying when its price rises, and an income elasticity near 1.8, because they cut back sharply when their income falls. The first number answers how buyers respond to the good's own price, the second answers how they respond to their own budget. Nothing in a demand curve forces the two to agree, since they are calculated from different data.
What does an income elasticity of demand of -0.5 tell you?
An income elasticity of -0.5 identifies an inferior good whose demand is income inelastic. The negative sign says quantity demanded moves opposite to income, so a 10 percent rise in income brings a 5 percent fall in quantity demanded. The size, below 1 in absolute value, says the response is proportionally smaller than the income change that caused it. Both halves earn credit on a free-response question, and the sign is the half students drop. Sellers of such goods, like discount bus travel or store-brand groceries, often see demand hold up during a downturn.
Which elasticity predicts how a recession hits a firm?
Income elasticity of demand is the right tool for a recession question, because a recession changes household income rather than the firm's own price. A firm selling goods with income elasticity above 1 loses sales more than proportionally when income falls, while a firm with negative income elasticity may sell more. Price elasticity answers a separate question: what happens to that firm's revenue if it responds by cutting its own price. A complete answer usually needs both, applied in that order.
Live Elasticity graph. Drag the curves, or open the full version.
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