Substitution Effect vs Cross-Price Elasticity of Demand
Substitution Effect and Cross-Price Elasticity of Demand are related concepts in AP Economics that students often mix up. The substitution effect is the change in quantity demanded when a price change makes a good relatively cheaper or pricier than its alternatives. Cross-price elasticity of demand measures how responsive the quantity demanded of one good is to a change in the price of another good. Here is how they compare side by side.
When a good's price falls, consumers substitute toward it and away from now relatively more expensive substitutes, raising quantity demanded. It always moves opposite to the price change. With the income effect, it explains the downward-sloping demand curve.
It is calculated as the percentage change in quantity demanded of Good A divided by the percentage change in price of Good B. If the ratio is positive, the goods are considered substitutes. If the ratio is negative, the goods are considered complements.
Substitution Effect vs Cross-Price Elasticity: One Price Change, Two Different Quantities
| Substitution Effect | Cross-Price Elasticity of Demand | |
|---|---|---|
| Whose price moved | The price of the good being analysed | The price of a different good |
| Whose quantity you track | The same good whose price moved | The other good |
| What kind of thing it is | A theoretical split of one movement along a demand curve | A measured coefficient you can calculate |
| Direction it takes | Always opposite to the change in relative price | Positive, negative or near zero depending on the pair |
| Formula | None, it is a decomposition | Percentage change in quantity of one good over percentage change in the price of another |
| What it is used to explain | Why demand slopes downward even for inferior goods | Whether two goods are substitutes, complements or unrelated |
| Its usual partner in the syllabus | The income effect | Income elasticity, the other classifying elasticity |
One price rise sets off two separate measurements
Push coffee from an illustrative $4 to $5 and watch two quantities at once. Coffee sales fall from 50 to 40 a day. Tea sales rise from 30 to 36. Take the coffee response first, using the midpoint method: quantity changes by 10 over the average of 45, which is 22.22 percent, and price changes by 1 over the average of 4.50, which is also 22.22 percent, so the price elasticity of demand for coffee is exactly 1. That total fall of 10 cups is what gets split. Part of it is the substitution effect, buyers moving to tea because coffee is now dearer relative to it. The rest is the income effect, since $5 coffee leaves the same wallet able to buy less of everything. Exams rarely ask for the size of each part. Now take the tea response, which is a different calculation entirely: quantity changes by 6 over the average of 33, which is 18.18 percent, and dividing by the 22.22 percent coffee price change gives about 0.82. Positive, so tea and coffee are substitutes. Run other pairs at /calculate/cross-price-elasticity.
The substitution effect has a fixed sign; the cross-price coefficient does not
Whenever a good becomes dearer relative to its alternatives, the substitution effect moves buyers away from it. That direction never changes, for normal goods and inferior goods alike, which is why it is the part of the story that keeps demand curves sloping downward. Cross-price elasticity offers no such guarantee, because it depends on how the two goods sit together. Suppose a printer rises from $80 to $100 and monthly cartridge sales fall from 60 to 48. The price change is 20 over the average of 90, which is 22.22 percent, and the quantity change is 12 over the average of 54, which is also 22.22 percent, giving a coefficient of negative 1. Cartridges and printers are complements, so buyers of one bought less of the other. A different pair, such as tea and coffee, returns a positive figure, and an unrelated pair returns something close to zero. So the substitution effect tells you the direction within one good, and the cross-price coefficient tells you the relationship between two. The other half of the split is at /glossary/income-effect.
Frequently asked questions
Is the substitution effect the same as cross-price elasticity of demand?
No, the substitution effect is one part of a consumer's response to a change in a good's own price, capturing the switch toward relatively cheaper alternatives, while cross-price elasticity is a number measuring how the quantity of one good responds to a change in another good's price. One is a theoretical split and the other is a calculation. They are related, since strong substitution between two goods usually shows up as a large positive cross-price coefficient.
Does a positive cross-price elasticity mean the goods are substitutes?
Yes, a positive value means a rise in one good's price pushes buyers toward the other, which is what being substitutes means. A negative value means the goods are complements and are bought together. A value near zero means the two are largely unrelated in the buyer's mind.
Can the substitution effect ever increase demand for the good whose price rose?
No, the substitution effect always moves buyers away from a good that has become relatively more expensive. Only the income effect can push the other way, and it does so for inferior goods. In the rare case where that opposing income effect outweighs the substitution effect, the result is a Giffen good and the demand curve slopes upward.
Live Elasticity graph. Drag the curves, or open the full version.
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