2.5 Other Elasticities

Other elasticities measure how quantity demanded responds to things besides a good's own price. Income elasticity of demand (Ey) tells you whether a good is normal or inferior, and cross price elasticity of demand (Exy) tells you whether two goods are substitutes, complements, or unrelated.

Why This Matters for the AP Microeconomics Exam

Elasticity questions show up as both calculations and interpretation. With income and cross-price elasticity, you need to compute a coefficient from data and then read the sign to classify a good or describe a relationship between two goods. On multiple-choice, expect numbers in a table or short scenario. On free response, you may need to calculate a value, state what it means, and explain how a demand curve shifts as a result. Getting the sign and the classification correct is where points are won or lost.

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Key Takeaways

• Elasticity can measure responsiveness to any determinant of demand or supply, not just the good's own price.
• Income elasticity of demand (Ey) = percentage change in quantity demanded / percentage change in income.
• A positive Ey means a normal good; a negative Ey means an inferior good.
• Cross-price elasticity of demand (Exy) = percentage change in quantity demanded of one good / percentage change in the price of another good.
• A positive Exy means the goods are substitutes; a negative Exy means complements; a value near zero means unrelated.
• For these elasticities, the sign matters, so do not drop negatives the way you might with price elasticity of demand.

Income Elasticity of Demand

Income elasticity of demand measures how sensitive quantity demanded is to a change in consumers' income. The core question: when income changes by some percent, does quantity demanded rise, fall, or stay the same?

The formula is:

Ey = %ΔQd / %ΔI

where I is income.

The sign of the answer classifies the good:

• Normal good: Ey is positive. When income rises, demand rises. Most goods fall here.
• Inferior good: Ey is negative. When income rises, demand falls. Examples include used textbooks or generic ramen, since people may switch to higher-quality options as income grows.

Keep the negative sign when you calculate income elasticity. Unlike price elasticity of demand, where the sign is always negative and often ignored, here the sign is the whole point.

Worked Examples

A 4% increase in consumer income leads to a 1% increase in the quantity demanded for pencils. What type of good are pencils?

• Answer: Normal good.
• Why: Ey = +1% / +4% = 0.25. The coefficient is positive, so pencils are a normal good.

A 12% increase in consumer income leads to a 10% decrease in the quantity demanded for used textbooks. What type of good are used textbooks?

• Answer: Inferior good.
• Why: Ey = -10% / +12% = -0.83. The coefficient is negative, so used textbooks are an inferior good.

A positive coefficient (normal good) means demand rises when income rises, shown as a rightward shift of the demand curve. A negative coefficient (inferior good) means demand falls when income rises, shown as a leftward shift. Firms can use income elasticity to predict how demand for their products will change as consumer incomes rise or fall.

Cross-Price Elasticity of Demand

Cross-price elasticity of demand measures how sensitive the quantity demanded of one good (good A) is to a change in the price of another good (good B). Economists use it to figure out whether two goods are substitutes, complements, or unrelated.

The formula is:

Exy = %ΔQd of good A / %ΔP of good B

The sign tells you the relationship:

• Substitutes: Exy is positive. When the price of one good rises, people buy more of the other. Example: if soda gets more expensive, demand for water may rise.
• Complements: Exy is negative. When the price of one good rises, demand for the other falls because they are used together. Example: printers and ink.
• Unrelated: Exy is near zero. A price change in one good has little to no effect on the other.

This elasticity answers questions like:

• If the price of Pepsi increases, what happens to the demand for Coca-Cola, a substitute?
• If the price of milk decreases, what happens to the demand for cereal, a complement?

These named brands and products are illustrative examples, not required AP content. What you are expected to know is how to compute the coefficient and read its sign.

How to Use This on the AP Microeconomics Exam

Problem Solving

• Identify which elasticity the question wants. If income changes, use income elasticity. If the price of a different good changes, use cross-price elasticity.
• Plug into the correct formula and compute a numeric coefficient. Show your work.
• Keep the sign. The sign drives the classification for both income and cross-price elasticity.

Free Response

• After calculating, state the classification clearly (normal vs. inferior, or substitutes vs. complements vs. unrelated).
• If asked, connect the result to a demand shift. For a normal good, a rise in income shifts demand right. For complements, a rise in one good's price shifts demand for the other left.
• Use ceteris paribus thinking: you are isolating one cause at a time.

Common Trap

• Mixing up the numerator and denominator. The numerator is always the percentage change in quantity demanded; the denominator is the percentage change in income or in the other good's price.
• Confusing a movement along a curve with a shift. Income and cross-price changes shift the demand curve for the good you are analyzing; they are not movements along its own demand curve.

Common Misconceptions

• "Drop the negative like in price elasticity." For income and cross-price elasticity, the sign is the answer. Keep it.
• "A high income elasticity means the good is expensive." Elasticity measures responsiveness, not price level. A good can be cheap and still be highly income-elastic.
• "Cross-price elasticity tells you about one good's own price." No. It compares one good's quantity demanded to a different good's price. Own-price effects are price elasticity of demand.
• "Slope equals elasticity." Slope and elasticity are not the same thing. Elasticity uses percentage changes, so it can vary even along a straight-line curve.
• "Zero cross-price elasticity means the goods are substitutes." A value near zero means the goods are unrelated. Positive means substitutes; negative means complements.

Related AP Microeconomics Guides

• 2.1 Demand
• 2.3 Price Elasticity of Demand
• 2.6 Market Equilibrium and Consumer and Producer Surplus
• 2.8 The Effects of Government Intervention in Markets
• 2.2 Supply
• 2.7 Market Disequilibrium and Changes in Equilibrium