Difficulty: Introductory to Intermediate | Prerequisites: Part 1 (Foundational Concepts) and Part 2 (Supply and Demand basics)
Elasticity answers a question that supply and demand alone cannot: by how much does quantity respond when price, income or the price of another good changes? Knowing the direction of a shift is useful, but knowing the magnitude is what lets firms set prices, governments predict tax revenue and economists forecast market outcomes. This unit introduces four types of elasticity, each with its own formula and interpretation. You need to be comfortable with percentage changes and the basic supply-and-demand model before this will click.
Elasticity measures how sensitive one variable is to a change in another, expressed as a ratio of percentage changes. Price elasticity of demand (PED) is the most tested type. If demand is elastic, a price increase causes a proportionally larger drop in quantity demanded and total revenue falls. If demand is inelastic, quantity barely moves and total revenue rises.
Price Elasticity of Demand (PED)
Measures how responsive the quantity demanded of a good is to a change in its own price. Calculated as % change in quantity demanded divided by % change in price. Always negative (law of demand), but typically reported as an absolute value.
Think of it as: how much do buyers flinch when the price moves?
Price Elasticity of Supply (PES)
Measures how responsive the quantity supplied is to a change in price. Calculated as % change in quantity supplied divided by % change in price. Always positive (law of supply).
Think of it as: how quickly can producers ramp up when the price rises?
Income Elasticity of Demand (YED)
Measures how responsive demand is to a change in consumer income. Positive for normal goods (demand rises with income), negative for inferior goods (demand falls with income).
In simple terms, this means: do people buy more or less of this when they get richer?
Cross-Price Elasticity of Demand (XED)
Measures how responsive the demand for one good is to a change in the price of another good. Positive for substitutes, negative for complements.
Think of it as: when Pepsi gets more expensive, do people buy more Coke (substitutes, positive XED) or less rum (complements, negative XED)?
Elastic Demand
PED > 1 (in absolute value). Quantity demanded is highly responsive to price changes. A small price increase leads to a proportionally larger drop in quantity.
Inelastic Demand
PED < 1 (in absolute value). Quantity demanded is not very responsive to price changes. Necessities like insulin or petrol tend to be inelastic.
Unit Elastic
PED = 1 (in absolute value). The percentage change in quantity demanded exactly equals the percentage change in price. Total revenue is maximised at this point.
Normal Good
A good for which demand increases when income rises. YED is positive. Examples: restaurant meals, new clothing, holidays.
Inferior Good
A good for which demand decreases when income rises. YED is negative. Examples: instant noodles, bus tickets (when people switch to cars).
Substitute Goods
Goods that can replace each other. When the price of one rises, demand for the other rises. XED is positive. Examples: Coke and Pepsi, butter and margarine.
Complement Goods
Goods that are used together. When the price of one rises, demand for the other falls. XED is negative. Examples: printers and ink cartridges, cars and petrol.
PED = % change in quantity demanded / % change in price.
Because demand curves slope downward, PED is negative, but the exam typically works with the absolute value.
Elastic (|PED| > 1): Quantity responds more than proportionally. Demand curves are relatively flat. Goods with many substitutes or that are luxuries tend to be elastic.
Inelastic (|PED| < 1): Quantity responds less than proportionally. Demand curves are relatively steep. Necessities, habit-forming goods and goods with few substitutes tend to be inelastic.
Unit elastic (|PED| = 1): Percentage changes are equal. Total revenue is at its maximum.
Perfectly elastic (|PED| = ∞): A horizontal demand curve. Any price increase causes quantity demanded to drop to zero.
Perfectly inelastic (|PED| = 0): A vertical demand curve. Quantity demanded does not change regardless of price.
Total revenue test: If price rises and total revenue rises, demand is inelastic. If price rises and total revenue falls, demand is elastic.
PES = % change in quantity supplied / % change in price.
PES is always positive.
Supply tends to be more elastic in the long run (firms can adjust capacity) and more inelastic in the short run (capacity is fixed).
Goods that are easy to store, produced with readily available inputs, or made with spare capacity tend to have more elastic supply.
YED = % change in quantity demanded / % change in income.
Normal goods (YED > 0): Demand rises with income. Subdivided into necessities (0 < YED < 1) and luxuries (YED > 1).
Inferior goods (YED < 0): Demand falls as income rises. Consumers switch to higher-quality substitutes.
XED = % change in quantity demanded of Good X / % change in price of Good Y.
Substitutes (XED > 0): When Good Y's price rises, demand for Good X rises. The higher the XED, the closer the substitutes.
Complements (XED < 0): When Good Y's price rises, demand for Good X falls.
Unrelated goods (XED ≈ 0): A price change in one has no meaningful effect on demand for the other.
PED = \frac{\%\Delta Q_d}{\%\Delta P}PES = \frac{\%\Delta Q_s}{\%\Delta P}YED = \frac{\%\Delta Q_d}{\%\Delta \text{Income}}XED = \frac{\%\Delta Q_d \text{ of Good X}}{\%\Delta P \text{ of Good Y}}Where %Δ means "percentage change in."
Percentage change is calculated as: (New Value - Old Value) / Old Value × 100.
On the AP exam, the midpoint method may be required: use the average of old and new values in the denominator rather than the old value alone.
Governments use PED to predict the effect of excise taxes. Taxing goods with inelastic demand (cigarettes, petrol) raises substantial revenue because consumers keep buying nearly the same quantity. Taxing goods with elastic demand raises less revenue because consumers switch to alternatives.
Supermarkets use XED to decide which products to place near each other and which to put on promotion. A deep discount on printers (complement) drives sales of high-margin ink cartridges.
Students often think that PED is positive. It is negative (quantity demanded falls when price rises). The exam uses absolute values, but the underlying sign matters when interpreting the formula.
Many students confuse elastic with inelastic. A flat demand curve is elastic (quantity is very responsive); a steep curve is inelastic (quantity barely moves). Students frequently get this backwards.
Students sometimes think YED tells you whether a good is a substitute or a complement. It does not. YED tells you whether a good is normal or inferior. XED tells you about substitutes and complements.
A common error is forgetting to use the midpoint method when the question asks for it. The midpoint method uses the average of old and new values in the denominator, which gives a consistent answer regardless of the direction of the change.
⚠️ PED and the total revenue test are among the most frequently tested concepts on the AP Micro exam. Be prepared to calculate PED from a table or graph and then explain what happens to total revenue.
⚠️ The exam will give you a scenario and ask whether a good is a substitute or complement based on the sign of XED, or whether it is normal or inferior based on the sign of YED.
⚠️ Free-response questions often combine elasticity with tax incidence: the more inelastic side of the market bears a greater share of the tax burden.
⚠️ Know the determinants of PED: number of substitutes, necessity vs luxury, proportion of income spent, and time horizon.
True or False: If PED = 0.5, demand is elastic. (False. PED < 1 means demand is inelastic.)
Fill in the blank: A positive cross-price elasticity means the two goods are ______ . (Substitutes.)
True or False: If a firm raises its price and total revenue increases, demand for its product is inelastic. (True.)
Fill in the blank: A good with a negative income elasticity of demand is called a(n) ______ good. (Inferior.)
True or False: PES is typically higher in the long run than in the short run. (True. Firms can adjust capacity over time.)
Q: The price of a good rises from £10 to £12, and quantity demanded falls from 100 to 80 units. Calculate PED using the simple percentage-change method.
A: % change in Qd = (80 - 100) / 100 × 100 = -20%. % change in P = (12 - 10) / 10 × 100 = 20%. PED = -20% / 20% = -1.0. In absolute value, PED = 1.0 (unit elastic).
Q: The income elasticity of demand for a good is -0.4. Is this good normal or inferior? Is demand for it income-elastic or income-inelastic?
A: Inferior (YED is negative, meaning demand falls as income rises). Demand is income-inelastic because the absolute value is less than 1.
Q: The price of tea rises by 10%, and the quantity demanded of coffee rises by 15%. What is the cross-price elasticity, and what is the relationship between the two goods?
A: XED = 15% / 10% = 1.5. The positive sign tells us tea and coffee are substitutes.
Q: A government imposes a per-unit tax on a good with very inelastic demand and relatively elastic supply. Who bears the greater burden of the tax?
A: Consumers bear the greater burden. When demand is more inelastic than supply, consumers cannot easily reduce their purchases, so sellers pass most of the tax on to buyers through higher prices.
Q: Why does PES tend to be higher in the long run?
A: In the long run, firms can build new factories, hire more workers, adopt new technologies and enter or exit the market. In the short run, capacity is largely fixed, so quantity supplied cannot respond as much to a price change.
Elasticity connects directly to tax incidence and deadweight loss. The more inelastic the demand or supply, the smaller the deadweight loss from a tax, and the more of the tax burden falls on that side of the market.
PED is central to understanding how firms with market power (monopolies, oligopolies) set prices. A monopolist chooses to produce where MR = MC, and the gap between price and marginal cost depends on the elasticity of demand it faces.
YED connects to the demand-shifter "income" from Part 2. When you are told income has risen, YED tells you by how much demand shifts and in which direction.
Price elasticity of demand, PED, price elasticity of supply, PES, income elasticity of demand, YED, cross-price elasticity, XED, elastic, inelastic, unit elastic, perfectly elastic, perfectly inelastic, total revenue test, midpoint method, normal good, inferior good, luxury good, necessity, substitute goods, complement goods, complementary goods, determinants of elasticity, tax incidence, tax burden, deadweight loss and elasticity, AP Micro elasticity, AP Microeconomics Unit 2