Difficulty: Introductory | Prerequisites: Basic algebra (percentages, ratios)
Tags: elasticity, price elasticity of demand, cross elasticity, income elasticity, supply elasticity, total revenue test, AP Microeconomics, ECON 101, Unit 2
Elasticity is the core measurement tool of Unit 2. It answers a single question: when one thing changes (price, income, the price of a related good), how much does quantity respond? Every policy question in microeconomics, from tax incidence to price ceilings, depends on the answer. If you can calculate and interpret elasticity coefficients, the rest of supply-and-demand analysis follows from it.
You should already be comfortable with percentage changes, the law of demand, and the basic supply-and-demand diagram. If the phrase "quantity demanded falls when price rises" still feels unfamiliar, review Unit 1 first.
Elasticity measures how sensitive quantity is to a change in price, income, or the price of another good. You divide the percentage change in quantity by the percentage change in the thing that moved. The size of the coefficient tells you whether demand (or supply) is elastic (responsive), inelastic (unresponsive), or unit elastic, and that classification drives everything from tax policy to firm pricing strategy.
Price elasticity of demand (PED)
The ratio of the percentage change in quantity demanded to the percentage change in price. In simple terms, this means: how much do buyers cut back (or buy more) when the price moves?
Elastic demand
Coefficient greater than 1. Quantity responds more than proportionally to a price change. Think of it as: buyers are very sensitive to price here.
Inelastic demand
Coefficient less than 1. Quantity responds less than proportionally to a price change. Think of it as: buyers barely change their behaviour when price moves.
Unit elastic demand
Coefficient equals exactly 1. The percentage change in quantity matches the percentage change in price.
Perfectly elastic demand
Coefficient equals infinity. Any price increase causes quantity demanded to drop to zero. The demand curve is horizontal.
Perfectly inelastic demand
Coefficient equals 0. Quantity demanded does not change at all regardless of price. The demand curve is vertical.
Cross elasticity of demand (XED)
The ratio of the percentage change in quantity demanded of one good to the percentage change in price of a different good. In simple terms, this means: when Good B gets more expensive, do people buy more or less of Good A?
Substitutes
Goods with a positive cross elasticity coefficient. When the price of one rises, quantity demanded of the other rises too.
Complements
Goods with a negative cross elasticity coefficient. When the price of one rises, quantity demanded of the other falls.
Income elasticity of demand (YED)
The ratio of the percentage change in quantity demanded to the percentage change in income. In simple terms, this means: when people earn more, do they buy more or less of this good?
Normal good
Income elasticity coefficient is positive. People buy more of it as income rises.
Inferior good
Income elasticity coefficient is negative. People buy less of it as income rises (they switch to something better).
Price elasticity of supply (PES)
The ratio of the percentage change in quantity supplied to the percentage change in price.
Total revenue test
A shortcut for classifying demand elasticity by observing what happens to total revenue (price times quantity) when price changes.
Measures how responsive quantity demanded is to a change in price
Calculated as: (% change in quantity demanded) / (% change in price)
The coefficient is always negative in theory (law of demand), but we use the absolute value for classification
Greater than 1: elastic (quantity is very responsive)
Less than 1: inelastic (quantity barely budges)
Exactly 1: unit elastic
Infinity: perfectly elastic (horizontal demand curve)
Zero: perfectly inelastic (vertical demand curve)
A practical shortcut to identify elasticity without calculating the coefficient directly.
Price rises and total revenue falls: demand is elastic (the quantity drop more than offsets the higher price)
Price rises and total revenue rises: demand is inelastic (the higher price more than offsets the quantity drop)
Price falls and total revenue rises: demand is elastic
Price falls and total revenue falls: demand is inelastic
Total revenue is maximised at the point where demand is unit elastic
Compares two different goods: (% change in quantity of Good A) / (% change in price of Good B)
The sign of the coefficient tells you the relationship:
Positive coefficient: the goods are substitutes (price of B rises, people buy more of A)
Negative coefficient: the goods are complements (price of B rises, people buy less of A)
Example: if the price of Coca-Cola rises and quantity demanded of Pepsi rises, the cross elasticity is positive, so they are substitutes
Measures how quantity demanded responds to a change in consumer income
Calculated as: (% change in quantity demanded) / (% change in income)
The sign of the coefficient classifies the good:
Positive: normal good (income rises, demand rises)
Negative: inferior good (income rises, demand falls, because consumers switch to a preferred alternative)
Measures how responsive quantity supplied is to a change in price
Calculated as: (% change in quantity supplied) / (% change in price)
The same coefficient thresholds apply (greater than 1 = elastic, less than 1 = inelastic)
Tax revenue = (price with tax minus price seller receives) multiplied by quantity
The more inelastic side of the market bears a larger share of the tax burden
A consumer maximises utility when they allocate spending so that the marginal utility per unit of cost is equal across all goods
Formally: (Marginal Utility of A / Price of A) = (Marginal Utility of B / Price of B)
If the ratio is higher for Good A, the consumer should buy more of A and less of B until the ratios equalise
\text{PED} = \frac{\%\Delta Q_d}{\%\Delta P}\text{XED} = \frac{\%\Delta Q_A}{\%\Delta P_B}\text{YED} = \frac{\%\Delta Q_d}{\%\Delta \text{Income}}\text{PES} = \frac{\%\Delta Q_s}{\%\Delta P}\text{Total Revenue} = P \times Q\text{Tax Revenue} = (P_{\text{with tax}} - P_{\text{seller receives}}) \times Q\frac{MU_A}{P_A} = \frac{MU_B}{P_B}The total revenue test is exactly how firms decide whether to raise or lower prices. A cinema with inelastic demand for tickets on a Friday night can raise prices and earn more, because few people will stay home. A petrol station on a busy road with three competitors faces elastic demand: raise the price by 5p and drivers go next door.
Cross elasticity matters to any company launching a product. If you sell tea and your competitor raises the price of coffee, your sales rise (positive XED, substitutes). If you make printer ink and the price of printers rises, your sales fall (negative XED, complements).
Students often think elastic means "demand changes." Every demand curve shows demand changing. Elastic specifically means quantity changes by a larger percentage than price.
The PED coefficient is technically negative (price up, quantity down), but we use the absolute value. Do not write a negative sign in your answer unless the question specifically asks for it.
A steep demand curve is not automatically inelastic, and a flat one is not automatically elastic. Slope and elasticity are related but not the same thing, because elasticity uses percentages while slope uses absolute changes.
Cross elasticity of zero does not mean the goods are complements. It means they are unrelated. Complements have a negative coefficient.
⚠️ The total revenue test is a near-guaranteed exam topic. Know all four combinations (price up/down paired with TR up/down) cold.
⚠️ You will be asked to classify goods as substitutes, complements, normal, or inferior using the sign of the elasticity coefficient. Positive/negative is the whole answer; do not overthink it.
⚠️ Expect at least one question asking you to calculate an elasticity coefficient from given percentage changes and then interpret the result.
⚠️ The utility maximisation rule appears on free-response sections. If MU/P is not equal across goods, you must be able to say which good the consumer should buy more of.
True or false: if the price elasticity of demand coefficient is 0.6, demand is elastic.
Fill in the blank: if price rises and total revenue also rises, demand is ______.
True or false: a positive cross elasticity coefficient means the two goods are complements.
Fill in the blank: a good with a negative income elasticity coefficient is called a(n) ______ good.
True or false: the utility maximisation rule requires MU/P to be equal across all goods consumed.
Answers: 1. False (0.6 < 1, so inelastic). 2. Inelastic. 3. False (positive = substitutes). 4. Inferior. 5. True.
Q: The price of good X rises by 10% and quantity demanded falls by 15%. What is the price elasticity of demand, and is demand elastic or inelastic?
A: PED = 15% / 10% = 1.5. Because 1.5 > 1, demand is elastic.
Q: When the price of butter rises, the quantity demanded of margarine increases. What type of relationship do butter and margarine have, and what is the sign of their cross elasticity coefficient?
A: They are substitutes. The cross elasticity coefficient is positive.
Q: A consumer's income rises by 20% and their quantity demanded of instant noodles falls by 5%. Is this a normal good or an inferior good?
A: Inferior good. The income elasticity coefficient is negative (quantity fell while income rose).
Q: A firm raises its price and total revenue increases. What can you conclude about the elasticity of demand for this product?
A: Demand is inelastic. The price increase was not offset by a proportional drop in quantity, so revenue rose.
Q: A consumer spends their entire budget on goods A and B. MU of A is 20 and its price is 5. MU of B is 30 and its price is 10. Is this consumer maximising utility? If not, what should they do?
A: MU(A)/P(A) = 20/5 = 4. MU(B)/P(B) = 30/10 = 3. The ratios are not equal, so utility is not maximised. The consumer should buy more of A and less of B until the ratios equalise.
Elasticity feeds directly into Unit 3 (Production Markets). The total revenue test reappears when analysing how firms set prices, and whether a firm faces elastic or inelastic demand determines its pricing power.
The tax revenue formula connects to Unit 5 (Government). The incidence of a tax, meaning who actually bears the cost, depends on the relative elasticities of supply and demand. The more inelastic side pays more of the tax.
The utility maximisation rule bridges to consumer theory more broadly and reappears in modified form in the resource markets unit (Unit 4), where the least-cost rule applies the same logic to inputs rather than consumer goods.
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