Difficulty: Intermediate | Prerequisites: Introductory microeconomics (supply and demand basics, profit concepts)
Demand analysis and elasticity sit at the heart of managerial economics. Every pricing decision, every revenue forecast, every market-entry call depends on understanding how consumers respond to changes in price, income and the prices of related goods. If you missed the first few weeks on basic supply-and-demand mechanics, revisit those before diving in here. This topic bridges pure micro theory and the applied decision-making that the rest of the course builds on.
The demand function maps the relationship between quantity demanded and the variables that drive it (price, income, preferences, related goods' prices). Elasticity measures how sensitive demand is to a change in any one of those variables. Managers use elasticity to set prices, forecast revenue and decide which markets to enter.
Demand function
A mathematical expression showing how quantity demanded (Qd) varies with price (P), consumer income (I), the prices of related goods (Pr), and other factors such as tastes or expectations. In simple terms, it is the formula that tells you how many units people will buy under a given set of conditions.
Price elasticity of demand (PED)
The percentage change in quantity demanded divided by the percentage change in price. Think of it as a measure of how jumpy consumers are when you move the price up or down. A PED of -2 means a 1% price increase causes a 2% drop in quantity demanded.
Elastic demand
Demand where |PED| > 1, meaning consumers are highly responsive to price changes. In simple terms, even a small price rise drives a proportionally larger drop in sales.
Inelastic demand
Demand where |PED| < 1, meaning consumers are relatively unresponsive to price changes. Think of it as products people will keep buying regardless of modest price shifts (petrol, insulin, salt).
Unit elastic demand
Demand where |PED| = 1. The percentage change in quantity demanded exactly matches the percentage change in price, so total revenue stays constant when price moves.
Income elasticity of demand
The percentage change in quantity demanded divided by the percentage change in consumer income. It tells you whether a good is normal (positive value, demand rises with income) or inferior (negative value, demand falls as income rises).
Cross-price elasticity of demand
The percentage change in quantity demanded of good A divided by the percentage change in price of good B. A positive value means the goods are substitutes (if B gets pricier, people switch to A). A negative value means the goods are complements (if B gets pricier, people buy less of A too).
The general form is Qd = f(P, I, Pr, T, E), where P = own price, I = income, Pr = related goods' prices, T = tastes, E = expectations.
A movement along the demand curve is caused by a change in the good's own price.
A shift of the entire demand curve is caused by a change in any other variable (income, preferences, related goods' prices).
Distinguish carefully between a change in quantity demanded (movement) and a change in demand (shift).
Formula: PED = (% change in Qd) / (% change in P)
PED is almost always negative (law of demand), but we often refer to its absolute value.
Determinants of PED:
Availability of close substitutes (more substitutes = more elastic)
Proportion of income spent on the good (higher proportion = more elastic)
Time horizon (longer time = more elastic, because consumers can adjust)
Necessity vs. luxury (necessities tend to be inelastic)
Revenue implications:
If demand is elastic (|PED| > 1): a price cut increases total revenue
If demand is inelastic (|PED| < 1): a price increase increases total revenue
If demand is unit elastic (|PED| = 1): total revenue is maximised at the current price
Formula: YED = (% change in Qd) / (% change in income)
Normal goods: YED > 0 (demand rises with income)
Necessities: 0 < YED < 1 (demand rises, but less than proportionally)
Luxuries: YED > 1 (demand rises more than proportionally)
Inferior goods: YED < 0 (demand falls as income rises, e.g. instant noodles, budget bus travel)
Formula: XED = (% change in Qd of A) / (% change in price of B)
Substitutes: XED > 0 (Coca-Cola and Pepsi)
Complements: XED < 0 (printers and ink cartridges)
Unrelated goods: XED ≈ 0
Pricing decisions: firms with inelastic demand can raise prices to boost revenue; firms facing elastic demand should consider cutting prices or adding value.
Product positioning: understanding cross-price elasticity helps firms anticipate how competitors' pricing moves will affect their own sales.
Market segmentation: income elasticity data guides decisions about which income brackets to target with premium vs. budget product lines.
PED = \frac{\%\Delta Q_d}{\%\Delta P}YED = \frac{\%\Delta Q_d}{\%\Delta I}XED = \frac{\%\Delta Q_d^A}{\%\Delta P^B}Midpoint (arc) elasticity formula, often used in exam calculations:
PED = \frac{(Q_2 - Q_1) / [(Q_2 + Q_1)/2]}{(P_2 - P_1) / [(P_2 + P_1)/2]}Airlines use price elasticity to segment business and leisure travellers. Business travellers have inelastic demand (they need to fly regardless), so airlines charge them premium fares. Leisure travellers are elastic, so airlines offer discounts and advance-purchase deals to fill seats.
Supermarkets use cross-price elasticity when deciding how to respond to a competitor's price cut on a substitute product, or when bundling complements (e.g. discounting razor handles to sell blades).
Students often think PED is always positive. It is not. PED is negative by definition (law of demand), though we frequently discuss its absolute value.
Students confuse a movement along the demand curve with a shift of the demand curve. A price change causes a movement; everything else causes a shift.
Students sometimes assume that inelastic demand means quantity demanded does not change at all. It does change, just less than proportionally to the price change.
Students mix up the revenue implications: they assume a price increase always raises revenue. It does so only when demand is inelastic.
⚠️ Elasticity and total revenue is one of the most commonly tested relationships. Know which direction revenue moves for elastic vs. inelastic demand when price changes.
⚠️ Midpoint formula calculations appear frequently. Practise plugging in numbers until the arithmetic is automatic.
⚠️ Interpreting the sign and magnitude of cross-price and income elasticity (substitutes vs. complements, normal vs. inferior) is a staple of multiple-choice sections.
True or false: If PED = -0.5, a 10% price increase will cause a 5% decrease in quantity demanded. (True)
Fill in the blank: A good with an income elasticity of -0.3 is classified as a(n) _______ good. (Inferior)
True or false: Cross-price elasticity between two substitute goods is negative. (False, it is positive)
Fill in the blank: Total revenue is maximised when price elasticity of demand equals _______. (Unit elastic, |PED| = 1)
Q: If the price elasticity of demand for a product is -2, and the company raises its price by 10%, what happens to quantity demanded?
A: Quantity demanded decreases by 20%. Since |PED| = 2 and the price rose by 10%, the percentage change in Qd = 2 x 10% = 20% (decrease, because PED is negative).
Q: A firm sells 1,000 units at £10 each. PED = -1.5. If the firm cuts price to £9, estimate the new quantity and the change in total revenue.
A: The price dropped by 10%. With PED = -1.5, quantity demanded rises by 15%, from 1,000 to 1,150 units. Old revenue = £10,000. New revenue = £9 x 1,150 = £10,350. Revenue rises by £350 because demand is elastic (|PED| > 1) and the price was cut.
Q: Coffee and sugar have a cross-price elasticity of -0.6. What does this tell you about the relationship between the two goods?
A: They are complements. The negative sign means that when the price of one rises, the quantity demanded of the other falls. Consumers buy them together.
Q: During a recession, demand for branded cereal falls while demand for own-label cereal rises. Classify each by income elasticity.
A: Branded cereal is a normal good (positive income elasticity, demand falls with falling income). Own-label cereal is an inferior good (negative income elasticity, demand rises as income falls).
This connects to Production and Cost Analysis because elasticity determines revenue, which in turn determines the profit-maximising output level when combined with cost curves. It also connects to Market Structures and Pricing: firms in monopolistic competition or monopoly have more control over price precisely because they face less elastic demand than firms in perfect competition.
Price elasticity, PED, income elasticity, YED, cross-price elasticity, XED, demand function, elastic, inelastic, unit elastic, normal good, inferior good, luxury good, necessity, substitutes, complements, total revenue test, midpoint formula, arc elasticity, demand curve shift, movement along demand curve, managerial economics MGT 301, demand analysis