Source: Demand Theory in Economics, Texas A&M University
Tags: price elasticity of demand, elastic demand, inelastic demand, unit elastic, total revenue test, income elasticity, cross-price elasticity, substitutes, complements, market demand curve, horizontal summation, income distribution, Giffen goods, perfect complements, perfect substitutes, law of demand
Elasticity measures how sensitive quantity demanded is to changes in price, income, or the price of related goods. The type of elasticity determines whether raising or lowering price increases a firm's total revenue. Special cases, including Giffen goods, perfect complements, and perfect substitutes, push the standard model to its limits and clarify exactly when the usual rules do and do not hold.
Market demand curve
The horizontal sum of every individual consumer's demand curve. At each price, add up all individual quantities demanded to get total market quantity demanded.
Law of demand
All else equal, as price falls, quantity demanded rises. The market demand curve therefore slopes downward (with rare exceptions such as Giffen goods).
Price elasticity of demand (ε)
The percentage change in quantity demanded divided by the percentage change in price. Measures how responsive buyers are to price movements.
Elastic demand
|ε| > 1. Quantity demanded changes by a larger percentage than the price change. Demand is highly responsive.
Inelastic demand
|ε| < 1. Quantity demanded changes by a smaller percentage than the price change. Demand is relatively unresponsive.
Unit elastic demand
|ε| = 1. The percentage change in quantity demanded exactly matches the percentage change in price.
Total revenue (TR)
Price multiplied by quantity demanded (TR = P × Q). The direction TR moves after a price change depends on elasticity.
Income elasticity of demand
The percentage change in quantity demanded divided by the percentage change in income. Positive for normal goods, negative for inferior goods.
Cross-price elasticity of demand
The percentage change in quantity demanded of Good A divided by the percentage change in the price of Good B. Positive for substitutes, negative for complements.
Substitutes
Goods that can replace each other in consumption. A rise in the price of one increases demand for the other.
Complements
Goods consumed together. A rise in the price of one decreases demand for the other.
Giffen good
A rare inferior good whose demand increases when its price rises, because the income effect dominates the substitution effect. Violates the law of demand.
Perfect complements
Goods consumed in a fixed ratio (e.g., left and right shoes). L-shaped indifference curves; the substitution effect is zero.
Perfect substitutes
Goods the consumer views as interchangeable at a constant rate. Linear indifference curves; the substitution effect can be total (switching entirely to the cheaper option).
The market demand curve aggregates individual demand.
At a given price, sum every consumer's quantity demanded to get the market quantity.
This is called horizontal summation because you are adding quantities (the horizontal axis), not prices.
The resulting curve slopes downward, consistent with the law of demand.
The aggregation assumes consumers act independently and their individual demand functions are known.
Elasticity is not the same as slope. Two demand curves with identical slopes can have different elasticities at different price-quantity points.
Along a linear demand curve, elasticity changes:
High prices / low quantities: demand tends to be elastic.
Low prices / high quantities: demand tends to be inelastic.
Midpoint: unit elastic.
Determinants of elasticity include availability of substitutes, proportion of income spent on the good, time horizon, and whether the good is a necessity or luxury.
This is the "total revenue test," a practical tool for firms and a common exam topic.
Elastic demand (|ε| > 1)
A price cut increases TR.
The gain in quantity more than offsets the lower price.
Inelastic demand (|ε| < 1)
A price increase raises TR.
The loss in quantity is proportionally smaller than the price gain.
Unit elastic demand (|ε| = 1)
Price changes leave TR unchanged.
Quantity and price effects exactly cancel.
Firms aiming to maximise revenue want to find the price where elasticity equals one, though profit maximisation also depends on costs.
Tells you how demand shifts when consumers get richer or poorer.
Normal goods have positive income elasticity.
Necessities: income elasticity between 0 and 1 (demand rises, but less than proportionally).
Luxuries: income elasticity greater than 1 (demand rises more than proportionally).
Inferior goods have negative income elasticity (demand falls as income rises).
Positive cross-price elasticity: the goods are substitutes.
Example: if the price of tea rises, demand for coffee increases.
Negative cross-price elasticity: the goods are complements.
Example: if the price of printers rises, demand for ink cartridges falls.
A cross-price elasticity near zero suggests the goods are unrelated in consumption.
Market demand depends on how total income is spread across consumers, not just the total level of income.
A good may be normal for high-income households and inferior for low-income households. Redistribution of income between these groups will shift the market demand curve even if aggregate income stays constant.
This matters for policy analysis: tax changes, transfers, and wage shifts can reshape market demand curves for specific goods.
Giffen goods are a rare, extreme case of inferior goods.
Key conditions for a Giffen good:
The good must be inferior (negative income effect on quantity demanded).
The good must take up a large share of the consumer's budget.
Close substitutes must be unavailable or unaffordable.
Mechanism: when the price of a staple rises, the consumer's real income drops so much that they cut spending on other (more expensive) items and buy more of the staple, even though it has become pricier.
Classic example: basic foodstuffs (rice, bread, potatoes) in very low-income settings.
Because the income effect overwhelms the substitution effect, the demand curve for a Giffen good slopes upward over some range.
Perfect complements
Consumed in a fixed ratio (one left shoe with one right shoe).
Indifference curves are L-shaped, with the corner on the line representing the fixed ratio.
When the price of one good changes, the substitution effect is zero; you cannot substitute one for the other.
The entire demand response comes from the income effect (the price change makes the consumer richer or poorer, shifting how many pairs they buy).
Perfect substitutes
The consumer is willing to swap one for the other at a constant rate.
Indifference curves are straight lines.
When relative prices change, the substitution effect can be extreme: the consumer may switch entirely to the cheaper good.
The income effect is negligible or zero if the goods are truly interchangeable.
These two extremes bracket all real-world goods and help build intuition for where the substitution and income effects are each most powerful.
Price elasticity of demand
ε = (% change in Q demanded) / (% change in P) = (ΔQ/Q) / (ΔP/P)
Total revenue
TR = P × Q
Income elasticity of demand
(% change in Q demanded) / (% change in income)
Cross-price elasticity of demand
(% change in Q demanded of Good A) / (% change in price of Good B)
⚠️ The total revenue test is one of the most frequently examined applications of elasticity. Know which direction TR moves for elastic vs inelastic demand after a price change.
⚠️ Elasticity is not the same as slope. A steeper demand curve is not necessarily more inelastic at every point.
⚠️ Giffen goods violate the law of demand. Exams often ask for the conditions required and why the income effect must dominate the substitution effect.
⚠️ For perfect complements, the substitution effect is always zero. For perfect substitutes, the income effect is negligible. These are clean, testable statements.
⚠️ Cross-price elasticity sign tells you the relationship: positive means substitutes, negative means complements. Do not mix this up with the sign convention for price elasticity of demand (which is typically negative but reported in absolute value).
Q: If demand for a good is inelastic and the firm raises its price, what happens to total revenue?
A: Total revenue increases. The proportional drop in quantity demanded is smaller than the proportional rise in price, so P × Q goes up.
Q: A 10% increase in consumer income leads to a 15% increase in demand for Good X. What is the income elasticity, and what type of good is X?
A: Income elasticity = 15% / 10% = 1.5. Good X is a luxury good (a subset of normal goods, with income elasticity greater than 1).
Q: The price of butter rises by 5% and the quantity of margarine demanded rises by 8%. What is the cross-price elasticity, and what is the relationship between butter and margarine?
A: Cross-price elasticity = 8% / 5% = 1.6 (positive). Butter and margarine are substitutes.
Q: Why does the demand curve for a Giffen good slope upward?
A: A Giffen good is an inferior good that absorbs a large share of the consumer's budget. When its price rises, the loss in real purchasing power (income effect) is so large that the consumer cuts back on other goods and buys more of the staple, overwhelming the substitution effect that would normally reduce demand.
Q: For perfect complements, what is the substitution effect of a price change?
A: Zero. Because the goods are consumed in a fixed ratio, a change in relative prices does not lead the consumer to substitute one for the other. The entire demand adjustment comes from the income effect.
Q: Where along a linear demand curve is demand unit elastic?
A: At the midpoint. Above the midpoint (higher prices, lower quantities) demand is elastic; below it (lower prices, higher quantities) demand is inelastic.
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