Price, income and cross elasticities of demand — AQA A-Level Economics

Elasticities of demand measure the responsiveness of quantity demanded to changes in price (PED), real consumer income (YED), and the price of related goods (XED). Mastery of these measures is essential for AQA A-Level Economics students to evaluate firm revenue strategies, product classification, and the incidence of government interventions.

Elasticities of demand quantify the sensitivity of buyers to key market variables: price, consumer income, and the prices of interrelated goods. Understanding these concepts enables economists to predict changes in market equilibrium and examine consumer behaviour beyond simple directional shifts in demand curves.

For AQA A-Level Economics, elasticity acts as a critical analytical engine across both micro and macro modules. It governs pricing strategies, profit maximisation, indirect tax incidence, subsidy efficacy, and international trade performance under exchange rate fluctuations via the Marshall-Lerner condition.

• →Price Elasticity of Demand (PED = % change in QD / % change in P): Measures responsiveness to price. Dictates whether total revenue moves with price (inelastic, PED < 1) or opposite to price (elastic, PED > 1).
• →Income Elasticity of Demand (YED = % change in QD / % change in Y): Measures responsiveness to real income changes. Distinguishes normal necessities (0 < YED < 1), normal luxuries (YED > 1), and inferior goods (YED < 0).
• →Cross Elasticity of Demand (XED = % change in QD of Good A / % change in P of Good B): Measures responsiveness of demand for one good to price changes in another. Identifies substitutes (XED > 0), complements (XED < 0), and unrelated goods (XED = 0).
• →Revenue Maximisation Condition: Total revenue is maximised at the price where PED = -1 (unitary elasticity), which corresponds to marginal revenue (MR) equal to zero.

• Correctly calculate the percentage change in quantity demanded using (new - original) / original × 100.
• Correctly calculate the percentage change in the relevant independent variable (price, income, or price of good B).
• Apply the correct elasticity formula by placing the percentage change in quantity demanded as the numerator.
• State the final elasticity value with the correct positive or negative sign, as this indicates the nature of the relationship.
• Define a normal good as having a positive income elasticity of demand (YED > 0).
• Define an inferior good as having a negative income elasticity of demand (YED < 0).
• Distinguish between normal necessities (0 < YED < 1) and normal luxuries (YED > 1).
• Explain that as real incomes rise during an economic boom, demand for normal goods increases while demand for inferior goods decreases.
• Define cross elasticity of demand and state its formula.
• Explain that a positive XED indicates substitute goods, as an increase in the price of one leads to an increase in demand for the other.
• Explain that a negative XED indicates complementary goods, as an increase in the price of one leads to a decrease in demand for the other.
• Interpret the magnitude of the XED value, noting that values further from zero indicate stronger relationships between the goods.
• Apply XED to business decision-making, such as anticipating the effects of a rival's pricing strategy.
• Define total revenue as price multiplied by quantity, and state its equivalence to consumers' total expenditure.
• Explain that when demand is price elastic, a reduction in price leads to an increase in total revenue.
• Explain that when demand is price inelastic, an increase in price leads to an increase in total revenue.
• Identify that total revenue is maximised when price elasticity of demand is exactly unitary.
• Use a diagram to illustrate the relationship between PED and total revenue along a downward-sloping linear demand curve.
• Identify the sign of the elasticity coefficient to determine the nature of the relationship (e.g., positive YED for normal goods, negative XED for complements).
• Evaluate the magnitude of the coefficient to determine whether demand is elastic (greater than 1 or less than -1) or inelastic (between -1 and 1).
• Explain the implications of a specific PED value for total revenue when prices change.
• Use XED values to assess the strength of the relationship between two goods, noting that values further from zero indicate stronger substitutes or complements.

• 💡Always write out the full formula before substituting your numbers to secure method marks if your final calculation is incorrect.
• 💡Double-check whether the question provides absolute figures or percentage changes before starting your calculation.
• 💡Pay close attention to the sign of your final answer, especially for XED and YED, as this defines the relationship between the variables.
• 💡Use specific examples, such as public transport for inferior goods and restaurant meals for luxury goods, to illustrate your explanations.
• 💡When evaluating the impact of a recession, explicitly link falling incomes to an increase in demand for inferior goods.
• 💡Remember that a good can change classification depending on the income level of the consumer; what is a normal good for a low-income earner might be an inferior good for a high-income earner.
• 💡Always state the XED formula before performing any calculations to secure method marks.
• 💡Use the sign of the XED result to explicitly state whether the goods are substitutes or complements in your analysis.
• 💡Discuss the implications of XED for a firm's pricing strategy or its vulnerability to competitors' price changes in evaluation questions.
• 💡Draw a total revenue curve below a linear demand curve to visually demonstrate where revenue is maximised at unitary elasticity.
• 💡When evaluating a firm's decision to change prices, always consider the likely PED of their product to determine the effect on total revenue.
• 💡Remember that consumers' total expenditure on a good is exactly equal to the firms' total revenue from selling that good.
• 💡Always state whether the numerical value indicates elastic or inelastic demand before applying it to the specific context of the question.
• 💡When given a data extract, use the specific elasticity figures provided to support your evaluation of pricing strategies.
• 💡Explicitly mention the strength of the relationship (e.g., 'strong substitutes') when interpreting XED values significantly greater than +1 or less than -1.
• 💡Always state the full formula before substituting numbers into calculation questions to secure partial method marks even if an arithmetic error occurs.
• 💡In 25-mark essay questions, use elasticity values as an evaluative tool: argue that the real-world success of an indirect tax or tariff depends entirely on the numerical magnitude of PED and the availability of substitutes.

• Inverting the formula by dividing the percentage change in price by the percentage change in quantity; always place quantity demanded on the top (numerator).
• Forgetting to include the negative sign for PED or inferior goods; always retain the mathematical sign resulting from the calculation.
• Calculating the absolute change instead of the percentage change; ensure you divide the difference by the original value and multiply by 100.
• Confusing inferior goods with goods of low physical quality; correct this by defining inferior goods strictly by their negative relationship with income.
• Stating that a YED of -1.5 indicates a normal good because the number is large; correct this by recognising that any negative YED signifies an inferior good.
• Failing to distinguish between necessities and luxuries within normal goods; always specify that luxuries have a YED greater than positive one.
• Confusing the sign of XED for substitutes and complements. Correction: Remember that substitutes have a positive XED because an increase in the price of one increases demand for the other, while complements have a negative XED.
• Inverting the XED formula. Correction: Always place the percentage change in quantity demanded of Good A on the numerator and the percentage change in price of Good B on the denominator.
• Ignoring the magnitude of the XED value. Correction: State whether the goods are close or weak substitutes or complements based on how far the value is from zero.
• Assuming that an increase in price always leads to an increase in total revenue. Correction: Explain that a price increase only raises total revenue if demand is price inelastic.
• Confusing total revenue with profit. Correction: Clearly distinguish between total revenue (price multiplied by quantity) and profit (total revenue minus total costs).
• Stating that inelastic demand means quantity demanded does not change at all. Correction: Clarify that inelastic demand means quantity demanded changes by a smaller percentage than the percentage change in price, not that it remains perfectly constant.
• Error: Ignoring the negative sign for PED and assuming a value of -0.5 is elastic because it is a 'large' negative number. Correction: Always look at the absolute value (magnitude) of PED; -0.5 has a magnitude less than 1, so it is inelastic.
• Error: Confusing the interpretation of positive and negative signs between YED and XED. Correction: Remember that a negative YED means an inferior good, whereas a negative XED means the goods are complements.
• Error: Stating that a YED of 0.5 indicates a luxury good. Correction: A YED between 0 and 1 indicates a normal necessity; luxury goods require a YED greater than 1.
• Mistaking elasticity for the gradient of the demand curve. Slope measures absolute change (change in P / change in Q), whereas elasticity measures proportionate change (% change in Q / % change in P); thus, a straight-line demand curve has a constant gradient but changing elasticity.
• Omitting algebraic signs or failing to explain their economic significance. A positive XED indicates substitutes, while a negative XED indicates complements; dropping the sign renders the analysis incorrect.
• Assuming necessities are always completely price inelastic (PED = 0). In reality, demand is rarely perfectly inelastic; consumers still adjust consumption at extreme prices or seek imperfect substitutes.

1. 1Day 1-2: Master calculations and definitions for PED, YED, and XED; construct flashcards for sign rules and coefficient categories.
2. 2Day 3-4: Draw and annotate diagrams showing PED along a linear demand curve and its direct relationship to Total Revenue and Marginal Revenue curves.
3. 3Day 5-6: Practise application to government policy, analyzing the incidence of specific indirect taxes and subsidies depending on relative elasticities.
4. 4Day 7: Complete timed AQA Paper 1 and Paper 3 data-response extracts focusing on multi-step elasticity calculations and evaluative paragraphs.

• 📋Calculation and multiple-choice questions (Paper 1 & Paper 3): 2-4 mark numerical questions requiring percentage change calculations, formula substitutions, or interpretations of sign coefficients.
• 📋Context data-response questions (Paper 1): 9-mark and 15-mark questions requiring students to use extract data to assess firm pricing decisions or government market interventions using elasticity analysis.
• 📋Extended evaluative essays (Paper 1, 25 marks): Evaluative questions asking whether indirect taxes reduce consumption of demerit goods, where elasticity of demand forms a primary counter-argument.