# Price, income and cross elasticities of demand > CIE A-Level Economics · Unit 2: The Price System and the Microeconomy > Source: https://www.owlsprep.com/study/cie-9708-u2-price-income-and-cross-elasticities/ This subtopic covers how to calculate and interpret three key demand elasticities: price, income, and cross elasticity of demand. You will learn how these values are used by firms and governments to make pricing and policy decisions. **Prerequisites:** [Law of demand and shifts vs movements along demand curves](https://www.owlsprep.com/study/cie-9708-u2-demand-and-supply-curves/) ## Learning objectives - Calculate price, income and cross elasticities of demand using percentage methods - Interpret the numerical value and sign of each elasticity to classify goods and relationships - Explain how firms and governments use elasticity values for decision making - Distinguish between normal/inferior goods and substitutes/complements using elasticity values ## Price Elasticity of Demand (PED) **Price Elasticity of Demand** — Measures the responsiveness of quantity demanded of a good to a change in its own price, holding all other factors constant (ceteris paribus). The negative sign reflects the inverse relationship between price and quantity demanded per the law of demand. *Notation:* $PED = \frac{\%\Delta Q_d}{\%\Delta P}$ *Example:* A 10% fall in price leading to a 20% rise in quantity demanded gives $PED = -2$. **Worked example:** The price of bread rises from \$2.00 per loaf to \$2.30 per loaf. Weekly quantity demanded falls from 500 loaves to 425 loaves. Calculate PED using the simple percentage method. 1. 1. Calculate percentage change in price: 2. $$%\Delta P = \frac{(2.30 - 2.00)}{2.00} \times 100 = +15\%$$ 3. 2. Calculate percentage change in quantity demanded: 4. $$%\Delta Q_d = \frac{(425 - 500)}{500} \times 100 = -15\%$$ 5. 3. Apply the PED formula: 6. $$PED = \frac{-15\%}{+15\%} = -1$$ 7. The value of PED = -1, so demand is unit elastic. > **tip** > > CIE examiners expect you to know that elasticity is judged by the absolute value of PED, not the sign. $|PED| > 1$ = elastic, $|PED| < 1$ = inelastic, $|PED| = 1$ = unit elastic. ## Income Elasticity of Demand (YED) **Income Elasticity of Demand** — Measures the responsiveness of quantity demanded of a good to a change in consumer income, ceteris paribus. The sign tells us if the good is normal or inferior. *Notation:* $YED = \frac{\%\Delta Q_d}{\%\Delta Y}$, where $Y$ = consumer income *Example:* A 5% rise in income leading to a 10% rise in quantity demanded of restaurant meals gives $YED = +2$. **Worked example:** Average consumer incomes rise by 10% in a year. Quantity demanded for public transport falls by 3%. Calculate YED and classify the good. 1. 1. Identify the given values: $%\Delta Y = +10\%$, $%\Delta Q_d = -3\%$ 2. 2. Apply the YED formula: 3. $$YED = \frac{-3\%}{+10\%} = -0.3$$ 4. 3. Classify the good: 5. Negative YED means public transport is an inferior good. The absolute value of $0.3 < 1$, so demand is income inelastic. - $YED > 0$: Normal good (Qd rises as income rises) - $YED > 1$: Normal good, income elastic (luxury good) - $0 < YED < 1$: Normal good, income inelastic (necessity) - $YED < 0$: Inferior good (Qd falls as income rises) ## Cross Elasticity of Demand (XED) and Applications **Cross Elasticity of Demand** — Measures the responsiveness of quantity demanded of good X to a change in the price of good Y, ceteris paribus. The sign tells us if the goods are substitutes or complements. *Notation:* $XED = \frac{\%\Delta Q_{d,X}}{\%\Delta P_{Y}}$, for goods $X$ and $Y$ *Example:* A 10% rise in the price of tea leading to a 5% rise in quantity demanded of coffee gives $XED = +0.5$. **Worked example:** When the price of printers falls by 20%, quantity demanded for ink cartridges rises by 30%. Calculate XED and state the relationship between the two goods. 1. 1. Identify values: $%\Delta Q_{X} = +30\%$ (ink cartridges = X), $%\Delta P_{Y} = -20\%$ (printers = Y) 2. 2. Apply the XED formula: 3. $$XED = \frac{+30\%}{-20\%} = -1.5$$ 4. 3. Interpret the result: 5. Negative XED means printers and ink cartridges are complements. The absolute value of $1.5 > 1$ means they are strong complements. Elasticity values are used widely in business and policy: firms use PED to predict how price changes affect total revenue, use XED to predict the impact of competitor price changes, and governments use YED to plan infrastructure and tax policy. This topic makes up a core part of almost all microeconomics questions in CIE A-Level Economics. **Exam command terms** CIE commonly uses these command terms for this topic: - **Calculate** — Show all working steps and give a final numerical value. Always write the formula before substituting values to earn full marks. - **Interpret** — Explain what the elasticity value means in context, including classification of the good or relationship. Do not just state the number. ## Common pitfalls - **Wrong:** Forgetting to include or use the sign of YED/XED when classifying goods/relationships - Why it fails: CIE mark schemes award specific marks for correct classification, which depends entirely on the sign of the elasticity - Correct: Always retain the sign through calculation and explicitly use it to classify the good or relationship - **Wrong:** Swapping the numerator and denominator in elasticity formulas - Why it fails: All demand elasticities measure responsiveness of quantity demanded to a change in another variable, so % change in quantity must always be the numerator - Correct: Memorise: **%ΔQd is always on top** for all demand elasticities - **Wrong:** Classifying a positive YED between 0 and 1 as a luxury good - Why it fails: Luxury goods are defined as income elastic, which requires YED greater than 1 - Correct: Positive YED between 0 and 1 is a necessity (normal good), YED > 1 is a luxury good - **Wrong:** Claiming negative PED means demand is inelastic - Why it fails: The negative sign for PED only reflects the inverse relationship between price and quantity, it does not indicate elasticity - Correct: Judge PED elasticity by the absolute value: |PED| > 1 = elastic, |PED| < 1 = inelastic ## Cheatsheet | Elasticity Type | Formula | Sign Meaning | Value Interpretation | | --- | --- | --- | --- | | PED | $\frac{%\Delta Q_d}{%\Delta P}$ | Negative (law of demand) | \|PED\|>1 = elastic; \|PED\|<1 = inelastic | | YED | $\frac{%\Delta Q_d}{%\Delta Y}$ | Positive = normal; Negative = inferior | YED>1 = luxury; 0