Cross Elasticity of Demand (XED)
1. What is Cross Elasticity of Demand?
Definition: XED measures the responsiveness of the % change in quantity demanded of one good (B) due to a % change in the price of another good (A).
% change = New − OldOld × 100
XED always links price of A to quantity of B — that is why diagram axes are labelled that way (e.g. Price of Coke vs Quantity of Pepsi).
| Value of XED | Sign | Type of goods |
|---|---|---|
| XED > 0 | +ve | Substitutes |
| XED < 0 | −ve | Complements |
| XED = 0 | zero | Unrelated goods |
2. Substitute Goods (XED +ve)
Definition: Substitutes are alternatives / options which can be used in place of another good. e.g. Coke / Pepsi, Tea / Coffee.
positive relationship ⇒ upward-sloping demand curve
Proof for analysis marks: An increase in price of Coke reduces QD of Coke (law of demand) → people switch to Pepsi → demand for Pepsi ↑ → positive relationship between price of Coke and quantity of Pepsi → upward-sloping curve. So whenever XED is positive it is a substitute good.
Close vs Weak Substitutes
| Close substitute | Weak substitute | |
|---|---|---|
| XED | > 1 (elastic) | < 1 (inelastic) |
| Relationship | stronger | weaker |
| Responsiveness | high — QD changes by a larger % | low — QD changes by a smaller % |
| Demand curve | flatter (upward) | steep (upward) |
| Example | Coke & Pepsi | Coke & 7up |
| Numbers | P Coke ↑ 10 %, D Pepsi ↑ 50 % | P Coke ↑ 50 %, D 7up ↑ 10 % |
3. Complementary Goods (XED −ve)
Definition: Complements are jointly demanded goods, demanded together at the same time. e.g. Car & Petrol, Car & tyres, TV & electricity.
negative relationship ⇒ downward-sloping demand curve
Proof: An increase in price of car contracts QD of car (law of demand) → it reduces demand for petrol (needed together) → negative relationship between price of car and quantity of petrol → downward-sloping curve (movement a → b). So whenever XED is negative it is a complementary good.
Strong vs Weak Complements
| Strong complement | Weak complement | |
|---|---|---|
| XED | −ve and size > 1 (elastic) | −ve and size < 1 (inelastic) |
| Relationship | stronger | weaker |
| Responsiveness | high — QD larger change | low — QD smaller change |
| Demand curve | flatter (downward) | steep (downward) |
| Example | Gaming console / game | Coffee & sugar |
| Numbers | P console 10 %, QD game 50 % | P coffee ↑ 50 %, QD coffee ↓ 10 %, D sugar ↓ 10 % |
4. Unrelated Goods (XED = 0)
Definition: Unrelated goods have no relationship with the other good — no functional connection, don’t affect each other, no responsiveness. e.g. Cars & tomatoes.
Price of A ↑ → QD of A ↓, but demand for B stays same (–). No relationship ⇒ vertical demand curve. P → P₁ (↑) and P → P₂ (↓): no change in quantity of good B.
So whenever XED is zero it is an unrelated good. Quantity demanded of B remains unchanged, creating no relationship between price of good A and quantity of good B.
5. Value & Size of the Coefficient
| XED | Sign | Size | Meaning |
|---|---|---|---|
| +1.4 (e.g. +5) | + | > 1 | Close substitute — elastic, flatter curve |
| +0.7 (e.g. +0.2) | + | < 1 | Weak substitute — inelastic, steep curve |
| −0.7 (e.g. −0.2) | − | < 1 | Weak complement |
| −5 | − | > 1 | Strong complement |
| 0 | — | — | Unrelated |
6. Factors affecting XED (Determinants)
① Closeness of substitutes / complements: price of one good ↑ and there are many close substitutes → consumers switch easily → high positive XED (close substitute) e.g. Coke & Pepsi. If goods are strongly tied (complements), demand for both falls significantly. Board example: Car & car parts (floor mat).
② Time period: short run — consumers unable/unwilling to find substitutes → demand for related goods less responsive → lower XED. Long run — more time to find alternatives → demand for related goods more responsive → higher XED.
③ Relationship to other factors: the above are direct determinants; others influence the relationship between products:
- Availability of substitutes — the number of available substitutes for a good affects its XED.
- Income — change in a consumer’s income changes purchasing power and so demand for goods, influencing the relationship with the other good.
- Habit — if a good is habitual, consumers may be less responsive to price changes, affecting XED with related goods.
7. Usefulness of XED to a Producer
Aim: producer wants to maximise Total Revenue (TR). He uses XED as information about the type of goods (close/weak substitute, close/strong complement) and sets his pricing strategy accordingly.
① Close substitute → LOWER prices → TR ↑
Close substitute → elastic demand. e.g. Coke price ↓ 10 % → QD Coke ↑ 50 % → demand for Pepsi ↓ 50 % (+ve). Cutting price by a smaller % extends QD by a larger % and takes customers from the rival.
② Weak substitute → HIGHER prices → TR ↑
Weak substitute → inelastic demand. e.g. Coke price ↑ 50 % → QD Coke ↓ 10 % → demand for 7up ↑ 10 % (+ve). Raise price by a larger % → QD contracts by a smaller % → TR rises.
③ Strong complements
Cinema tickets = main product → price ↓ to attract more customers. Popcorn & drinks = complementary good → price ↑ (greater profit margin) → TR ↑. Customers are "bound" to buy the complement. (Red scribble on board: 500 → M.T., 300/700, 500 + 300 → 800 — an illustration that revenue from both goods is added up.)
Exam wording: The usefulness of XED to a producer is that he will identify the type of substitute and complement and plan a pricing strategy accordingly to maximise total revenue. In case of close substitutes, since they carry elastic demand, the producer should reduce price by a smaller % which extends QD by a larger %, increasing TR. In case of weak substitutes (inelastic) increase price by a larger % → QD contracts by a smaller % → TR ↑. Moreover, in case of strong complements such as cinema tickets and popcorn, reduce the price of the main product to attract more customers and increase profit margin on the complementary good, increasing TR.
8. Price Elasticity of Demand (needed for the 12-marker)
Definition: PED measures the responsiveness of % change in QD due to % change in price.
| Elastic demand | Inelastic demand | |
|---|---|---|
| PED | > 1 | < 1 |
| Responsiveness | high ⇒ QD larger change | low ⇒ QD smaller change |
| Substitutes | more available, easy to switch | fewer available, hard to switch |
| Product | luxury | necessity |
| Curve | flatter | steeper |
PED and Total Revenue (pricing strategy)
Elastic: producer reduces price by a smaller % → QD extends by a larger % → TR rises from OPAQ to OP₁BQ₁ (Diagram 1). Inelastic: producer raises price by a larger % → QD contracts by a smaller % → TR rises from OPAQ to OP₁BQ₁ (Diagram 2). Also: price discrimination — charging different prices to different customers for the same product.
9. Past-paper questions (model answers)
Q1 · 12 marks — PED vs XED for a producer
Discuss whether price elasticity of demand is more useful than cross elasticity of demand for a producer to maximise his total revenue. (12)
Marks: 4 K · 4 A · 4 E. Linked (a)/(b)? Don’t repeat XED definitions in (b).
- K (4): define PED + formula; define elastic and inelastic demand.
- A (4): usefulness of PED → pricing strategy + diagrams showing TR area (diagrams 1 & 2) + price discrimination line.
- A (continued): usefulness of XED → straight into pricing strategy (close substitute ↓ price; weak substitute ↑ price; strong complement: main product ↓, complement ↑). No XED definition needed.
- E (4): conclude PED is more useful.
Evaluation — "To conclude…": PED is more useful than XED for a producer as prices are in the control of the producer, so he can set pricing strategy to maximise TR. But XED is difficult to use: identifying types of substitute & complement needs research — time-consuming, costly, and harder to interpret accurately, especially in markets with related products. Moreover, PED is more applicable as it can be used for day-to-day pricing and policy decisions.
Q2 · O/N 2020 Paper 2 Variant 1, Q3(a) — 8 marks (3K 3A 2E)
XED for bread w.r.t. price of rice = +1.4, while XED for bread w.r.t. price of butter = −0.7. Explain why the XED figures for bread differ.
+1.4 → positive and > 1 → close substitutes. −0.7 → negative and < 1 → weak complement.
- Define XED + formula.
- Define substitutes → close substitute → diagram + explanation.
- Define complementary goods → weak complement → diagram + explanation.
- Evaluation (not really required in this old-style question, added for practice): depends on value & size of XED, type of good, elasticity varies from individual to individual.
Write-up: XED measures responsiveness of % change in QD of good B due to % change in price of good A; XED = %ΔQD of B ÷ %ΔP of A. Substitutes are alternatives that can be used in place of another good, e.g. Coke/Pepsi. An increase in price of good A reduces its QD, consumers shift to good B, increasing its demand, creating a positive relationship, upward-sloping curve; XED +ve ⇒ substitute. Bread and rice are close substitutes since XED = +1.4, which is greater than 1 → high responsiveness.
Complements part: Complements are jointly demanded goods, e.g. car & petrol. An increase in price of good A reduces its QD → reduces demand for good B as they are demanded together → negative relationship → downward-sloping; XED −ve ⇒ complement. Bread and butter have XED = −0.7, less than 1 (size) → weak complement → inelastic demand → downward sloping but STEEP curve.
Evaluation: To conclude, it depends on the value and size of XED and the type of good (substitute or complement). Moreover, elasticity varies from individual to individual — for one it might be a close substitute, for another a weak substitute.
Q3 · O/N 2018 Q1 — 8 marks: "Analyse using XED, explain values that are positive, negative and zero"
Analyse using cross elasticity of demand: explain values that are positive, negative and zero. (8)
Old pattern ⇒ 4 K + 4 A (full 8 possible). No evaluation in this wording, but it is good practice; under the new pattern it would be 3K 3A 2E.
- Define XED + formula.
- Define substitute good + XED +ve + link with diagram.
- Define complementary good + XED −ve + link with diagram.
- Define unrelated good + XED 0 + link with diagram.
- Evaluation (forced): can be close or weak substitute; strong or weak complement; varies from individual to individual.
Substitute: Substitutes are alternatives/options that can be used in place of another good, e.g. Coke/Pepsi. Price of Coke ↑ → QD of Coke ↓ → people shift to Pepsi → demand for Pepsi ↑ → positive relationship between price of Coke and QD of Pepsi → upward-sloping curve (diagram 1). So whenever XED is positive it is a substitute good.
Complement: Complements are jointly demanded together at the same time, e.g. car & petrol. Price of car ↑ → QD of car contracts → demand for petrol ↓ → negative relationship → downward-sloping (diagram 2). Whenever XED is negative it is a complementary good.
Unrelated: Unrelated goods have no relationship with the other good, e.g. car & tomato. Price of A ↑ has no effect on QD of B (no responsiveness) → unchanged → no relationship → vertical curve (diagram 3). Whenever XED is zero it is an unrelated good.
Evaluation ("forced"): To conclude, elasticity varies from individual to individual — for one it might be a close or weak substitute, or a strong or weak complement. Moreover, it depends on the value of XED and size of coefficient.
Q4 · O/N 2024 Paper 2 Variant 2, Q2(a) — 8 marks (3K 3A 2E)
With the help of a diagram(s), briefly explain how the cause of a movement along the demand curve differs from the cause of a shift in the demand curve, and consider the impact on the demand for one good of price changes in other goods. (8)
- K (3): define demand · reason for movement along curve + diagram link · reason for shift + diagram link.
- A (3): define XED + formula · substitute good: XED +ve → price of A ↑, QD of A ↓, demand B ↑ · complement: XED −ve → price A ↑, QD A ↓, demand B ↓ · unrelated: XED 0 → demand B unchanged.
- E (2): value and size of XED → type of substitute/complement (+ve, −ve, zero) and (XED > 1, XED < 1).
Demand & movement vs shift: Demand represents the willingness and ability of a consumer to purchase a good or service. Movement along the demand curve is due to a change in price, causing contraction/extension in QD, other factors constant (diagram 1). A shift is due to a change in other (non-price) factors, causing demand to increase or decrease — rightward / leftward shift, prices constant (diagram 2).
XED analysis: XED = %ΔQD of B ÷ %ΔP of A. Substitutes (+ve XED): price of one good ↑ reduces its QD, demand for the other ↑ as consumers switch. Complements (−ve): price of one ↑ reduces its QD, demand for the other ↓ as they are demanded together. Unrelated (XED 0): no impact on demand for the other good — no functional relationship.
Evaluation: To conclude, the impact of a price change of one good on demand for another depends on the value and size of the coefficient. Moreover, in theory movement along the demand curve happens only with price changes, but in the real world price changes often come with changes in income too — it is difficult to isolate one factor and consider the other.
10. Evaluation Phrase Bank & Cheat-sheet
- XED = %ΔQD of B ÷ %ΔP of A; % change = (new − old) ÷ old × 100.
- +ve = substitute (upward curve) · −ve = complement (downward curve) · 0 = unrelated (vertical).
- Size > 1: close substitute / strong complement (elastic, flatter curve). Size < 1: weak substitute / weak complement (inelastic, steep curve).
- Examples: Coke/Pepsi (+5) · Coke/7up (+0.2) · gaming console/game (−5) · coffee/sugar (−0.2) · car/petrol · car/tomato (0) · bread/rice +1.4 · bread/butter −0.7.
- Producer: close substitute → lower price; weak substitute → higher price; strong complements → cut main product, raise complement; goal TR ↑.
- Determinants: closeness of substitutes/complements · time period (short run lower, long run higher) · availability of substitutes, income, habit.