Cross Elasticity of Demand (XED)
🍎 XED for beginners – what does it actually tell us?
Imagine you are at a school cafeteria. You usually buy a slice of pizza for $2.50. Suddenly the price of a burger rises from $3.00 to $4.00. Do you buy more pizza? Probably yes – because burgers became expensive and pizza is a tasty alternative. This switch is captured by Cross Elasticity of Demand (XED). It tells us if two goods are rivals (substitutes), partners (complements), or strangers (unrelated). For elementary learners: XED is like a friendship meter between two products.
The basic formula looks like this:
$XED = \frac{\text{% change in quantity demanded of Good A}}{\text{% change in price of Good B}}$
If the number is positive (like +0.8 or +2.1), the goods are substitutes. If it is negative (like –0.5 or –1.3), the goods are complements. A number near zero means the goods are independent – they don’t care about each other.
🔄 Substitutes, complements, and the sign of XED
Let’s unfold the three main relationships with everyday examples that middle schoolers can instantly recognize.
- Substitutes (XED > 0): Coca‑Cola and Pepsi, Nike and Adidas, butter and margarine. When Pepsi gets cheaper, people buy less Coke. The change is in the same direction → positive XED.
- Complements (XED < 0): Printers and ink cartridges, PlayStation and games, cars and gasoline. If the price of PlayStations falls, more games are bought (quantity of games rises). Different directions → negative XED.
- Unrelated (XED ≈ 0): Shoes and bananas, textbooks and ice cream. A change in the price of bananas will not affect how many shoes you buy.
| Sign of XED | Type of relationship | Everyday example |
|---|---|---|
| $XED > 0$ | Substitutes | Tea ☕ and coffee ☕ |
| $XED < 0$ | Complements | Smartphone 🔋 and charger 🔌 |
| $XED = 0$ | Unrelated / independent | Milk 🥛 and movie tickets 🎟️ |
🧮 The math behind XED – step by step for high school
Now we put numbers into the formula. Do not worry – it is only division with percentages. The precise formula used by economists is the midpoint method (also called arc elasticity), which gives the same answer whether the price rises or falls.
$XED = \frac{\frac{Q_{2A} - Q_{1A}}{(Q_{2A} + Q_{1A})/2}}{\frac{P_{2B} - P_{1B}}{(P_{2B} + P_{1B})/2}}$
Let’s work through a complete example with e‑books and physical books (substitutes).
- Original price of physical book: $P_1 = \$20$ → New price: $P_2 = \$24$
- Original quantity of e‑books demanded: $Q_1 = 100$ → New quantity: $Q_2 = 130$
Step 1 – % change in quantity of e‑books (midpoint):
$\frac{130 - 100}{(130+100)/2} = \frac{30}{115} = 0.2609 \rightarrow 26.09\%$
Step 2 – % change in price of physical books (midpoint):
$\frac{24 - 20}{(24+20)/2} = \frac{4}{22} = 0.1818 \rightarrow 18.18\%$
Step 3 – XED:
$XED = \frac{26.09\%}{18.18\%} = 1.435$
Interpretation: XED = +1.435. Positive and greater than 1 → strong substitutes. When physical books become 18.18% more expensive, the demand for e‑books jumps by 26.09%.
⚙️ Real‑world application: how Netflix and Disney+ watch each other
Let’s open a streaming platform scenario. In 2023, Disney+ raised its monthly subscription from \$10.99 to \$13.99. A small survey found that during the same period, the number of Netflix subscribers in the same region grew from 55 million to 62 million. Are Netflix and Disney+ substitutes? Let’s compute XED (using midpoint again).
- $\Delta Q_{Netflix} = 62 - 55 = 7$ million, average quantity = $(62+55)/2 = 58.5$ million → %ΔQ = $7/58.5 = 0.11966$ (≈11.97%)
- $\Delta P_{Disney+} = 13.99 - 10.99 = 3.00$, average price = $(13.99+10.99)/2 = 12.49$ → %ΔP = $3.00/12.49 = 0.24019$ (≈24.02%)
$XED = \frac{11.97\%}{24.02\%} = 0.498$
The result +0.498 is positive but less than 1. Netflix and Disney+ are substitutes, but not extremely strong substitutes. Some viewers are loyal, others switch only if the price gap becomes very large. Companies watch XED closely: if XED is high, a small price cut by the rival steals many customers. They might react with loyalty programs or bundles.
| XED value (substitutes) | Strength | Example |
|---|---|---|
| 0 < XED ≤ 0.5 | weak substitute | Butter vs. cream cheese |
| 0.5 < XED < 1.5 | medium substitute | Netflix vs. Disney+ |
| XED ≥ 1.5 | strong substitute | Coke vs. Pepsi |
🧾 Important questions about XED
If two goods are completely unrelated, a price change in one causes no change in the quantity demanded of the other. For instance, the price of bicycles rises but your demand for orange juice stays the same. In the formula, the numerator (%ΔQ) is zero, therefore XED = 0. These goods are called independent goods.
Theoretically, yes, if the goods are perfect substitutes. Imagine two identical vending machines side by side selling exactly the same water bottle. If one machine raises its price by just 1 cent, demand for the other machine’s water becomes enormous (almost all buyers switch). The percentage change in quantity is huge → XED approaches infinity. In real life, perfect substitutes are rare.
If a company knows its product has a high positive XED with a competitor’s product, it understands that cutting its price will attract many customers from the competitor. Conversely, if it raises the price, it will lose many sales. For complements (negative XED), a firm might lower the price of the main product to sell more of the complementary good (e.g., cheap printers, expensive ink).
Cross elasticity of demand is not just a classroom formula; it is a daily compass for shoppers, companies, and even governments. When you compare prices of Uber and Lyft, you are intuitively using XED. When a business plans a “buy one, get one” offer, it predicts the XED between its items. Antitrust authorities[1] also calculate XED to decide if two big brands are so strongly substitutable that a merger would harm competition. From the lunch line to international markets, XED quietly organises the invisible web of “this affects that”.
📚 Footnote – abbreviations & terminology
[1] Antitrust authorities – government agencies (like the U.S. Federal Trade Commission) that prevent unfair business practices and ensure healthy competition. They examine cross elasticity to see if products are close substitutes.
XED – Cross Elasticity of Demand: the full term for the measure discussed in this article.
Substitutes: goods that can replace each other (tea/coffee).
Complements: goods used together (car/tires).
Unrelated / independent goods: goods with zero or near‑zero cross elasticity.