2.6 - Cross Elasticity of Demand
The meaning and formula for cross elasticity of demand
Cross elasticity of demand (XED) measures how the quantity demanded of one product changes in response to a price change in another product. It measures how the quantity demanded is affected by a change in price of a related product, assuming all other factors remain constant.
Formula for cross elasticity of demand
Interpreting the value and sign of XED
The value of XED reveals the strength of the relationship between two products, while its sign shows the type of connection.
Types of XED based on value
- Cross elastic demand - When the quantity demanded changes more than proportionately to the price shift in the other product (XED > 1)
- Cross inelastic demand - When the quantity demanded changes less than proportionately to the price shift in the other product (XED < 1)
Meanings of XED signs
- Positive (+) - An increase in the price of one product leads to an increase in demand for the other. These products are substitutes (products that can replace each other).
- Negative (-) - An increase in the price of one product leads to a decrease in demand for the other. These products are complements (products used together).
- Zero (0) - A price change in one product has no effect on demand for the other. These products have no relationship (unrelated products).
Examples of substitutes and complements
Products can be linked in different ways, affecting how demand shifts when prices change. Substitutes compete, while complements are often consumed jointly, and some items have no connection at all.
XED calculations help quantify product relationships. The sign indicates the type of link, and the magnitude shows its strength.
Substitute products
Substitutes are goods that can be used in place of each other. If the price of one rises, consumers may switch to the alternative, increasing its demand.
Examples of substitute products:
- An increase in the price of butter might boost demand for margarine as shoppers opt for the cheaper option.
- In a shopping centre, a price hike for meals at an Italian restaurant could lead to more customers choosing a nearby Mexican eatery.
Complement products
Complements are goods that are typically used together. A price rise in one can reduce demand for the paired item.
Examples of complement products:
- A higher price for smartphones might decrease sales of protective cases, as fewer people buy the main device.
- If concert ticket prices go up, demand for band-related clothing and accessories could fall among fans.
Products with no relationship
Some goods are entirely unrelated, so a price change in one does not affect the other. For example, a shift in the cost of kitchen appliances would have no impact on the demand for gardening tools.
Worked example - Calculating XED for substitute products
The average price of a basic smartphone is £400, with daily sales of 300 units. After a 5% reduction in the price of rival feature phones (a substitute), smartphone demand drops to 273 units per day at the original price. Calculate the XED and interpret the result.
Step 1: Identify the values
- Original quantity demanded of smartphones = 300 units
- New quantity demanded of smartphones = 273 units
- % change in quantity demanded = ((273 - 300) / 300) × 100 = -9%
- % change in price of feature phones = -5%
Step 2: Apply the XED formula
Step 3: Interpretation
The positive XED of +1.8 indicates the products are substitutes, with demand responding more than proportionately (cross elastic), showing they are reasonably close alternatives.
Worked example - Calculating XED for complement products
The average price of tablet covers (a complement to tablets) decreases by 8%, leading to an increase in tablet demand from 250 to 262 units per day at the original tablet price. Calculate the XED and interpret the result.
Step 1: Identify the values
- Original quantity demanded of tablets = 250 units
- New quantity demanded of tablets = 262 units
- % change in quantity demanded = ((262 - 250) / 250) × 100 = +4.8%
- % change in price of tablet covers = -8%
Step 2: Apply the XED formula
Step 3: Interpretation
The negative XED of -0.6 shows the products are complements, with a cross inelastic response indicating a relatively weak joint demand relationship.