What this lesson teaches
I can use price, income and cross elasticities to judge how large those changes will be.
Syllabus 9570, 2.1.2(g). Demand and Supply Analysis and its Applications: These outcomes can be affected by price elasticities of demand and supply, income and cross elasticities of demand
Make a guess
The price of coffee rises by 10% and demand for tea rises by 3%. What does the XED tell you?
- They are substitutes, but only weakly.
- They are unrelated, because 3% is too small to matter.
- They are complements, because demand moved.
Show the answer
They are substitutes, but only weakly.
XED = +3 / 10 = +0.3. Positive means substitutes; a small number means few coffee drinkers switch to tea.
XED shows how demand for one good responds to another good's price: positive for substitutes, negative for complements.
Cross elasticity of demand (XED) = percentage change in demand for good A / percentage change in the price of good B, ceteris paribus.
If XED is positive, the goods are substitutes. When bus fares rise, demand for MRT rides rises.
If XED is negative, they are complements. When COE premiums rise, demand for new cars falls.
The bigger the number, ignoring the sign, the closer the relationship. A firm uses XED to see how much a rival's price cut will hurt it.
- XED
- % change in D for A / % change in P of B.
- Substitutes
- XED > 0.
- Complements
- XED < 0.
| XED | Relationship | Example |
|---|---|---|
| Positive | Substitutes | Bus and MRT rides |
| Zero | Unrelated | Bread and phone cases |
| Negative | Complements | Cars and COEs |
Worked example: Rail fares and bus demand
Rail fares rise by 10%. Demand for bus rides rises by 6%, with bus fares unchanged.
- XED = +6 / +10 = +0.6.
- XED is positive, so bus and rail rides are substitutes.
- 0.6 is a fairly weak relationship: many rail users do not switch, perhaps because buses are slower.
Watch out for this
XED is negative, so the goods are substitutes.
It is the other way round. Substitutes have a positive XED; complements have a negative XED.
Check your understanding
A printer maker knows the XED between its printers and its own ink cartridges is -2. Why might it sell printers cheaply?
- Cheaper printers raise sales of the ink it also sells.
- Cheaper printers cut ink sales, since the two are substitutes.
- A negative XED means printer demand is price inelastic.
Show the answer
Cheaper printers raise sales of the ink it also sells.
Right. A negative XED means complements. Each cheap printer brings ink sales, which can carry the profit.