Every percentage change in an elasticity calculation needs a base, and you must use the same rule for both the price and the quantity. Mixing rules, such as the old price for one change and the new quantity for the other, gives an answer that is close but wrong. The fix is a written habit, not more formulas.
What does the error look like?
- Your PED is 1.25 when the mark scheme value would be 1.
- You divided by the new number for one change and by the old number for the other.
- You used the average for one percentage and the starting value for the other.
- You get different answers when you work from “before to after” and from “after to before”.
Why does it happen?
Percentages always answer the question “a change of what, compared with what?” In a table, price and quantity appear next to each other, and the eye grabs whichever number is nearest. Under time pressure, one column uses the first row and the other uses the second.
Elasticity is especially exposed because it divides one percentage by another. A slip in either base changes the result.
Worked example: a fictional notebook seller
A seller raises the price of a notebook from RM10 to RM12. The quantity sold per week falls from 100 to 80.
Starting-value method, step by step:
- Price change: 12 − 10 = +2. Base is the starting price, 10. So %Δ price = 2 ÷ 10 = +20%.
- Quantity change: 80 − 100 = −20. Base is the starting quantity, 100. So %Δ quantity = −20 ÷ 100 = −20%.
- PED = −20% ÷ +20% = −1.
The response is exactly proportional, so demand is unit elastic here.
The mistake to watch for
A student writes:
%Δ price = 2 ÷ 10 = 20%. %Δ quantity = −20 ÷ 80 = −25%. PED = −25 ÷ 20 = −1.25.
The price used the starting value (10), but the quantity used the new value (80). The two changes do not share a rule, so −1.25 describes neither method.
The correction is to name the base before calculating. Write “base = starting value” at the start and use it twice.
What about the midpoint method?
A different, valid method uses the average of the old and new values as the base:
- Price average = (10 + 12) ÷ 2 = 11, so %Δ price = 2 ÷ 11 ≈ 18.18%.
- Quantity average = (100 + 80) ÷ 2 = 90, so %Δ quantity = −20 ÷ 90 ≈ −22.22%.
- PED = −22.22 ÷ 18.18 ≈ −1.22.
Check the exact form: (20 ÷ 90) ÷ (2 ÷ 11) = 220 ÷ 180 = 1.222.
Both −1 and −1.22 are legitimate for this data under their own rule. The error is mixing the two rules, or quoting a value without the method. The elasticity and percentage-base tutor shows each denominator, and compares methods only when you ask it to.
A routine that removes the slip
- Write the base rule in one line: “starting value” or “midpoint”.
- Write each change as a fraction with its base: change over base.
- Convert to a percentage for both, keeping full decimals.
- Divide the quantity percentage by the price percentage, and keep the sign.
- Round once, at the end, then state what the value means.
You can test a base choice on any sequence of changes in the percentage-base explorer. It shows the base at each stage, using fictional numbers only.
Check yourself
1. Price RM20 to RM25, quantity 400 to 300. Find PED using the starting-value method.
Show answer
%Δ price = 5 ÷ 20 = +25%. %Δ quantity = −100 ÷ 400 = −25%. PED = −25 ÷ 25 = −1.
2. Price RM8 to RM6, quantity 50 to 65. Find PED using the starting-value method.
Show answer
%Δ price = −2 ÷ 8 = −25%. %Δ quantity = +15 ÷ 50 = +30%. PED = 30 ÷ (−25) = −1.2. Demand is elastic, because the size is above 1.
3. A student finds price 40 to 44 is +10%, and quantity 100 to 85 is −15 ÷ 85 = −17.6%, giving −1.76. Find the error and the correct answer.
Show answer
The price used the starting value (40) while the quantity used the new value (85). Using the starting value for both, %Δ quantity = −15 ÷ 100 = −15%, so PED = −15 ÷ 10 = −1.5.
Where to go next
Work through calculating percentage changes using the specified base, then interpreting an elasticity value and sign, and avoid comparing elasticities from incompatible methods. The elasticity module has a practice set, and the original practice hub has more.
When might tuition help?
If your method is right in principle but slips keep appearing in longer questions, a teacher can watch you work and point out the habit as it happens. Online one-to-one Economics tuition starts with a paid one-hour trial, at the assigned teacher’s confirmed rate from RM80.