A percentage change is the change divided by the starting value (the base), multiplied by 100. In elasticity questions you calculate two of them, one for price and one for quantity, so an error here carries into every step after it.
This is the opening skill in elasticity. It also helps with growth rates, inflation and revenue questions later in the course.
What does “the specified base” mean?
Every percentage change answers the question “percent of what?”. The base is the number that follows “of”. Unless a question says otherwise, the base is the original (old) value.
The formula is: percentage change = (new value − old value) ÷ old value × 100.
A positive answer is a rise. A negative answer is a fall. Keep the sign, because later lessons use it.
Step by step
- Write down the old and new values and label them.
- Subtract new minus old, so the sign shows the direction.
- Divide by the base, which is the old value.
- Multiply by 100 and attach the sign.
- Check the direction: a smaller new value must give a negative answer.
Worked example
Kopi Sudut is a fictional café. It raises the price of its iced coffee from RM4.00 to RM4.60. Weekly sales fall from 200 cups to 170 cups.
Price change: (4.60 − 4.00) ÷ 4.00 × 100 = 0.60 ÷ 4.00 × 100 = +15%.
Quantity change: (170 − 200) ÷ 200 × 100 = −30 ÷ 200 × 100 = −15%.
The ratio of the two, quantity change over price change, is −15 ÷ 15 = −1. You will meet that ratio properly in interpreting an elasticity value and sign.
The mistake to watch for
A common slip is dividing by the new value, because it is the number the eye lands on last.
Mistaken working: price change = 0.60 ÷ 4.60 × 100 = 13.04%, quantity change = −30 ÷ 170 × 100 = −17.65%.
Both figures use the new value as the base. They describe a different calculation from the one the question set.
The fix is to circle the old value before dividing. In the café example, the original price is RM4.00 and the original quantity is 200. A quick check helps: 15% of 200 is 30, which matches the drop in cups.
Check yourself
1. A fictional tailor, Jahit Maju, raises the price of a shirt from RM50 to RM60. Find the percentage change in price.
Show answer
(60 − 50) ÷ 50 × 100 = 10 ÷ 50 × 100 = +20%.
2. Weekly sales of the shirt fall from 400 to 340. Find the percentage change in quantity.
Show answer
(340 − 400) ÷ 400 × 100 = −60 ÷ 400 × 100 = −15%.
3. A price falls from RM80 to RM68. Find the percentage change. Then find the percentage change needed to return from RM68 to RM80, and explain why the two figures differ.
Show answer
Fall: (68 − 80) ÷ 80 × 100 = −15%. Return: (80 − 68) ÷ 68 × 100 = 12 ÷ 68 × 100 ≈ +17.65%. The base differs: the fall is measured from RM80 and the rise from RM68.
Where this leads next
Next, use these percentages in interpreting an elasticity value and sign. The percentage-base explorer lets you change the base and watch the answer move, and the elasticity tutor checks your full working.
Students who understand the formula can still pick the wrong base under time pressure. Our teachers look for that pattern in online one-to-one Economics tuition.