When you calculate a percentage in economics, the base is the number you divide by. For a change over time it is the starting value, and for a share it is the total. This skill appears in growth rates, price changes, market shares and the elasticity calculations in economics data responses.
Why does the base matter so much?
A percentage always says “this much compared with that much”. Change the “that” and the answer changes, even though the arithmetic is correct. A data question may tempt you to use whichever number is nearer your pen.
Ask two questions before dividing. First, is this a change or a share? Second, what is the reference point that the question is measuring against?
How do you choose the base, step by step?
- Underline the thing being measured, such as sales, price or output.
- Decide: change or share? A change needs a “from” and “to” value. A share needs a part and a whole.
- Pick the base. For a change, it is the “from” value. For a share, it is the whole.
- Calculate (difference or part) ÷ base × 100.
- Sense-check. A rise from a small base to a larger one gives a percentage rise bigger than the matching percentage fall in reverse.
Worked example
Kestrel Bakery is a fictional business. Its weekly revenue was RM40,000 in March and RM50,000 in April. In April, bread made RM30,000 of that revenue.
(a) Percentage change in revenue. Change = 50,000 − 40,000 = RM10,000. The base is March, the starting value. 10,000 ÷ 40,000 × 100 = 25%.
(b) Share of April revenue from bread. This is a share, so the base is April’s total, RM50,000. 30,000 ÷ 50,000 × 100 = 60%.
(c) The reverse movement. If revenue later falls back from RM50,000 to RM40,000, the base is now RM50,000. 10,000 ÷ 50,000 × 100 = 20%.
A 25% rise followed by a 20% fall returns to the start. Notice that the same RM10,000 gives two different percentages, because the starting point changed.
The mistake to watch for
Mistaken answer: “Revenue rose from RM40,000 to RM50,000, so the rise is 10,000 ÷ 50,000 = 20%.”
The student divided by the newer figure because it was the larger number and looked like the “total”.
The correction is to ask “what did it start at?” The change is measured against RM40,000, so the answer is 25%. Dividing by the ending value turns the percentage rise into the percentage of the new figure that the change represents, which is a different quantity.
A related slip is to treat a 25% rise and a 25% fall as cancelling out. Starting at RM100, a 25% rise gives RM125. A 25% fall from RM125 is RM31.25, so the result is RM93.75, not RM100.
Check yourself
1. The fictional price of a notebook fell from RM8 to RM6. Calculate the percentage fall.
Show answer
Change = 8 − 6 = RM2. The base is the starting price, RM8. 2 ÷ 8 × 100 = 25% fall.
2. In a fictional market the total sales are 120 units. Firm A sells 30 units and Firm B sells 42 units. Find the market share of each.
Show answer
The base is the total, 120. Firm A: 30 ÷ 120 × 100 = 25%. Firm B: 42 ÷ 120 × 100 = 35%. Check: 25% + 35% = 60%, which leaves 40% for the other firms, or 48 units, and 30 + 42 + 48 = 120.
3. The fictional unemployment rate in Marlow moves from 5% to 6%. State the change in two ways.
Show answer
It is a rise of 1 percentage point. Measured against the starting rate, 1 ÷ 5 × 100 = 20% rise in the rate. Both are correct, but you should say which you mean.
Where this leads next
With the base secure, move on to describing a trend with a qualification, then try the mixed practice set. The percentage-base explorer lets you swap the base and watch the answer change, and the elasticity and percentage-base tutor applies the same idea to price and quantity.
Some students calculate smoothly once the base is named, but pick it instinctively under time pressure. That is a habit our teachers can look at in online one-to-one Economics tuition.