A price index compares basket costs
Definition
Real income: income measured by what it can actually buy, after allowing for the change in prices.
- A price index is found by dividing the cost of the basket now by its cost in the base year, then multiplying by 100.
- Keep the base year on the bottom of the fraction, because the index measures how far prices have moved away from it.
- An index above 100 means prices have risen since the base year, and below 100 means they have fallen.
Example
- A basket of goods and services cost £200.00 in the base year and £205.80 in the year being compared.
Step 1: divide this year's cost by the base year cost and multiply by 100:
price index=205.80200.00×100 \text{price index} = \frac{205.80}{200.00} \times 100 price index=200.00205.80×100Step 2: work out the answer:
price index=102.9 \text{price index} = 102.9 price index=102.9- The basket cost 2.9% more than it did in the base year.
The inflation rate is the index change
- The inflation rate is the change in the index divided by the earlier index, then multiplied by 100.
- Divide by the earlier index, because the rate measures the change against where prices started.
- A negative answer means the price level fell over the period, which is deflation rather than low inflation.
Example
- A CPI index rises from 132.0 in an earlier period to 135.8 a year later. These two figures are illustrative.
Step 1: find the change in the index:
change in index=135.8−132.0=3.8 \text{change in index} = 135.8 - 132.0 = 3.8 change in index=135.8−132.0=3.8Step 2: divide by the earlier index and multiply by 100:
inflation rate=3.8132.0×100=2.9% \text{inflation rate} = \frac{3.8}{132.0} \times 100 = 2.9\% inflation rate=132.03.8×100=2.9%- Prices rose 2.9% over the year, which is the rate UK CPI inflation actually recorded in the twelve months to July 2026 (Source: ONS).
Inflation changes what a price buys
- To find what a price becomes after a year of inflation, multiply it by one plus the rate written as a decimal.
- To find the change in real income, subtract the inflation rate from the percentage rise in pay.
- That subtraction is an approximation, but it is accurate enough at the low rates a GCSE question uses.
Example
- A season ticket costs £1,200 and inflation over the next year runs at 2.9%.
Step 1: multiply the price by one plus the rate as a decimal:
new price=£1,200×1.029=£1,234.80 \text{new price} = \pounds1{,}200 \times 1.029 = \pounds1{,}234.80 new price=£1,200×1.029=£1,234.80- A worker whose pay rises 2% over the same year still faces a fall in real income.
Step 2: subtract the inflation rate from the percentage pay rise:
change in real income=2%−2.9%=−0.9% \text{change in real income} = 2\% - 2.9\% = -0.9\% change in real income=2%−2.9%=−0.9%- The cash figure on the payslip went up, but the pay buys about 0.9% less than it did a year earlier.
Finish by naming the units
- An index has no units, so it is quoted as a plain number and compared with 100.
- An inflation rate is a percentage and a price is in pounds and pence, so label whichever the question asked for.
- Keep any minus sign, because a negative answer is the whole message: prices or real income fell.
Exam technique
- Check whether the question wants an index number or a rate, because both come from the same figures and answer different questions.
- Keep the earlier value on the bottom of the fraction, since using the later one gives a rate that is wrong in a way that is easy to miss.
Self review
- Write down the formula for a price index.
- A basket costs £250 in the base year and £260 now. Calculate the price index.
- A CPI index rises from 120.0 to 123.0. Calculate the inflation rate.
- Pay rises 3% while inflation is 4%. What happens to real income?
- Why must you divide by the earlier index rather than the later one?
