Final answer:
The price index for each period relative to the base period is calculated by dividing the cost of the basket in each year by the cost in the base year and multiplying by 100. The base year is always set to a price index of 100. Different base years generate different index numbers, but the inflation rate between two years remains consistent irrespective of the base year.
Step-by-step explanation:
To determine the price index for each period relative to a base period, one needs to follow a straightforward mathematical approach. Assume 2003 as the base year and that the basket cost $15.35 in that year. The price index for 2003 would be set to 100, as it is the base year. For every other year, the price index is calculated by dividing the cost of the basket in that year by the cost of the basket in the base year and then multiplying the result by 100. For instance, if the basket cost $16.00 in a subsequent year, the price index would be ($16.00 / $15.35) × 100, giving a price index higher than 100, indicating inflation over the period.
When calculating two price indices using different base years, even though the individual price index numbers will differ, the measure of inflation between two specific years remains the same, as inflation is represented by the percentage change in the price indices between those years. If we set year 1 (with a basket cost of £940) as the base year and calculate the price indices for subsequent years, and then use year 4 (with a basket cost of £1070) as the base year for a second set of calculations, the inflation rate between years, say year 1 and year 3, will still be equivalent regardless of the base year chosen.