Final answer:
To compute price indices and inflation rates, one must calculate the index for each year compared to a base year, set at 100. The inflation rate is the percentage increase from one year to the next. Changing the base year alters the numerical inflation rates but does not affect the underlying trend of price level changes.
Step-by-step explanation:
Calculating Price Indices and Inflation Rates
The problem involves calculating price indices and inflation rates based on given data of a basket of goods in the United Kingdom over four years using two different base years. The first step is to set each base year equal to 100 and then calculate the respective price index for each of the other years. To calculate the inflation rate, we look at the percentage increase from year to year, using the first year as the initial reference point for comparison. When using a different base year, such as year 4, the inflation rate would be reflected differently. This is due to the base effect, which changes the reference point from which changes are measured. However, the overall trend of inflation remains the same; what changes is the perspective of measurement. Hence, the selection of a base year can influence the numerical representation of the inflation rate.
Example Calculation
Using year 1 as the base year (year 1 price index = 100):
- Year 2 price index = (970 / 940) * 100 = 103.19
- Year 3 price index = (1000 / 940) * 100 = 106.38
- Year 4 price index = (1070 / 940) * 100 = 113.83
Inflation rate from year 1 to year 4 based on year 1 as the base year:
((113.83 - 100) / 100) * 100 = 13.83%
Using year 4 as the base year (year 4 price index = 100):
- Year 1 price index = (940 / 1070) * 100 = 87.85
- Year 2 price index = (970 / 1070) * 100 = 90.65
- Year 3 price index = (1000 / 1070) * 100 = 93.46
The calculations illustrate that the inflation rate itself does not change when a different base year is used, as it is a measure of the overall increase in prices across a set period, regardless of the base year selection.