Final answer:
Price indices show the change in the cost of a basket of goods over time, relative to a base year. Calculating a price index using year 1 as the base, year 4 shows an inflation rate of 13.83%. Using year 4 as the base, year 1's index indicates that prices were 12.15% lower compared to year 4.
Step-by-step explanation:
The question involves calculating price indices and the inflation rate using two different base years. To calculate the price indices, we take the total price of the basket of goods for the year in question and divide it by the price in the base year, then multiply by 100. Using year 1 as the base year the price index for year 4 will be (1070/940)*100 = 113.83, meaning prices have increased by 13.83% since year 1.
Using year 4 as the base, the price index for year 1 would be (940/1070)*100 = 87.85, indicating that prices were 12.15% lower in year 1 compared to year 4.
To calculate the inflation rate between year 1 and year 4 using the first price index, we subtract the base index (100) from the year 4 index (113.83) to get 13.83%. Had we used the index based on year 4, which would have required comparing it against year 1, the process to determine the inflation rate would have been essentially the same, but the interpretation of the percentage difference would be in the context of the selected base year.
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