Question

Which one is correct ??

When we are calculating the consumer price index and the inflation rate for a certain year,

                1.the value of the consumer price index may depend on the choice of a base year, but the inflation rate does not depend on the choice of a base year.

                2.both the value of the consumer price index and the inflation rate may depend on the choice of a base year.

                3.the inflation rate may depend on the choice of a base year, but the value of the consumer price index does not depend on the choice of a base year.

                4.neither the value of the consumer price index nor the inflation rate depends on the choice of a base year

Answer 1

The correct option would be

• 1. the value of CPI may depend on choice of base year, but inflation rate does not depend on the choice of a base year.

The reason being that the change in base year changes the CPI as shift in origin (but not scale), but the inflation, which is the rate of change in CPI, stays the same since the rate of change is not affected by changes in origin only.

Consider for example, the CPIs for year 1,2,3,4 as 100, 110, 121, 133.1. The base year is 1 with 100 CPI. The subsequent years increases by consistent inflation rate of 10% per year. It is to be noted that the price rises in year 2 from year 1 by 10%, in year 3 from year 1 by 21% and in year 4 from year 1 by 33.1%. This change in price level from the base year is what is seen in the CPIs.

Suppose that we change the base year to year 2, then the CPI would be as 90.909 (approx), 100, 110, 121. The formation is the same as before, the CPI rises per year by 10%. But what is to be noted is that, in this case too, we have the price rise in year 2 from year 1 by 10% (approxed from 10.00011%), in year 3 from year 1 by 21% (approxed from 21.000121%) and in year 4 from year 1 by 33.1% (approxed from 33.1001331%). Hence, the change in the CPI from the base year is preserved.

The formula used is , representing the rise in price or inflation in year i from year k.The graph is as below.