If the yearly average CPI change for ten years is 10%, does this mean CPI has increased by 100% in 10 years?

Question

CPI=consumer price index

What is the diferrence between CPI and inflation or are they the same?

Answer 1

It all depend on how the yearly average is worked out. If it is a geometric mean growth rate, it is closed to the compund groth rate and hence 10%growth rate on an average, would mean much more than 100% growth in 10 years. 100% growth means doubling of the initial figure. There is a thumb rule. If you want any thing to increase 100% or double in x years, the annual growth rate be y such that x multiplied by y gives you 72. So, if 10% is the annual growth rate, then 10*y should equal 72. That is y=7.2 years.

But this is about geometric average or compuond growth rate.

If the average is a simple average, there are problems. We can show a case where the 10 year average growth rate of 10% will mean 100% growth in 10 years. Consider this: for the first 9 years there was 0 growth and in the last year there was 100% growth. This means the yearly average growth rate is (0+0+0+0+0+0+0+0+0+100)/ 10= 10%. And the figure say 500 initially remained at 500 for 9 years and then increased to 1000 in the 10th year. You have yearly average growth rate of 10% and 100% growth in 10 years. But consider another example: the yearly growth rate percentages for 10 years are: 0,0,0,0,0,0,0, 30, 30, 40. This means that the arithmatic average growth rate is   (0+0+0+0+0+0+0+25+50+25)/ 10 = 10%. But the 10 year period grwoth is much higher. 500 remained constant for seven years, then increased to 600, then to 900 and finally to1125 in the 10th year. So the growth for the 10 year period is (1125-500)*100/500= 625/5= 126%.

So, it is not necessarily true that If the yearly average CPI change for ten years is 10%, that the CPI has increased by 100% in 10 years: it may or may not be.

CPI measures the average level of prices for the products and services the household consumers buy for their living. The CPI therefore can indicate the inflation relevant from the household consumers point of view. But many things are produced which are not consumed by household directly: for example iron ore, or metallurical coal used by steel plants or timber that goes into the making of furniture or the macinery that produces fertilizers. When all kinds of primary, intermediates, secondary and final consumption goods prices are considered we have the general price index - sometimes called wholesale price index sometimes called producers' price index. This general price index is the true indicator of general inflation

Even otherwise, please note that no price index is a measure of inflation. Aprice index is a price index. To measure the inflation rate one has to find out thec rate at which the price index is changing over time.

Answer 2

NO - CPI will not increase by 100% over 10 years, growth will be +159%

Here is dynamics:

Year.......Multiplier

0.............1.00

1.............1.10

2.............1.21

3.............1.33

4.............1.46

5.............1.61

6.............1.77

7.............1.95

8.............2.14

9.............2.36

10...........2.59

CPI is not the same as inflation (though general public often confuses them).

CPI measures only consumer prices while inflation shows overall price level changes e.g. includes producer index too in appropriate weights.