Let's say I have a "friend" who is interested in the inflation adjusted price of oil in 1981 from 2004 to 2008. My friend uses the CPI to calculate the inflation adjusted price.
What cost $40 in 1981 would cost $83.12 in 2004.
What cost $40 in 1981 would cost $85.94 in 2005.
What cost $40 in 1981 would cost $88.71 in 2006.
What cost $40 in 1981 would cost $91.24 in 2007.
What cost $40 in 1981 would cost $92.88 in 2008.
But, many of the goods in the basket used to calculate the CPI are related to the price of oil. So, a real increase in the price of oil (an increase that has nothing to do with inflation) will make the cost of the goods in the basket higher. Right? But the CPI would call that increase "inflation" when part of it might be a real increase in price.
So, in that case, isn't using the CPI a little circular if you want to know if the price of oil has increased in real terms? Of course, you'd run in to this problem with ANY product since markets are interdependent, but with a commodity like oil, that is so central to so many economic activities how can you really tell if the price is inflating, or if the price is actually rising and driving prices up all over the market in real terms?
How do economists deal with this?