More Than One Inflation Rate
For example, if prices on alcohol and tobacco rises substantially, then people who are both teetotallers and non-smokers will see no reduction in purchasing power at all, while people who are heavy drinkers and/or smokers will see a significant reduction in purchasing power.
Similarly, if prices of luxury goods rises, then that will have almost no effect on the purchasing power of the poor while significantly reducing the purchasing power of the rich, while higher prices on cheaper forms of food or clothes will have almost no effect on the purchasing power of the rich while significantly reducing the purchasing power of the poor.
Sometimes the rich spend more money on certain items, like food, clothes and fuel, yet people with low income might still be hit harder from rising prices of the commodities used, because first of all their income is by definition lower and the spending on these items may therefore still be a higher percentage of their total spending, and secondly because they to a higher extent buy food and clothes whose production costs to a higher extent consists of commodity inputs.
Most statistical bureaus around the world either are unaware of or ignores this insight, but Hong Kong's statistical authority has interestingly created, besides the general CPI, three sub-indexes for people with low income (called CPI-A), middle income (called CPI-B) and high income* (called CPI-C) earners. In the latest year, despite having a higher food price inflation, low income earners have had somewhat lower inflation rate than middle income earners, with middle income earners similarly having a somewhat lower inflation rate than high income earners despite having higher food price inflation.