# CPI and RPI

Discussion in 'Mathematics' started by florapost, Dec 21, 2011.

1. ### florapost

Ok - i know CPI is a geometric mean, so it comes out smaller than RPI, which is an arithmetic mean.
i also know that the theory behind having a lower inflation rate for benefits and pensions is that we will substitute - if the price of oranges goes through the roof, we will buy fewer oranges and buy more apples instead
what i don't see, and i have googled for elightenment but failed, is why a geometric mean models substitution shopping
any help?

2. ### florapost

Ok - i know CPI is a geometric mean, so it comes out smaller than RPI, which is an arithmetic mean.
i also know that the theory behind having a lower inflation rate for benefits and pensions is that we will substitute - if the price of oranges goes through the roof, we will buy fewer oranges and buy more apples instead
what i don't see, and i have googled for elightenment but failed, is why a geometric mean models substitution shopping
any help?

4. ### PiranhaStar commenter

There is some logic to this, but only if we assume substitution is always possible. Within a catagory, substitution is very likely. However, it is not always the case. For example, energy prices have risen across the board. Even if they hadn't, substitution is difficult; I am not going to rip out my gas boiler because oil becomes cheaper than gas. I am certainly not going to turn off the heating to buy a 50 inch 3D TV!
IMO, the switch to CPI is political; Governments want inflation to look low. The UK was one of the last countries to stay honest on this. They still do now, but only if you have a student loan! CPI is particularly unfair when applied to pensions etc as much of the spending of lower income groups is on energy, food etc where little substitution is possible.

5. ### florapost

thanks illumination - i shall go through that with a spreadsheet in a separate window
pirhana - i totally agree it's political - as well as your 'can't substitute' subset, categories have to be wider than 'brands of potato' in illumination's cited article - for example, 'fruit' rather than 'apples' or 'oranges' - and if i end up buying apples, which i don't like as much, instead of oranges, because their price has hiked, i reckon i'm worse off