Inflation, apples and oranges.

Inflation screws up all our thinking about prices, but if we’re careful to avoid meaningless numbers, it’s easier to reason about.

I’m somewhat obsessed with inflation. It’s hard to reason about increases/decreases in prices, market sizes, and so on when a 1994 pound is to all extents a different unit to a 2011 pound. And in our culture of shallow infographics where we’re invited to compare THIS to THAT constantly it’s really important to get accurately to the meaning of monetary information.

@RoryTweet posted this brilliant picture showing two rail tickets, one from 1994 the other from 2011. Now, they show different things – one a travelcard bought under the now defunct Network Card scheme, and the other an off-peak return – but if we assume they’re the same for a minute, what can we say about the change in prices?

Well, obviously £4.20 < £10.20. But how much less? Looks like less than half. The difference is £6. So an 140% increase. Wow.

But 1994 pounds aren’t 2011 pounds, so let’s use different units – how about apples and oranges? Would it make sense to say 4.20 oranges < 10.20 apples? Maybe, but not really, right?

A 1994 pound is worth around 50% more than a 2011 pound, so let’s say to convert an orange amount to an apple amount, we need to times by 1.5. Or with proper units, our conversion rate is 1.5 apples/orange. We’ll need to know that conversion rate, and its units in a bit.

So – using our conversion rate. We can say:
4.2 oranges * 1.5 apples/orange = 6.30 apples.
10.2 apples – 6.3 apples = 3.9 apples less.

Or we can go the other way and say:
10.2 apples / 1.5 apples/orange = 6.8 oranges.
6.8 oranges – 4.2 oranges = 2.6 oranges less.

We can now see that the cost has risen by 61% – 3.9 apples/6.3 apples or 2.6 oranges/4.2 oranges. We don’t need any units here, apples cancel apples, oranges cancel oranges. And the percentage calculation works no matter which fruit (or year) we take as a base.

This is much less than the 140% we originally guessed at. We overestimated the increase by 2 and a third times. Goddamned inflation, scourge of dramatic infographics everywhere, does this.

Now here’s where it gets tricky. It’s tempting to say – of the increase of 6 fruit, a certain amount of that increase is down to apple/orange conversion (or inflation) and a certain amount is down to a price rise.

But, I hope you can see that the idea of a 6 fruit increase is kind of meaningless in itself. The rise doesn’t have meaningful units, it’s, in our example, literally comparing apples and oranges.

So, the trick is to convert to a base unit – either 1994 or 2011 pounds and then talk about percentage increases. That works, the units make sense.

And we can avoid meaningless statements. If you see an infographic or statement comparing £ amounts without having converted them to an annual base first or talking about absolute increases due to inflation, well, beware, they’re likely to be very wrong.