My brief explanation has confused you more, so here's a fuller one. Today's real post (which includes pictures of the wall!) will come later this evening.

Right. Let's say that there is £100 to pay and there are six groups to pay it; they equally share the service it provides. To start with, because group A has more money than the others, it agrees to help out by paying most of it, but after two or three years (the composition of the group having changed somewhat) a new member points out that A pays £80 and each other group is paying £4, and this in no way reflects the relative incomes, nor is it fair. So she suggests that A should pay £50 and the others each pay £10; that is, that A pays half. She appreciates that this is a large jump and proposes that the amount that A pays should reduce over a period of 6 years, so that in year 1 they pay £75, year 2 £70 etc. At the same time, the other groups each pay the rest; that is, in year 1 they each pay £5, in year 2 £6 etc. This is agreed to be reasonable and is agreed.

After 5 years, a representative of the other 5 groups points out that they had expected to pay an increase of 5% each year, but it has always been a lot more than that. They start to feel hard done by and suggest that they pay the same amount as they did the previous year, although there is a contract to pay the full £100. They are too polite to say so, but clearly it's believed that it's Group A's problem, although by now Group A, whose income stays the same although other expenses have gone up, is finding it hard to pay its own bills by now and needs the full contribution.

The thing is, the total bill (100%) is being shared out differently each year, in that A's share reduces by 5% of the total each year and each other group's share increases by 5% of the total each year. But that doesn't mean that the actual money increases or reduces by 5% each year, because the percentage increase or decrease starts at a different number.

That is, A pays £80 (which is 100% of A's contribution) one year and £75 the next, which is (roughly, if anyone cares to do the sum it'd be great, but I can only do simple sums) 6.5% reduction on £80, whereas each other group pays £4 (100% of their contribution) one year and £5 the next. This is a simple sum - it's a 25% increase. Looks massive, doesn't it? - but they're still paying only 5% of the whole, even though it's 25% more than they did the previous year.

The actual sum involved is several thousand pounds and there's a cost of living increase each year, but the sum paid by each is still paid in the agreed proportion.

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## 8 comments:

I understood what you were saying the first time.

Yes darling, but you've spent a lot of time in my company in the last few months and have learned to interpret my vague utterances. Others haven't been so lucky.

Me too.

Still fun to contemplate the angles though.

I feel that some people at the meeting last week were quite obtuse.

So, the percentage is the same for all but A, but the amount has changed? For that to be so, it seems to me that something else had to change; ie more people or groups, lower actual sum to pay, or higher sum to pay. Guess coffee doesn't help with figuring.

No, it's that the percentage isn't being calculated from the same figure. It's 5% of £100, which is the whole, but the people who thought they were paying too much didn't realise that a reduction of 5% from the whole is not the same percentage as an increase from the small sum they paid. If they paid 5% more than their original £4, that would mean they paid £4.20 each rather than £5, which would mean that all 5 together would only pay £21 after the first year rather than £25.

I think I see now but please don't ask me to explain it to anyone else . . . .

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