Explanation of price structure
for "Identity" badges

You don't need to understand what's on this page, as both the Quick calculations page and the order form itself will tell you how much your badges are going to cost. But I thought some people might be interested anyway.

So here's the story...

I was thinking I wanted to start charging a bit less for larger orders, so as to encourage people to sell the badges in their local groups, or just buy more for their friends, or maybe stock them at stalls or in shops. Although I decided I didn't particularly want to encourage people to order more than 150 at a time. (That's quite enough badges to make all in one go )

Traditionally that would imply a stepped price structure, so I thought of having one something like this...

But then you end up with a silly situation where, for instance, 49 badges costs more than 50, and the total price rises jaggedly like this:

graph of totals for stepped price structure

When I'm buying stuff myself, and I encounter prices like that, I tend to start thinking things like "hmm I've chosen 90 badges but if I go up to 100 it gets cheaper, shall I do that? but there's certainly no point in choosing 96, or then again maybe I should only choose 50 now and save the rest and do 50 again next time"... and if you care about getting the best value, it gets rather complicated. Which is not the experience that I would like my customers to have. So I thought surely there must be a better way

And there is - and how come people don't do it more often is probably mainly because it's got an equation in it. But as I'm having the computer do all the calculations, there's no reason why not.

So instead, I decided to have a middle section with prices that change incrementally with every badge, like this. Here, they start getting cheaper after 12 badges, and the price per badge decreases quickly till 50 badges, and then more slowly...

Which gives a rather elegant curve of total prices, like this!
(Dotted line shows how much the badges would cost without any discounts.)

graph of totals for smoothly varying price structure

For the humans, this is much simpler than the steppy version. For every additional badge from 12 to 150, you know that they're always getting a tiny bit cheaper. How cool is that?!

For the maths fans: the badge price within the sloping sections of the third graph is given by the following equation:

badge price = lowprice + {(hightotal - badgetotal)(highprice - lowprice)/(hightotal - lowtotal)}

where: highprice is the top price in the section (e.g. 65p)
lowprice is the lowest price in the section (e.g. 50p)
hightotal is the max number of badges bought in that gradient section (e.g. 150)
lowtotal is the min number of badges bought in that gradient section (e.g. 50)
and badgetotal is the variable of how many badges you're buying.

Explanation of price structure for "Identity" badges

Explanation of price structure
for "Identity" badges