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First off, I'd like you guys to take into consideration that I have no clue what I'm trying to do "mathematically speaking". I am here trying to find help with a function for my website where I sell intangible goods.

I am selling a limited number of products online and would like to increase the charge per item as the remaining number of products decreases. However, I do not want to keep a fixed rate across, as I dont want the final price to be over inflated. Therefore, I would like to increase the price in a descending pattern. Can you supply me with a function for this?


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I'm not sure what you mean by "increase the price in a descending pattern"—could you give an example of what the price of the item might be originally and at a few points where the remaining number has decreased? – Isaac Jan 29 '12 at 4:51
There are literally an infinite number of different ways for you to increase a price in decreasing increments following your criteria. Giving us more stringent requirements (or better yet, an example, as Isaac says) would help us greatly in giving you a good answer. – Lopsy Jan 29 '12 at 5:26
Thank you for the comments, the function I am looking for here is one that would let's say increment the price by 2% when I decrement the remaining numbers of that item. But then that 2% would stack up on each sale and the price would be too high. Let's say the standard price is 1000$ for a product and there are 1000000 available items of that product. When it reaches 1 remaining the price would be too high due to the stacking of that 2%... I am just giving an example here hoping that I can get my idea across. Please if you need more info I will try my best. Thanks again :) – user1027620 Jan 29 '12 at 6:46
So what I am saying is that there should be someway to also reduce that percentage depending on the product initial price. Where in my example 2% should be variable and not static. – user1027620 Jan 29 '12 at 6:47
It sounds to me like what you really want is a monotonic function $f$ mapping the number of items to the price of each item, such that $f(1,\!000,\!000) = 1,\!000$, and $f(1)$ is higher than $1,\!000$ but not "too high" in some way that you haven't specified. Is that right? – Rahul Jan 29 '12 at 7:38
up vote 0 down vote accepted

My suggestion would be use a Geometric series which limit is bounded.

another example is: increase = $ \frac{1}{k!}$

set variable k = amount left of the item

$ Price_{k-1} = Price_{k} + increase_{k}$

this way the Price of the item will increase by a fraction each time.

the limit of the series used for the variable increase is e.

That should keep the price from being over inflated, you are just summing backwards of the series.

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