Mathematical dilemma for creating stock-market style price fluctuations in java program

Question

Ok, basically I have a base price r, and a base stock amount a for item y. Item y's price is x.

Lets call the item a pencil.

so: r is a base price, lets say $1. a is the typical base stock, lets say 100. y is the current amount in stock. x is the price of the item.

If half the normal supply of pencils is available, then the price goes up, or x = r * (a / y), which would be x = 2 if only half stock available, or y=50.

The flaw with my primitive system is if the stock dwindles to only 1 left, x becomes 100, and nobody in their right mind is going to pay $100 for a pencil!

How can I create a mathematical equation that would create a slope in this ridiculous graph, so that, lets say, if stock is 50, price is 2, but if stock is only 10, the price is 2.50... There is a word for what I'm trying to describe, and it's on the tip of my tongue, but I can't find it...

I hope I'm conveying this question correctly!! lol, I'm so mind-f*cked right now...

Answer 1

You say no one in their right mind would pay $100 for a pencil... but they would, if it was the last pencil left on Earth!! But typically most simulations like this one wouldn't deal with such low supply. Typically you would want to write a function that is accurate from 1000 to 100000 or something, and just ignore the crazy numbers that result at 1.

Anyway, have a look at this document: http://www.csun.edu/~dgw61315/PTlect2y.pdf Page 4 has a simple mathematical example of a market.