On Thu, Nov 6, 2008 at 2:56 PM, Elliott Hird <[EMAIL PROTECTED]> wrote: > 17. Every midnight (UTC) that the PBA has zero of a given Eligible Currency, > that currency's exchange rate goes up by 2. Every Monday midnight (UTC) that > the > PBA has a non-zero amount of a given Eligible Currency, that currency's > exchange > rate goes down by 2.
Now, I was going to say that in theory, this results in undefined behavior around non-Monday midnights when the PBA has 0 of something, but then I realized that this is only true when the PBA's exchange rate is equal to the value, i.e. the PBA has at least 1 of it. When the PBA has 0 of something, the exchange rate is merely less than or equal to the value, and so it's free to vary without regard for price. I guess Monday midnights are more interesting. When the PBA's holdings are non-zero, exchange rate is equal to value, which means that it cannot change in a predictable manner. However, non-zero Monday midnights do have exchange rate (equal to value) changing in a predictable manner, which means that non-zero Monday midnights cannot exist. But there is no economic motivation to withdraw everything in preparation for a Monday midnight, as prices are about to fall, not rise. This all seemed inconsistent until I realized that there's another way for values to remain unpredictable: the exchange rate can fall to 0 as people *deposit*, as they are economically motivated to; an exchange rate of 0 cannot go lower. So, in theory, every Monday midnight, either the PBA's holdings or the exchange rate will go to 0. I don't think we've actually seen this happen, which goes to show you that mathematics is interesting but useless. --Warrigal
