A few reasons why your analogy is flawed. First, M0 (which is one of the more conservative definition of money, is about 4 trillion, so the value loss from a billion dollars is not going to be anywhere near 10% to start off with). Secondly, by printing money you're again only affecting M0, but there are a lot of debt-based instruments that are probably better characterizations of "total money", but since they are debt-based it creates some level of 'springiness' to the total money supply.
Finally, it's not clear to me what you mean by 'functioning properly'. Even if a small change triggers a bigger effect (it will, these things are categorized by cascading effects) - Is the market coordinating individual values with prices? Probably, it is: it's just that the individuals' value systems have gone a bit out of whack in a spate of mania. But who are we to judge if people get a little silly from time to time?