You read the original comment differently than I did. I assumed some magical doubling, as if every dollar bill in someone's pocket duplicated itself.
If you want to play "What If?" I guess we need to figure out if we're magically erasing everyone's memory of their previous holdings. If not, the world would go a bit crazy. Journalists would report it, we'd learn about the existence of magic, etc. So, I guess we'll need to assume that the magic doubling also makes people forget what they had before.
Let's see ... there might be a bit of a wealth effect [0], but if we're saying people don't remember their old balances, would they really perceive themselves as wealthier? This question is just too nonsensical to really pursue. It could be a fun thought experiment, but it's hit the point where I'd rather get some work done instead.
OK, so walk us through it. What are the mechanics that transmit the money supply increase to wages and prices?
If the money supply instantly doubled by magically changing Treasury bonds and collateralized mortgages into cash, what would happen?
Cash balances would go up for banks, brokerages and wealthy investors but cash balances would stay the same for most people who don't own these securities.
Would that cause an instant doubling of wages and prices throughout the economy? Or would banks, brokerages and wealthy investors just hold on to their new, bigger balances?
This isn't really about timing, since even if the money supply instantly doubled, you'd probably see velocity instantly cut nearly in half.