"If the Fed wants to increase all nominal variables by 100 fold, it simply increases the base 100 fold."
This is a fairly standard "money neutrality" argument. (Money neutrality is an argument that changing the amount of money in an economy just changes the price level without affecting real activity. In Scott Sumner's example, if the monetary base is multiplied by a factor of 100, all prices increase by a factor of 100, but volumes of real goods produced should be unchanged.) Nick Edmond's response involves a somewhat complex Stock-Flow Consistent model in which he models the impact of changing the monetary base.
I have a much simpler take on the issue of money neutrality.
In order for money to be neutral, the change in the money supply cannot have a "distributive impact" (an impact on the distribution of wealth and income). As an extreme example, if the Government of Canada decided to double the Canadian monetary base by cutting me a rather large cheque, the pattern of economic activity in Canada would decidedly change (trust me). More reasonably, changing the monetary base by the central banks buying bonds does have a distributive impact - the government has rearranged assets for some members of the private sector, and you end up with the "portfolio balance effect" that allegedly causes Quantitative Easing to work. Keeping in mind that debt is unequally distributed across households and firms, it is very difficult to change the money supply without having distributive effects.
But there is one way to change the money supply without having a distributive impact - re-denominate the currency. For example, replace $1 in "old dollars" with $100 in "new dollars". Debts and other monetary contracts are also re-denominated by the same ratio. Countries have done this in the aftermath of severe inflationary episodes (although they have gone the other way, lopping a few zeros off of their currency values). In this case, there are no apparent distributive impacts of the move, so money should be neutral. But since the authorities did make the change in order to affect economic activity (to end inflationary psychology), money is possibly not neutral even in this case.
In summary, I argue that in any economy with debt, an operation that preserves money neutrality is equivalent to the trivial case of a re-denomination of the currency.
(c) Brian Romanchuk 2013