> But if there's a fall in aggregate demand at a given price level, there are _fewer_ dollars chasing the same number of goods for a period of time. So if government spending is greater than taxation for that given period, it doesn't necessarily cause inflation.

I actually completely agree, but with a caveat. It may not cause inflation in terms of this years price level being higher than last years price level, but it will cause a decline in the purchasing power of the dollar. For example, let's say in the absence of intervention the price level would fall by 2%, but with intervention the price level would stay the same. That's still a 2% decline in purchasing power.

> The "monetary base" increases because of the way they define the monetary base.

The monetary base is defined as the sum of all currency (including coin) plus bank deposits. It increases or decreases completely at the Fed's discretion, because the Fed has the unique ability to create reserves. This isn't some semantic trickery.