But what CAUSES velocity to increase?
People's demand for goods and services.
Also, people's demand to hold money. The demand-level for money affects the price of money even more strongly and directly than the demand-level for goods.
Suppose you have two similar countries, each with their own fiat currencies. Country A decides to double its monetary base. Country B leaves its monetary base unchanged. An Austrian economist predicts prices will rise sharply in country A.
No, an Austrian economist would not predict that. An Austrian economist could only say that *
all else equal*, if everything else is held constant, then yes: an increase in the money supply will result in a decrease in the price of that money, and that this will (eventually) result in the prices of other products being higher than they would otherwise have been, priced in terms of money (not necessarily up [much less "sharply"], just higher than otherwise). The problem is,
all else is never equal. There are many variables involved. Supply of money is a critical factor, yes, but also:
demand to hold money,
demand to purchase goods,
supply of goods,
changes in time preference,
etc.
The prices of goods may go down or stay the same, as they did in the 1920s: despite massive monetary inflation going on, there was no price inflation, because a rapid rise in productivity outpaced the inflation. So in the 1920s, supply of money rapidly increased, and demand for money probably stayed about the same, but supply of goods rapidly increased as well (due to increased productivity). All together, these factors resulted in price levels being flat.