V is part of the monetarist definition of money - the Fisher Equation, MV=PT, where M is the money supply (bills, coins, and demand deposits [checking accounts], so-called "high-powered money"), V is the velocity of money, P is total prices and T is total output.
Every dollar in circulation is passed from hand to hand. The dollar you pay me, I pay the grocer, who pays the wholesaler, who pays the trucker, who pays the mechanic, who pays the dentist, round and round and round. The rate of exchange is the velocity of money.
In Classical macroeconomic theory, the velocity of money is constant. In real life, it isn't.
I believe, although I can't prove, that a decrease in V due to such circumstances as a decrease in spending, an increase in hoarding, business failures, bank failures, exchange rate shocks, and the like, is the "cause" of recessions and depressions, although it may well be simply the result.
At any rate, in recessions and depressions, V decreases. By definition, T decreases, too, that's how we define recessions and depressions.
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