The cash value equation I’ve been using rests on an assumption that the money supply of any economy is exactly equal to the inventory of all the goods that it can buy. Any difference reflects an error of pricing (or production). The principle resembles the quantity theory of money, where as money supply expands prices tend to increase, and when it contracts, there is a downward pressure on prices. Money supply is one of many factors that affect the price a merchant chooses to charge for an item or that the buyer chooses to pay for it.
Having discussed monetary velocity in the last post I can now defend this assumption a little better. If there were a difference between the supply of money and prices of goods in the inventory, velocity is the mechanism by which the two are reconciled. If availability of money greatly outweighs the prices charged of the inventory for sale, things would be bought up quickly. A lot of money would be spent and inventory would quickly contract. If a merchant easily sells items quickly at a given price, it would increase his or her profit margin to raise prices. So if goods are cheap (cash supply > inventory prices; in other words say there were $1,000,000 in the economy and an inventory of 100 tacos for sale at $2 each) inventory shrinks as people buy up supplies—to restore equilibrium prices have to increase.
Conversely, if prices charged for items are greatly in excess of the money supply, then at any given moment not everything could be bought. If an economy consisted of 100 tacos for $2 a piece, and there were only $100 in the economy, then only half the tacos could be bought from the taco shop owner. If all 50 tacos that could be bought were, then monetary velocity stops. In a real economy, if prices are in excess of the supply of cash then velocity would slow, and inventory of both supplies and unused production capacity would build. In order to clear the inventory, prices would have to drop to levels commensurate with the available money supply.
In this way, money velocity pushes prices to equilibrium where money supply equals inventory. Velocity is the mechanism that restores the cash-inventory equivalency.