Why not just stop expanding the money supply?

A story from the BBC says that Zimbabwe's central bank is to introduce new higher-denomination banknotes (the highest value note is worth 10m Zimbabwean dollars) in an effort to ease the critical shortage of cash in the country. But according to the report the $10m note will be worth less than US$3.90 or £2 or 2.60 euros on the black market.

There is any interesting question as to why you run out of currency when hyperinflation is driven by rapid growth of the money supply. And Zimbabwe is suffering from hyperinflation, it has an annual inflation widely thought to be in excess of 50,000%.

There are two possible reasons for a currency shortage. The first is that currency is just a subset of the broader money stock which also includes bank deposits in the form of cheque accounts. Currency (dollar bills for example) can become too small a proportion of the broad money stock if the currency printing presses can't keep up with growth in the broader money stock. Growth in the broader money stock is driven by central bank expansion of bank reserves. So your cheque account went up by $2 but the currency supply only went up by $1 and thus you can't convert the cheque account balance into cash. The second reason is that an excess demand for money can occur if prices begin to rise even faster than the money stock is growing. Here the problem is that people anticipate ever faster shrinkage in the value of the dollar and increase their prices to compensate. One wonders what the velocity of money is.