Central Banking: Determining Total Reserves
The reserve rate is not entirely arbitrary: it must be managed in reaction to "several determinants," though Rothbard classifies them into two categories: factors under control of the market, and factors under control of the central bank.
The Demand for Cash
A market factor: people's demand for cash deals with the amount of currency they wish/need to keep on hand, specifically as it comes to redeeming their deposits to obtain it.
Banks go to the central bank to obtain the cash, which prints it up. However, the banks now have less cash in their reserves relative to the amount of loans outstanding.
Unless the reserve rate is changed, banks will need to contract (sell off) loans to maintain the required ratio. Due to the money multiplier, the banks must contract a proportionate amount of loans (if a 20% reserve is required, banks must contract $5 in loans for every $1 in cash their customers withdraw).
The inverse is also true - if demand for cash decreases and customers leave more in deposit accounts, the bank can issue more loans, in the exact same proportion.
The federal reserve may act to soften the blow for banks, being more liberal with its reserve rates when money is in demand (so that banks do not need to contract their loans), but this is brinksmanship: decreasing the reserves means increasing the amount of currency, means currency is worth less, means demand is higher. The problem may compound itself.
The Demand for Gold
The demand for gold, presuming that currency remains on a gold standard, can also impact the reserve rate. Whether the gold is consumed (industrial products, jewelry) or produced (mining, reverting products into base metal), the effect is the same.
Since countries have abandoned the gold standard, the point is moot, except to note that debasement also becomes an issue, similar to inflation.
Loans to the Banks
The central bank can control the loans it extends to commercial banks. In a fundamental sense, the central bank will require a certain reserve level of its customers, and their compliance with this reserve will dictate the amount that the central bank will make available to them.
The central bank can also increase or decrease the interest rate on loans to encourage or discourage borrowing.
Open Market Operations
The refers to instances when the central bank makes a purchase on the open market, and pays for that purchase with a check. When the check is deposited in a commercial bank, that bank will redeem it at the central bank, which will issue additional currency to cover the check (thereby increasing the currency supply).
Note that when the commercial bank redeems the check with the central bank, it receives currency, on top of which it may then pyramid loans, subject to the money multiplier.
In rare instances, the central bank may sell assets on the open market and retire currency, decreasing he money supply. The ent effect on the bank is that the customer decreases funds on deposit - the main difference is that, instead of being transferred to another bank, the funds go to the central bank, and are thus retired.
In general, the items the central bank purchases and sells are debt instruments (loans, bonds) from commercial banks rather than physical assets.