The following comes from an interesting new book Austrian Economics: A Primer by Eamonn Butler, Adam Smith Research Trust, 2010. Butler writes
Many Austrians would also like to take action on bank lending. At present, banks are required to keep only a small fraction (say, 10%) of their depositors' money in their vaults to provide for customers' requests for repayment. The rest they can lend. If they lend to other banks, those banks in turn can lend 90% of that amount to others. So if banks get in more deposits, or ease their lending terms, it is possible for this extra money to be magnified many times through the banking system. Thus a modest increase in the supply of a government's fiat currency, for example, can have a much larger impact on the real economy, making its malign effects that much larger too.So there is nothing to stop Austrian economists from believing in both free banking and fractional reserve banking. Fractional reserve banking is seen by some as the worst of all possible world, but this need not be the case. If the system is allowed to function without interference there is no reason it can not work.
Some Austrians would scap the fractional reserve banking system entirely, and force banks to keep on hand 100% of the cash their customers deposit. They argue that this would neutralize the potential dangers of the money multiplier, and would end bank runs, because depositors would know that all their money was held safely. In practical terms, though, it is doubtful that many customers would be willing to pay banks to look after their money, rather than getting interest on their deposits as they do at present.
Again, competition might provide a solution. Lawrence White has wrrtten much on the history and practicality of free banking. Banks, he argues, performed much better when they were not as closely regulated by governments as they are today, and were not subject to fixed reserve requirements set down by the authorities. They would keep on hand as much cash and other liquid reserves as they thought necessary to keep paying their depositors' daily withdrawals. And they would (quite literally) make money by printing more banknotes than they had money in their vaults to back them all. As long as people thought a bank's financial management was sound, they would accept its notes at face value. But if people began to get worried about the security of a bank, they would grow more cautious - perhaps accepting its notes at a discount rather than full value, to reflect the risk of the bank suffering a run and being unable to pay its depositors and note holders. However, the fact that a bank's notes were trading at a discount would send it a strong signal that it needed to strengthen its financial position and so avoid these dangers, and this was enough to keep the banks sound.
In the nineteenth century, the Suffolk Bank, in Boston, acted as a clearing house that would exchange the notes of other banks that customers might find it hard to get to, applying discounts where it was concerned about their soundness. There is no need for central banks in such a system because there is no state issued national currency. For the system to work, however, there can be no government bailouts of failing banks: that would simply encourage banks to take bigger and bigger risks, knowing that taxpayers would bail them out. It is precisely the fact that worried customers would pull out all their money that would make free banks keep their business and their currency sound enough to retain customers' trust - which is perhaps more than one can say of the government-regulated commercial banks and government run central banks of today. (Butler 2010: 78-9).
Perhaps given the current situation this bit of the above comment should be emphasised:
For the system to work, however, there can be no government bailouts of failing banks: that would simply encourage banks to take bigger and bigger risks, knowing that taxpayers would bail them out.This seems like a general rule for banking to me. Governments shouldn't have deposit insurance in place at all. As Not PC notes such schemes have a number of bad effects.