In a fractional reserve banking system, banks can lend out more money than they hold in cash. For example, with a 10% reserve requirement, they can lend out 9 times as much money as they hold in reserves.
One downside of fractional reserve banking is that it can lead to bank runs, i.e. a situation where most people try to withdraw their money because they believe that the bank is about to go bankrupt. On the other hand, there may be some benefits to allowing banks to lend more than they would be able to if constrained by a 100% reserve ratio.
My question is simple: wouldn't it simply be better to impose a 100% reserve requirement (no fractional reserve banking) but simultaneously increase the money supply so that banks have exactly as much money to lend as before? This would seem to leave banks' ability to lend unaffected while eliminating the risk of bank runs.
Or, if you prefer a less normative framing:
Q: What would be the consequences of simultaneously eliminating fractional reserve banking while increasing the money supply so that the total amount that banks can lend remains unaffected?
While I would welcome well informed speculation on this, I would be particularly interested to learn what effects this policy would have in standard macro models which incorporate a banking system.