Suppose for a moment that someone with legislative power decides to abolish Fractional Reserve Banking and passes a law that forces banks to only lend the money they own, that is M0. What would be the economy-wise implications of such a change in the long run and what in the short run? In particular with such a criteria in mind as mortgages, interest rates and dispossessions.
There is a long standing problem in most discussions of Fractional Reserve Banking (FRB), around the precise definition of money. Cash money (that is M0) is an asset on the banking system balance sheet, while deposit money (the liability) is the money that is created by lending.
Ever since the introduction of cheques specifically, and in general the ability to make direct transfers between two deposit accounts, deposit money has been the de facto form of money that is used in the economy. Cash money is maintained at a fractional reserve of deposits (it used to be a regulator of total deposits and lending, but in practice this isn´t the case anymore), and used primarily for inter-bank liquidity settlements, as transfers occur between bank accounts at different banks. Reserve requirements are now down to 2% or less in most countries.
So taken literally, the question is what happens to an economy when its money supply is reduced by 98%, and at the same time total lending shrinks by whatever proportion bank lending is of total lending in the economy (typically 1/3 or more).
In the short run, congratulations, you no longer have an economy. Nobody can pay their non-bank debts any more, because there isn´t enough money to pay them with. Bear in mind debt payments do not automatically adjust to changes in the money supply. That triggers a debt cascade causing wide-spread company failure. The accompanying impact on all prices causes massive disruption in the supply chain, because everything in the economy is now completely mis-priced relative to everything else. A 20% reduction in the liability money supply in the US in 1930-33 for example caused the price of food bought from farmers in some parts of the USA to be less than the cost of the fuel required to get the food to the market for sale. This event would clearly be far worse than that. Market based systems can and will adjust prices over time to compensate for money supply changes, but that´s the long term. It has been said that 'every civilisation is only 2 meals away from barbarism', and I´m afraid you just pushed yours over the edge.
In the long term, after a period of market exchanges being performed with cigarettes, and other money-substitutes, and those responsible for this mess being hunted down and dealt with appropriately, people will probably feel that fractional reserve banking wasn´t such a bad idea after all. Some form of Germany Year 0 event will take place and the banking system will be restarted. Since all debt was effectively discharged during the "unfortunate event" the next few decades will probably be referred to as a golden age. By the survivors.
If instead we assume that rather than reducing the money supply (which we know is a bad idea), the banking system is instead converted so that there is no fractional reserve lending, asset cash is injected to replace debt, and maintain the current quantity of deposits. All deposits in the system are simply held constant from this point on, and you now have a constant money supply economy.
As a side note, everybody now has to pay for their bank accounts, because since banks are no longer lending institutions, they need a revenue source to fund their operations. Quite a large revenue source - ATM networks aren´t cheap.
The problems caused by a sudden drop in total lending are still present. In practice this will disrupt the economy in the short term, but hopefully not quite as badly as in the previous scenario.
The short answer though, is we simply don´t know how a constant money economy behaves in practice. There hasn´t been a constant money economy since fractional reserve banking was invented, and that´s at least 3-400 years now (depending where you put goldsmith banking in the banking continuum, and what country you´re in).
A lot of financial statistics would probably start looking very strange, since even correcting for CPI doesn´t adequately control for the impact monetary growth has on price measurements. It´s possible that the economy would settle down after a few years as everything adjusts around the constant money supply - that´s essentially the general equilibrium theory argument. It´s also entirely possible that the growth in the money supply that FRB provides over time makes it easier for adjustments to occur - a lot of arguments in favour of small positive inflation amounts essentially revolve around this - and that a bunch of issues we didn´t previously know about emerge and cause new problems.
While this is very much an open research question, it´s interesting to note that a side effect of some of the recent Basel 3 regulatory changes is that at least for the last couple of years, several countries including the UK have experienced stable money supplies. If this continues (it´s perfectly possible to regulate fractional reserve banking so that it doesn´t expand the money supply if you know what you´re doing - whether the central banks really know what they´re doing is also an open research question), then we may start to have some empirical data that can help shed light on this very interesting question.
Here's a hypothetical society.
The currency is gold coins. These can't be created virtually or counterfeited. There's a limited number of them in our society.
I happen to have 1000 myself, and because I own them, I create a bank and I can lend them out.
If people deposit their coins into my bank, I can't lend those coins out. Therefore I have no reason to look after them for them, unless I start charging 'safe keeping' fees.
Because I only have 1000 coins to lend, but lots of people to lend to, I lend my coins to who's paying the highest
(interest rate * chance of paying the loan back).
I can't make a new loan until the old one is paid back.
This means that it's much much much harder for anybody to borrow money. They can either borrow money now and pay exorbitant interest, or they must save money before they spend it.
Somebody that has a great business idea, but needs the capital to fund it, needs to wait five years while saving money for it, or else he sells shares in his business.
I guess he's allowed to borrow the supplies he needs directly from the suppliers. But this means that the suppliers assume all the risk in the case that business fails.
Suppliers would subscribe to 'risk assessment' services who match ideal borrowers to the suppliers, since it's now the supplier holding the risk.
When someone purchases something with gold coins, the gold coins then sit the seller's vault doing nothing, as the seller doesn't need to spend the coins right now but may need to use them tomorrow, so he can't lend them out, unless he's doing some 'day to day' lending scheme, which would be hard for the borrower in this case to payback unless they had some surefire way to pay the loan back each day.
M0 is different than MB. M0 is just cash and I assume you meant MB.
If a bank can only lend what it has, what definitions of money and lending do you include? A bank operates by mismatching short term debt (much of which is deposits) with long term assets. An untenable situation regardless of the type of assets (deposits vs non-deposits).
If we stop say banks from mismatching say 0 second maturity deposits to long term assets, do we then stop 1 second debt? 1 day? 10 days? 100 days?
The other clarification to ask if if the open market would still function?
So say yes the open market would function, but banks must now back M1 demand deposits 100% with MB.
What would banks do? They would no longer offer free checking. Instead they would relabel their service to avoid the new requirements. They could call them "power deposits". They might yield .000000001% and maybe withdrawels might be limited to say one day after deposits. Little would change under such a system. The core concept of maturity mismatching is still creating problems for the economy and the Fed is still bailing the system out through the open market.
What would be a more practical solution? Offer the public an alternative to private bank deposits. Allow for public bank deposits (aka deposits directly at the Fed). The Fed allows private banks to hold debt-free deposits with them...why not the public? It would be a simple matter to let the Fed issue debit cards and checks for these accounts.
What about broad money? Banks could be released from constant Fed bailouts because public deposits are no longer at risk...only investors are now. Individuals who wanted to foolishly lend to banks without the backing of the Fed could do so if they REALLY wanted to, but few would as the banking system would burn up in a liquidity fire without Fed support to prop up maturity mismatching by constantly providing artificial levels of short term debt to the banking system.
What about outstanding debt? The Fed could in the meantime introduce more MB into the economy to compensate for the collapse of higher monetary aggregates (by buying assets).
What are the long term implications? Imagine if the government let people counterfeit money...but ONLY if they bought couches. What would be the result? Couch prices would be higher than normal. Well banks pretty much are only allowed to buy fixed income securities so interest rates are artificially low now, but without FRB interest rates would go up. Not a bad thing though. It would reward honest, non-bubble creating investment/savings. There would be less inflation. And there would be less need of borrowing to pay back all the FRB loans.
The national depository solution is IMO the only practical solution to fractional banking. It would also allow for more gradual transition from FRB to non-debt backed deposits. Here is an article on how it may work: http://wfhummel.cnchost.com/nationaldepositorysystem.html
Although there's a lot of important points in the other answers, there is something important missing:
Prohibiting FRB means that you cannot borrow to invest. Effectively, it means that you can't create debt contracts because in a debt contract you take somebody's money and promise to repay it, but you don't keep the money, instead, you use it for some type of investment. If borrowing is forbidden, other social mechanisms for intermediation would take its place, like issuance of shares. You would buy shares in the bank rather than open up a deposit account, much like investment banking used to be when i-banks were not levered.