Implications of abolishing Fractional Reserve Banking on mortgages and interest rates 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.