What if only the government could create money? If I understand correctly, under the dominant system of fractional reserve banking, many (all?) private banks can create money by lending.  See, for example, Implications of abolishing Fractional Reserve Banking on mortgages and interest rates.  So, money created when people (or other entities) go in debt, and destroyed when those debts are paid back.

Some organisations, such as Positive Money, advocate there would be considerably advantages if we step away from this system, and only the government could create money.  Quoting from their website:


  History has shown that when banks have the power to create money, they create too much in the good times, causing financial crises, and then create too little money in the bad times, making recessions and unemployment even worse. They put most of the money that they create into house price bubbles and speculation on financial markets, and only put a small amount into businesses outside the financial sector. We simply don’t think that banks, with all their incentives and need to maximise their profits, can be trusted with something as powerful as the ability to create money. And it’s not enough to regulate them, because regulators have already failed to keep them under control, and there’s no reason why they should get it right this time around. We need to stop banks being able to create money. Instead, we want to see the power to create money transferred to a democratic, accountable and transparent process (...)


My question:

What would be the consequence if only a single institution, accountable to the national government, had the ability to create money?  Assume that this institution would use a more or less objective set of criteria to determine how much money to create, for example, in order to meet particular targets.

Edit: A commenter requested more background motivation why this question is specifically about banks.  Allegedly, the system leads to increasing house prices and debts, along with other problems.  My question here is not whether the issues that Positive Money are correct in attributing those problems the current system of private banks creating money; regardless of their correctness, my question is, as stated above, what the consequences would be of having only a single government-controlled institute create money.
When you dig down, this questions is very nearly a duplicate of this:

Implications of abolishing Fractional Reserve Banking on mortgages and interest rates

but based on the comments, it seems that the connection isn't obvious.

This question asking about what would happen if only a government institution could create money, but equally you say the proposal is not to have a fixed money supply.  They are, in practice, the same thing.

The central bank makes the money base, M0, and then the banks create the money supply, with some multiplier to this.  In a full reserve system, that multiplier is 1.0, and so the money supply is always equal to the money base.

In your question, we consider having a M0, but also have a state run bank that chooses the money multiplier to some number, that may or may not be 1.0.

From that point on things become almost identical - it doesn't really matter from the point of view of the economy, whether you make M0 ten times larger or smaller, if you offset it with changing multiplier.  It should be the total money supply that matters - the money base never leaves the central bank, and so may be thought of as a "construct" onto which the monetary system is hung.  The important point is that the government gets to directly control the money supply.

Before the era of quantitative easing, when a central bank wanted to increase the money supply, they lowered rates and that increased the multiplier.  With quantitative easing, they simply increase M0 and force the money supply up in a 1:1 ratio.  Either works (for a given value of "work").

There is, however, one very important difference:


With full reserve banking borrowing money is very expensive - it is economically the same as capital
With a state run lending bank, borrowing could be done at any rate the government chooses, including at an economic loss.


So, in your system, you could have a state run bank, that effectively subsidises business and/or people's mortgages using money raised from taxes or elsewhere.  This would be like an extreme version of the UK forcing RBS and Lloyds to increase lending.