The standard Keynes model from Krugman

Optimal fiscal policy in a liquidity trap (ultra-wonkish)

Now here is where things get confused when the model talks about an interest rate, one rate.  It is not that way.

When the consumer perceives that current savings earn more then current consumption, he will save more.  Let's eliminate the intermediate bank and assume there is one fiat bank.  That fiat bank is sees  reserves pile up when the consumer increases savings.  So the fiat banker is paying ink and paper out to the consumer as a deposit rate.  There is more ink and paper into the economy, not less, and at equilibrium the result is inflationary.

So the fiat bank lowers consumer lending rates, and the consumer begins to save less and borrow more.  That is an increase in the flow of ink and paper to the fiat banker, a reduction in outstanding money in the economy, at equilibrium. The result is a move toward deflation.

But wait, you say, if the consumer borrows more, then the consumer is buying more goods, price must go up! Not necessarily unless we know the supply conditions, there may just be an increase in supply.  If savings were increasing, then supply was likely decreasing also, so if lowering the lend rate moves toward equilibrium, then supply should increase and the system remains price neutral.

The equations Keynesians show assume disequilibrium to have their effect, which Paul notes.  But as long as the fiat banker moves toward equilibrium, then by construction, the solution will move toward price neutrality. By construction, what I mean is a full Euler system, with a second differential; continous compounding.  Any move toward equilibrium in that system is a move toward price neutrality, within the margin of profit for the fiat banker.

How does the fiat banker know when it is at equilibrium?  When deposit and loan balances are about equal. At that point, the fiat banker can collect his 1% ATM fee from the inventory of ink and paper. By construction, it is up to the economy to make balances more toward inequality, and the banker will move one or both of the two rates and restore balance.

Wait, you say, what about monetary illusion? Whose illusion? The fiat banker knows less about the economy then the agents.  He is deliberately adjusting lending and savings rates so as to make his future estimation optimally uncertain.  He always works toward a net savings and lending flow of zero, the point at which he knows the least. At the point where uncertainty is optimally spread, then the no arbitrage condition is met and he is price neutral.

So how did the fiat system become screwed up?

Republicans presidents repeatedly inserted a unit root making prices cycle over the presidential eight year term.  That is the borrow, spend and crash model of the Republican Party.

So the fiat banker, being government obligated, could not maintain the no arbitrage conditions and the private banks took over its function.  The economy is not zero bound, the government in DC is zero bound. Private banks, especially the bond market, have forced the government onto a narrow band of the curve where it can no longer cycle.  That is why money still works, private enterprise needs accurate money more than it needs government to cycle.