> Doesn't reducing the price of lending tend to lead to more lending?
Theoretically, yes. If loans are 2% instead of 4% then that may induce people to take one up to do some kind of economic activity (start business, renovate house, buy a new car, etc).
But it is not guarantee: people may feel too financial vulnerable to take risks with borrowed money. This is where the limits of monetary policy are run it.
There are points where the government starts spending on various projects: if a contractor is hired to build a bridge, and it will take "x" years, then all of its employees may feel more confident and do more spending because for the next "x" years they're set. Their money then goes into other people's pockets, into other people's pockets, etc.
Public/government spending to kickstart demand is what Keynesian economics basically is.
Sure, there are limits. But fundamentally, holding all else constant, increasing bank reserves decreases the cost of lending, which increases the quantity of lending, which increases the money supply.
Not necessarily. When rates are low, banks are more cautious with who they lend it to. And in times like these, it's especially risky for a bank to lend, and couple that with absence of high rates for a bank to mitigate the risk, you end up with actually less lending.
On this chart [0] you can see how lending increase when crisis started, kind of matching inflation of the dollar. But lending is slowing down, and no amount of QE can speed it up, indicating probable deflation of the dollar.