It has been a bit since I have studied this stuff, but to my memory the fed mostly control money supply (which only matters in respect to velocity) via open market operations of government bonds. I don't think the fed actually has to "lend" the government money. It can just give the government money, which creates inflation, which is simply a tax on all holders of money. IIRC, the way the fed injects money into the system is to issue a bond, this means that they get money from borrowers on the promise of giving them more money later. They can then create this money when they need to. Now there is money to pay for government debt.
So yeah, they can "pay" the government debt with massive inflation, which would wreck temporary havoc on pretty much everything. But this tax would mostly hit the holders of government debt, so its not too far removed from defaulting (except, cue Gooch, we can't default because its based on our money.). The downside of this act is that future borrowing would be extremely difficult, pegged to another currency, or at a very high interest rate.
Edit: All of which, long term situation, lowered standard of living for Americans than what we currently enjoy.
Check out Mr. Businessman
He bought some wild, wild life
On the way to the stock exchange
He got some wild, wild life
Bookmarks