Well, it took embarrassingly long for me to see this but there’s really a very simple resolution to the quandary I posted Monday. The key point is this:
In a flexible price world, anybody can supply money at a social cost of zero. In a fixed price world, only the government can.
To be more precise: I currently hold $11. Suppose I agree to hold a twelfth. In a flexible-price world, I can get this dollar from the government (which prints it up at zero cost) or I can get it from my friend Jeeter, whereupon the price level adjusts and the rest of the world’s real balances (including Jeter’s) are restored to their original level. No social cost either way. In a fixed-price world, I can get this dollar from the government (which prints it up at zero cost) or I can get it from my friend Jeeter, whereupon prices don’t move and the rest of the world’s real balances are reduced. Zero social cost one way, positive social cost the other way.
This turns Monday’s question into a non-question. The question was, in essence: “If I demand money from a zero-cost supplier, there should be an efficiency gain. When the supplier is not the government, who gets the gain?” The answer is: If the supplier is not the government, he’s not a zero-cost supplier.
It also impacts on Friday’s problem: It seems to me that in a fixed-price world, you’d absolutely want the government to flood the economy with zero-cost money up to the point where people are satiated with real balances. If people hold money only because of a cash-in-advance constraint that’s no longer binding (i.e. in a liquidity trap) then there’s no point in printing any more.
I have not fully digested all the comments. My apologies to anyone who tried to explain this to me but failed to penetrate my thick head. Apologies also to others who said interesting things I haven’t yet digested. And many thanks to Jim Kahn who instantly saw the answer so clearly that he couldn’t figure out what the question was, and expressed it in language that forced me to see the light.