The tradional US Federal reserve

Lets talk about the corridor fiat system.  First consider how the current system is supposed to work:

Assume the government does not take excess gains from the Fed and it used this system, the way it is supposed to

In the U.S., the Federal Reserve most commonly uses overnight repurchase agreements (repos) to temporarily create money, or reverse repos to temporarily destroy money, which offset temporary changes in the level of bank reserves.^[4] The Federal Reserve also makes outright purchases and sales of securities through the System Open Market Account (SOMA) with its manager over the Trading Desk at the New York Reserve Bank. The trade of securities in the SOMA changes the balance of bank reserves, which also affects short-term interest rates. The SOMA manager is responsible for trades that result in a short-term interest rate near the target rate set by the Federal Open Market Committee (FOMC), or create money by the outright purchase of securities.

Now we think this might work, and it certainly works much better than having government hand in the excess inventory. The Fed should use its monopoly power to buy at high prices, and sell low; injecting money into the economy, or buy low and sell high extracting money. But it puts the primary dealers in an arbitrage battle with the Fed.

Instead lets make the Fed neutral, and let the borrowers and savers have an arbitrage battle between themselves.  Consider the corridor system as a queuing network. The Fed always wants the deposit balance and lending balance about equal.  It can always adjust both deposit and lending rates independently to make that happen.  But it also wants to make the transaction variance and mean equal for each of the two groups, moving both rates up or down in tandem to make that happen.  So it has two levers, the average rate and the differential rate.

Does this drive the system to zero mean inflation? I think so, even in the face of growth. When borrowers drive up the outstanding lending balances, the Fed raises deposit rates; and visa versa.  Savers will avoid inflation and borrowers will avoid deflation.