Well, I certainly didn't mean to imply that you would sit idly by and let massive inflation ruin the game -- but I do see the following scenario as a concern and want to bring it to your attention if you haven't already considered it.
As I understand it, the game economy is set up with four basic money inputs, and five basic money outputs. The inputs are: arena revenue (gate receipts), tournament prizes (cup & BBB), TV revenue, and merchandise. The outputs are: player salaries, staff salaries, arena expansion, transfer market agent fees, and staff acquisition & firing costs. To simplify the analysis, let's net player salaries and staff salaries against the gross revenues, leaving net operating revenues. As stated in this thread and other places, net operating revenues should be positive most of the time. Thus, for money supply change to be zero, the net operating revenues should be exactly offset by the other three cost areas -- arena, player transfers, and staff transfers.
Transfer market inflation, then, can happen in one of two ways. First, net operating revenues could increase, which would raise the total amount of money available for each of the three outflows. Some (although possibly not all) of this money would be expected to go to the transfer market, where it echoes around until agent fees destroy enough to re-balance the money supply. There would be a magnifying effect of the money supply change (similar to the reserve ratio effect in a real-world bank), because agent fees are less than 100% of the transfer cost. For illustrative effect -- assume that global net operating revenues increase by $100M per season, and all of that money goes into the transfer market. Further, assume that the average agent fee paid on each transfer is 10%. As a result, for $100M in additional agent fees to occur, a total of $1,000M extra (or $1 billion in American terms) would be spent in the transfer market that season. This would be what I would term "monetary based inflation", and it seems that the auto-tuning mechanisms are designed to control for this, and I have faith that the BB team will be generally successful at keeping this stable.
The second way that transfer market inflation would occur is through a change in preferences, or a change in the ratio in which money outflows via arena, player transfers, and staff transfers. This is what I would term "non-monetary inflation", and it is my contention that the current system has several pillars that are already and will continue to actively encourage this. First, arena expansion is a one-time outlay--there is no maintenance cost of any sort for arenas in the game. Economically, I would expect this to mean that as teams become more established, their expenditures on arenas will decrease, especially now that there is an explicitly-defined soft-cap on arena size. In addition, there have been a number of announced and/or implemented changes that will further induce teams to reduce arena spending. As the money shifts out of arena spending, it must by nature go into either agent fees or staff acquisitions. Either movement will cause inflation in the effected market, and the volume of money will be magnified by the inverse of the average agent fee in the player transfer market.