Inflation is not due to the price of certain items going up. For example, if he charges more for these eclairs, then there is less money in the system for other things. So if there is less money in the system elsewhere, people would have to lower prices to convince people to buy.
Inflation is caused if there is an influx of gil into the market, which was eventually what was found out. A new version of gilfarming where they used explots in monsters and quests to get gil, not drops. They were then able to bypass having to sell drops on the AH, and went straight to selling said Gil.
This happened on all servers because the people behind this wanted to have a market that reached every member of FFXI. When this was found out, their accounts were banned(stopping the spiking influx of gil) and vast quantities of thier gil were sized. Because of this, gil inflation has dropped down to pre-christmas rates, and the rate of inflation is back to what it was.
This has been FFXI Economy 101.