For example, for a level 20 Summoner, Carbuncle's perpetuation cost is 3MP per tick. When the Carbuncle Mitts are equipped, the cost is reduced by half, to 1.5MP per tick. That is then rounded down to 1 MP/tick actual perpetuation cost.
For a level 25 Summoner, Carbuncle's perpetuation cost is calculated like this: 3MP/tick halved to 1.5MP/tick, rounded down to 1MP/tick. Then Auto Refresh is applied, which brings the actual cost to 0MP/tick.