Each Great person costs some amount of GP points (those are usually produced by special districts and possibly by some wonders).
After each GP is "made" (either by GP accumulation or by purchase), the cost of the next one usually goes up substantially. This can be used strategically - if the race for a GP becomes close, player can purchase the GP and never allow other players to have any GP of that type.
The cost increase does not happen always though, sometimes even on really low costs (such as 120 points). What are the factors that contribute to that (or stop increase of the cost altogether)?