They do sadly. Their base price is 180 Blood Echoes and they are close to the four digit category currently in my playthrough, though I only have some of the Chalice Dungeons, the DLC, and the second half of the Nightmare of Mensis to complete, so I'm pretty much at the end game.
EDITGA: Whoops, my bad. It isn't as severe as I thought, probably cause I don't pay too much attention to the consumable screen as I should. While the price does go up, it seems to be based on doubling and then tripling and so forth from the base price. So Blood Vials cost about 720 now in my game, which to me, is a bit of a steep price for a healing item, especially one where I would need three of them to take me from 10% of my health back to full. Molotove Cocktails and antidotes are where things are in the 4 digit territory and the damn blood tangent cocktail (a diversion item for those who don't understand what we're talking about) is about 10,000 Blood Echoes.
Here's some advice about fusing new demons. You might have noticed some of these, but generally a persona's affinity for a move is based on their Arcana and in some cases, their design/history.
Examples:
Fool and Judgement - Can learn anything
Magician, Priestess, and Emperess - Magic orientated
Chariot, Strength, and Tower - Physical
Justice - Hama Focused
Death and Devil - Mudo Focused
There are some serious overlap as well but rule of thumb is that the higher level the demon is within their arcana, the more they will exhibit the traits of their arcana and lose the ability to use certain skills.
Another tidbit, melee skill transfer is often based on the design of a demon, for instance, a skill that is weapon based like Vorpal Blade can only be transferred to a persona carrying a weapon. Likewise, a Fire based demon like Surt or Pyro Jack won't learn Bufu skills but that is pretty obvious but some persona may require knowing a bit about their lore to figure things out. I would honestly try to do some of Elizabeth's fusion quests to help learn the ins and outs of Persona fusions as you would be surprised how very likely it is to get a skill on a desired Persona with enough work.
Also, the game never mentions this but fusing two persona of the same arcana will always result in a persona of the same arcana, though the whether it will be an upgrade or downgrade will depend on where the Persona's rank within their own arcana, so that can be a quick way to "upgrade" a persona with good skills into one with better stats to use them.
A final tip is that as your MC gains the ability to hold more personas, it's often better to stop focusing on making a few versatile personas and focus on making specialty personas, cause you'll need them to start doing their job well when you get to the later stages of the game and the focus shifts from "exploit enemy weakness" to "prevent enemy from getting extra turns" as later enemies will eventually drop all pretense of having a weakness, and so you'll need the extra boost of using elemental boost and Amp skills to make your spells more powerful. I highly recommend creating Anubis eventually, once your levels allow you to do so, as he is one of the earliest personas you can make that has a natural immunity to both types of instant death magic and no major weaknesses either, making him a perfect baseline Persona to have equipped whenever encountering new enemy types. His stats are also pretty good and he learns most of the Hama/Mudo skills as well making him great for speeding through later sections of Tartarus.





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