I feel Arsenal's position in these negotiations isn't as weak as people are making it out to be. Sanchez is already 28-29 and should Arsenal insist on keeping him, teams would be knowing that the player they are trying to sign is already on his last legs with 1 or 2 seasons left in him at max as, despite his smaller frame, he relies on physicality-pace, energy, strength.
And looking at transfer strategies of PL clubs, everyone is looking for the next big thing which means City may not even be interested in his services next season.
Finally his worth to Arsenal is way more than 50m IMO. Lets just say, they win the EL this year, I do think they are the favourites, that's 20-25m guaranteed plus CL football guaranteeing another 15-20m (?) For next season. They would finish atleast a position or maybe even 2 higher with Alexis than withoit him so that's a few million more. It gives them global visibility and having a World class player would help them get a few million more in any sponsorship deals. And finally a few million they could get by Shirt sales. All this combined, that's worth 50m at the very least.