You should also mention that this medicine rich people are collecting also has dozens of other alternative medicines with hundreds of thousands in volume because other cities exist.
Also you should mention that some of these rich people are not rich people at all, but working class people who's lived in a location for decades which has become a desirable location in recent years thanks to some other people who generated wealth in the area.
Also you forgot to bring up the local government ran by some of these rich people who are blocking any measure to increase the supply of the medicine in the area. This certainly can crash the entrenched medicine cartel in the city, but some of these cities are North Korean style de facto one party system where no other opposition may challenge the status quo.