No offense, but I think you guys are running out of doctors because of the socialization of your medical system, not because of an increase in demand. Plain and simple, no one wants to go through the intense hassle of becoming a doctor if there isn't enough economic payoff. Left alone, the medical system would automatically produce enough doctors to fill the increasing demand; because as the demand increases, prices/wages would increase. More prospective doctors would be lured in to claim the increased payoff, and things would come back to equilibrium.

But in a socialized system, there's no increase in wages/prices to match the increasing demand of the higher proportion of old folks. It's the effective equivalent of a price cap. And as we all know, price caps create shortages.