The City of New York is just building a new police station in an area that's been fully built up for roughly 150 years. http://www.dezeen.com/2016/02/01/big-bjarke-ingles-new-york-... I expect the Vancouver police department also ends up paying its officers extra to cover the boomtown rents.
(Not just police, of course. All public services.)
When my car wears out and I need a new car, I don't go to my boss and say "hey, I need money for a big down-payment on a new car, so I need you to give me a big raise." And then, 5 years later, come back to my boss and say "I need yet another new car, so I need yet another big raise to pay for it."
Instead, I save money over time so that when I need that new car, I have the money already saved up for it. In fact, I've saved the money because, over time, my old car has gotten cheaper to own (lower insurance, lower registration fees, loan paid off), and I've budgeted for transportation expenses over all that time so that the new
car cost isn't a big surprise.
So please explain to me why the existing taxes for police services aren't enough for them to save up and budget and buy new buildings as necessary.
As for boomtown rents, that's not a problem either. The boomtown means that property values are skyrocketing, which means that property tax revenues are also skyrocketing, so they're already making more money without even having to raise taxes. So why do they need even more?
You started by asserting that the police budget need not increase when there's a property boom.
Perhaps the town of Starnberg is an instructive example. It's a small town in Germany which hasn't grown much in terms of population, but its property market has boomed, BOOMED, enough that the city's employees had problems. Rents increase, their salaries don't.
Last time I was there the local newspaper reported that for several years, the only police officer who worked there voluntarily was the chief. The force hadn't had a single application to any of its job postings for years, and all the old police officers had gotten better-paying work or moved to lower-rent towns. German police can be ordered to serve for a while, and the Starnberg city police force was composed of newly educated police officers who had been ordered there by the state, lived on 10m² while they had to, and who left Starnberg as soon as they were legally able to.
I understand the city council was trying to find some way to solve this. To pay the employees a sizable extra to compensate for the high cost of living. (Haven't followed the news there.) Anyway what employees said wasn't "I need another new car, so I need a new raise", they said instead "I need another new car, so I got a better-paying job, goodbye" or "I need another new car, so I'm moving, goodbye".
The police can get their money from the property tax for any new residents who have built new houses.
If there's no new houses, then there's no net increase in population, and there's no need for more police, or more police buildings.