A local homeowner is locked into their mortgage, and it doesn't matter how expensive other homes around them become because their principal is already locked in.
The only way for locals to no longer afford their home would be if their budget was so thin they couldn't afford the increasing property tax, which is a relatively minor proportion of one's annual income.
Mortgage payments get easier over time because they are a fixed rate, and inflation tends to adjust incomes up over time. A $1,000 monthly mortgage payment 20 years from now should be a lot easier to pay. The increasing property taxes should somewhat be washed out by inflation.
It's a pretty good problem to have that one's home appreciates in value so drastically that it becomes burdensome to afford the property tax.
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