There is very limited new purpose-built rental construction and it is not significantly higher since rent control on new builds was lifted, again, by the province.
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This is not correct. The City absolutely has the financial means to build, its a question of whether they choose to raise the requisite sum and prioritize housing construction with same.
Rent control in Ontario has never completely frozen rent; its generally permitted to increase every year in line with inflation.
Landlords in Ontairo can also seek above-guideline increases beyond that inflationary amount for large capital projects.
The discussion here would be about the extending that level of rent control to new buildings, for existing tenants (vacancy de-control is also normative right now, meaning when a tenant leaves the rent can be re-set to market)