@ZachWeinersmith yes. Lowering rates reduces mortgage carrying costs, less expense to be recovered by rent.

And no. Lower rates reduces mortgage carrying costs, making larger mortgages more attractive and causing more money to chase the available properties or construction driving up prices .

Govts have to work hard at ensuring supply will increase. It can't really be done just with rates. Or even just with money. It requires legislative, policy, and direct action. Like... building housing.