Capping the cost of rent (rent control) is a terrible idea (and an old one).

Rent controls invariably worsen shortages (just look at New York and San Francisco). It seems like a simple solution, but price controls are literally cited in Economics 101 handbooks as examples of perverse incentives.

What we need to do is increase the supply of housing. This can be accomplished by:

1. Loosening zoning restrictions to allow for more multi-family units and higher density development.
2. Limiting the power of NIMBY homeowners to block new development with frivolous lawsuits
3. Eliminate the mortgage interest tax credit on second homes to discourage viewing home ownership as an investment

https://sites.lsa.umich.edu/mje/2022/12/30/the-economics-of-the-housing-shortage/

​

>By contrast, economists are less in favor of rent control programs. While rent control can lower displacement and insure tenants against rent increases, most economists believe it to be an ineffective and counterproductive long run solution. By setting the rent at less than the market equilibrium, rent control laws result in an excess demand for local rental units, which further feeds into the housing shortage. A 2018 study on evidence from San Francisco found that a rent control policy reduced the rental housing supply and likely increased market rents in the long run despite being designed to improve affordability.