Suppose we aim that moderately poor people (let's say 1.5× minimum wage) can afford the rent for an apartment meeting minimum quality standards and located within city limits. This may be a political aim.
What economic policies are effective to achieve this?
Rent control. Popular, but economics appears to tell us it creates more problems than it solves. See also the questions Why did Berlin freeze the rent prices as opposed to letting the market set the price? and What is the likely result of rent control in Berlin?.
Increase supply? In cities, it appears supply may create demand (the more people in a city, the more services, the more people want to live there) so this may not always work either, or only under limited circumstances (perhaps unless building huge amounts, but developers hate vacancies, so I doubt that limit would be surpassed in a free market).
Social housing, owned by the government? I don't know what economic theory says about this.
Reduce demand? Not sure how that would work without harming the city.
Impossible? Should we give up on the idea that poor people can live in alpha world cities such as London, New York, Tokyo, Paris, Singapore, Amsterdam, Seoul, Berlin, Hong Kong, or Sydney?
I'm aware that most economists say that rent control "doesn't work" — what are the alternatives that economists may prefer?