I learned a piece of algebra recently. Did you know that rent per month = ($/sqft)*sqft? Where "sqft" = square feet of the apartment and $/sqft = price per square foot. In major coastal cities, price per square foot continues to rise. This is caused by both supply and demand forces. One way to continue to have affordable housing units in desirable cities is to allow developers the ability to supply micro-apartments. This article talks about the demand for 400 square foot apartments. I recognize that this would be a tight fit for families with kids but increasing the menu of housing options will be very attracting to the 20-29 year olds just starting out in the big city. Relax building height restrictions in Manhattan and allow micro-apartments and much of the "housing crisis" that the NY Times drones on about will vanish. These free market solutions are much better policies than rent control or requiring developers to set aside a % of their new units but having them build "poor doors" as these units are set aside for lower income populations.
UPDATE: As urban crime falls in big cities, young people (both men and women) are more willing to go out at night and don't need a big apartment. In fact, they do not need their own kitchen. Cities are about gains to trade and why not engage in comparative advantage and purchase your food in the city. If apartments no longer need their own kitchen, then think about our future ability to arrange economic activity. In a free market, you would be faced with a menu where some apartments do and do not have kitchens. A kitchen takes up space and that could be your home office!