You do not solve the housing problem by equating it to some simple economic principles. If you build, you also have an effect on the area around it. People tha

You do not solve the housing problem by equating it to some simple economic principles. If you build, you also have an effect on the area around it. People that do not already live in skyscrapers do not want to live next to skyscrapers. Gentrification is a real effect. Apart from that you are probably even reducing supply: High income housing usually means way too big apartments. It is also often actually an unused investment object and not used for housing. Case in point: Manhattan has a lower inhabitants/km² than Eixample: https://en.wikipedia.org/wiki/Eixample https://en.wikipedia.org/wiki/Eixample