Pointing to low growth and high prices tell us that isn't simple supply and demand pushing the prices up. Berlin even more as large swaths of the city are still underdeveloped after losing 2 million inhabitants since the 1940s-1950s.

How can Berlin, a city with ample free space and free buildings still see a massive increase in housing prices if it was a simple issue of supply and demand? There's undoubtedly something else much fishier going on.

(American POV):

Here in most places it is because supply is suppressed by government policy and the planning and approval process. Want to add a room to your house? That could be 10's of thousands in planning fees if it is even allowed and it still could be denied. Want to turn your laundromat into an apartment complex? Denied: the proposal will cast shadows across a lot where the city is thinking of building a playground for a local school[0].

Overall its very much in the interests of those who own property to keep more from being built and they naturally act for those interests.

[0]Not hyperbole - this is an actual example.