How can we have a housing shortage and a bubble at the same time? The power elite has found out they don't have to build houses and cars in order to make money

How can we have a housing shortage and a bubble at the same time? The power elite has found out they don't have to build houses and cars in order to make money - just constrain the supply and raise prices. Easy peasy. Remember - the corporations can sit on foreclosed houses for years and not feel any pain. Tell me how the free market solves this?