> The only thing that affects housing prices is the supply of houses.
Well yes and no. I would argue, treating housing as an investment vehicle for both corporate and foreign interests has had the biggest influence on low end housing prices around the world. Corporate buy-ups, government backed loans and "affordability" scemes have all actually pushed pricing higher.
To be clear A large percentage of corporate and foreign ownership isn't actually needed to have a large influence on pricing simply because of where they are most likely to invest. Just a couple of percent adds significant upwards pressure on the low end of the market where affordability is felt the most keenly. After all buy low sell high.