[bangoimby]

No. People always say density helps availability, and price increases are due to the denser areas being more desirable.

The major factor driving housing inflation is restricted supply, which is relative to demand. Demand is created primarily by jobs. The difference between jobs and employed residents (with overhead for non-working family members etc) drives the imbalance. If demand was being met, prices would plummet.

This factor is orthogonal to overall density. The Bay Area is expensive because there is not enough housing for the jobs. If San Jose became as dense as SF, it would not help anything, unless that growth was focused primarily on housing. But San Jose already supplies net housing and SF supplies net jobs. These are not small imbalances either; they are both 6 figures in 2008 ACS commute data. (Unfortunately that dataset seems to be compiled very infrequently, but I doubt things have changed much other than density increasing.)