According to a recent report in the San Francisco Chronicle, housing inventory has actually increased in San Francisco (25.6 percent from May 2020) and San Jose (30.3 percent from May 2020). This, of course, is contrary to rends in other parts of the country.
However, there are a few caveats to this: last ear inventory was so low that there was bound to be an increase. Also, despite the higher inventory, prices have climbed at a high rate as demand remains strong.
Rental rates are also increasing with small but steady rises over the last several months.