Taxable incomes haven't dropped by 50% in CA. What has dropped is the taxable incomes of the small fraction of CA folks who pay the bulk of CA's income taxes.
CA's income taxes are very progressive. That makes them very volatile.
Prop 13 has nothing to do with the volatility of CA's income tax revenues.
It has nothing to do with the volatility of income tax revenues, but it has everything to do with volatility in the budgeting process. By gutting the ability of local governments to fund themselves it pushed all of the taxation up to the state level (and the state turns around and hands most of the money back to the local jurisdictions.) Since the primary revenue generators at the statewide level are income and sales taxes this introduces volatility that is directly tied to the general economic condition, unfortunately the new burdens placed on the state budget as a result of Prop 13 are mostly independent of the general economic condition. This lethal combination leads to a never-ending cycle of boom and bust in the state budget.
Prop 13 doesn't make state-level taxation volatile.
Obviously not a resident of the central valley.
Also due to the way assessment is triggered, a 50% drop in home prices doesn't imply a 50% drop in total property tax revenue -- only for homes that are sold. [EDIT: But apparently one can appeal to have property reassessed without selling, which presumably many people will do with prices dropping significantly.] Furthermore, if sales forced by foreclosure are bias toward the lower price range -- as is the case -- that will further limit the effect on total property tax revenue.
EDIT: See also http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2009/01/25/... -- a little short on hard data, but suggesting that the variation in property tax revenue is not going to be anywhere close to the 40-50% drop in sales and income tax reported in the OP.
How? I've owned for a while, so the post-crash zillow-value is more than value-for-tax-purposes because Prop 13 limits the year-to-year increase in the latter.
I can't find the report now, but the Merc reported that Santa Clara county's property tax revenues would drop 2%. Counties with a lot of recent construction were seeing 10% drops.
To be fair, however, fundamentally, CA continues to vote for a government which creates more goods and services than we want to pay for. Schwarzenegger papered this over with a bunch of loans, but eventually we will run up against a wall and be forced to align our desires with our willingness to pay.
Also, worst financial crisis since the Great Depression accompanied by a drop in real industrial output that, IIRC, actually exceeds the Great Depression in speed, and so forth and so on. Plus a state that has been particularly devastated by the housing bubble.