It's still linear, but it was more my point that when property values fall, incomes, prosperity and tax revenues take a bath.
But not to the same extent, so with a more diverse tax base the effect on revenue is more diffuse.
Famously, one of the (many) problems that the Irish government faced with the 2008 property crash was its heavy reliance on stamp duty revenues. In 2007, 2% of (inflated) Irish GDP accrued directly to the government in the form of stamp duty revenue. By international standards, that was
huge. The property crash caused a double whammy here; property values fell and, since stamp duty is a percentage of sale price, the average stamp duty revenue per transaction fell commensurately. But, in addition to that, the volume of transactions in the market also dropped off a cliff, and of course the stamp duty revenue from a transaction that doesn't happen is zero. The combination of these two factors led to a 60% fall in stamp duty revenues in the first year of the crisis. This was much, much larger than the fall in income tax revenue, which was 7.4%.
This isn't just a property versus income thing; because stamp duty is a transaction tax, it's hugely volatile to market slumps which involve fewer transactions happening. (So is CGT.) If, instead of stamp duties, we'd had an annual property tax, like a grown-up country, the fall would have been nothing like 60% (though it would still have been more than 7.4%).
The point of all this is that a country should prefer a diverse tax base. The narrower your tax base, the more volatile your revenue stream will be, and in particular the more vulnerable to economic shocks of one kind or another.