Private spending constitutes a larger portion of healthcare spending in Singapore than in the US. Also, much of that private spending is out of pocket:
https://thehearttruths.files.wordpress.com/2013/10/slide4-1....
Which is very unlike the US, where, as a result of government intervention, spending through insurance companies is the norm.
> there seems to be a trend toward healthcare spending as a percentage of GDP increasing with level of wealth
This can be expected under my model, too. The monopolistic prices depend on the demand curve, which depends on the level of wealth.