I would think that medicare becomes a sort of single-payer system; you get the same Basic Income and the costs of the insurance come from the pool.

I do think that some aspects of our tax system could be reworked. Creating a wealth tax and removing income and other redundant taxes seems to be a popular idea[1]

[1](http://www.nytimes.com/2012/11/19/opinion/to-reduce-inequali...)