Other financial discussions

My wife and I are retired. I have a government pension, and my wife has SSI pension. 

Let say, I start a single member LLC.   The self-employment tax rate is 15.3% consists of 12.4%  for social security and 2.9% for Medicare. 

Why pay Medicare again as we both pay Medicare Premium every month? Can we deduct that?

If so and if I am the single member LLC and my wife wasn’t,  can I deduct her Medicare premium too if we file jointly?