Free markets are characterized by voluntary exchange between buyers and sellers. Mapping that relationship is absurdly simply, as this image indicates.
Indeed, the only reason I even bothered to include that image was for purposes of comparison. Here is a new flowchart prepared for the Joint Economic Committee showing the healthcare system under Obamacare.
It's worth noting, by the way, that the system already was a disaster even before Obamacare was enacted. In the health care sector, free markets are only allowed to operate in very rare cases, such as cosmetic surgery, laser eye surgery, and (for better or worse) abortion. The rest of the sector was heavily distorted by government intervention. Obamacare simply makes a bad situation worse.