Competition and Health Care Savings

Can someone point me in the direction of an article or any evidence (at all) that competition lowers health care cost? Where does this idea come from? Who shops around for the best price? Who clips coupons and scours the "ads" for a "cheap" doctor - no one. So why do the republican candidates keep talking about competition lowering the cost of health care. Here is my alternative for the "unfair" public mandate that has come out of the Afordable Care Act - lets just have medicare for all.