There may be differences in sectors. I can only speak to construction.
In construction, most reputable studies that have been done on the issue show a premium of between 12% and 18%. That's overall. When you look at specific regions where there's further shrinkage of competition, it can be as high as 30% to 40%.
Really, the question that governments have to ask is, why would they want to pay 30% to 40% more for public infrastructure simply to restrict bidding? There's no reason to do it for quality or safety. There's no reason to do it. By allowing it to happen, and by other levels of government funding projects that are under closed-tendering provisions, you're paying up to, in the City of Montreal report on aqueduct projects, 85% more. I know that as a citizen, if I'm funding a $100-million or a $1-billion subway expansion or hospital expansion, I'd rather have two hospitals than throw $85 million down the drain, because there's no reason for it to happen.