Then you should see this week's BBC Panorama about Tesco's procurement practices. Only available in the UK unfortunately. I was aware that supermarkets made good money from "commercial deals" (ie, flogging suppliers) but was unaware of the size of the problem. It is big.
Public procurement is probably inefficient if one looks into the how the private sector does business and the headline prices paid by the public sector, but suppliers should remember the grass on the other side is not exactly greener, especially if they are working with supermarkets.
This leads me to reversing the question from my good friend Albert Sanchez-Graells about the impact of large public buyers in the rest of the market (they can be ultra-competitive and/or have a huge impact on specific markets, forcing suppliers to raise prices elsewhere): so, can large private buyers have the same effect on suppliers working with the public sector?