Has there been any research into identifying a good benchmark that would explain, on average, what kind of effect good/effective competition would have on total cost? I've seen a few research papers that seem to cite individual cases and the savings experienced in addition to a large amount of sources that explain effective competition would have a positive effect on cost, but no specific or rough savings benchmark/estimate that would be typical.
You asked if there has been any research into identifying a good benchmark... competition would have on total cost. Yes, much research has been done and I recommend you read, A Review of the Literature: Competition Versus Sole-Source Procurements By William N. Washington
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This article can be found in the Acquisition Review Quarterly Spring 1997