Reports that compare Medicare prices with commercial payer prices or other prices (Medicaid, Medicare Advantage) appear at regular intervals.
There's new interest in commercial vs Medicare rates, often on the view that nationalized Medicare-for-All rates would save money for the economy as a whole by lowering healthcare prices.
Here's a new report from Harvard, and some links to older recent ones.
New Harvard Report Comparing Prices - Chernew et al., 2020
Chernew et al. look at inpatient and outpatient prices and compare them to commercial prices. They find there is wide state-to-state variation. For example, in Alabama commercial and Medicare prices are fairly close; but in Wyoming, Indiana, Oregon, and Colorado, commercial prices are much higher than Medicare. (One might imagine, for example, that where there are highly consolidated hospital systems that might raise prices; where there is a highly consolidated private insurer, that might lower them.)
Find Chernew et al. 2020 in Health Affairs here (subscription). Find a report on the study in Healthcare Dive here.
Additional Earlier Reports
Lab - OIG 2013
If you track the lab industry, find an opposite report by OIG in 2013 asserting that Medicare lab prices back before PAMA were higher than commercial lab prices - here. This report was critiqued in the lab industry, which even offered rebuttal data. But there was great concern that pegging CMS prices to PAMA-survey prices of commercial labs would lower CMS prices too much - acknowledging at a minimum that big commercial lab prices were, in fact, lower than Medicare for lab tests, whereas it's widely accepted the opposite is true for hospital outpatient and inpatient services.
2019 RAND Report. See a large study by RAND in 2019. Covered at Advisory Board here. RAND Report here.
2017 CBO Report. See Healthcare Dive on a 2017 Congressional Budget Office report, here. See the report on physician payment rates (commercial) here. See the report on Medicare Advantage rates here.