However, I also read an article [3] that seems to indicate that the complete opposite was true as farmers who use BLM land have to maintain it which made public land cost $1.20 more than private (2011). However, I don't really trust this that much as the guy who wrote it was a farmer and on the "Public Lands Council" which is a pro ranching organization. [4]
[1] https://www.blm.gov/press-release/blm-and-forest-service-ann... [2] https://sgp.fas.org/crs/misc/RS21232.pdf [3] https://thehill.com/blogs/congress-blog/economy-budget/27344... [4] https://publiclandscouncil.org/
(I didn't spent a lot of time researching but I found those articles interesting so hopefully you will as well!)