In most of the cases I’m aware of, the contractors in D.C. need special security clearances and are very specialized. That could account for most of the difference, though it probably doesn’t account for all of it.
Like the Bay Area and the need for “mobile” engineers now, there was so much demand for contractors in D.C. that the rates went up very quickly over the past decade or so.
But yes, when you combine powerful lobbyists, lots of tax money, and the desire to “spend it into the economy, right now” there is a lot of room for all kinds of shenanigans. This is why I say that the #1 place to look for fraud and abuse is where public money and private enterprise meet. Always was the case, and always will be.
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Also, though I do not know this for sure, the cost of the contractor might be the cost that the govt pays a private company for the contractor (usually the case as far as I’ve seen). This cost would include all the overhead and profit for the corporation, this is not necessarily what the contractor is receiving individually. There is a lot of bloat, as usual, where the middleman is concerned.