The truth is weirder, especially since most military and federal contracts and money spent is service contracts, such as Fixed Price Incentive Target Firm.

Government executives and contracting officers - who's sole job is the serve the government and prove they do it well - do research and set a budget for a job, like providing IT services for an agency. They then let contractors bid on the job.

The idea is that (1) no job that isn't inherently governmental should be done by government employees, and (2) the private sector is powered by magical thinking that somehow makes it more efficient. In reality, they just hire bad employees or underpay good employees.

Anyway, the magic happens when the winning contractor gets the government to pay for the employees. Say the target cost is 100 million, and the total bill from the contractor comes out to 70 million for labor and administrative overhead. The government says "Thanks! Since we came in under budget, you can keep this extra 10 million in profit, while we'll keep 20 mullion in cost savings" and everyone is happy. Particularly the contractor, since this was in the contract and they already leveraged the projected profit years ago in the stock market.

It doesn't work for workers, but nobody cares about that. They can always get a better job.