Short answer: definitely. There are many cases where the government is basically the only purchaser of the good so there is no market to determine the price. For instance
1. Military weapons
2. Medicare items
3. Large scale infrastructure projects
For instance, when I was at a think tank in DC we had a contract to try to come up with alternative reimbursement measures for durable medical equipment. The problem was that medicare paid for like 98 percent of many types of durable medical equipment. The preexisting policy was that medicare reimbursed 80 percent of the MSRP. But once a firm knows that they reimburse 80 percent of whatever price you set, then firms have an incentive to set really high prices. So the government was stuck in a bad eqbm.
Other approaches were a functional technology assessment where the government tries to do an engadget style teardown of the thing to determine how much it cost to make it.
Another approach could be a hedonic approach to price attributes of goods to see how much an additional attribute should be priced. Of course, that assumes you can get the right prices of the attributes to begin with....