Doesn't make sense for them to sell it at a loss, probably very low profit. The reason the carriers sell it for so much is because they know people who do buy it through them aren't aware of the Google Play cost.
Here's my theory: Google is betting that selling the Nexus devices at a cheap cost is good for their long term business model. Google isn't in this to make money giving free software to manufacturers, and they certainly aren't going to make money buying phones and selling them at a cheaper cost.
Google' business is information they can use for ad revenue, be it mapping data, music trends, etc. Look at how many apps Samsung includes that duplicates. Their own browser, chat client, email client, and even their own store (and now a Developer's conference to go along with all this). And Samsung DOMINATES Android. Any time someone uses Samsung browser, Chat-On, or even (shutters) S-Voice; vice Chrome, Hangouts and Google Now, Samsung gets that information rather than Google. And I know that us within these forums know better, but for the average consumer, they'll just use whatever was on the phone. A good friend of mine got the Galaxy S 4 this spring, and was using S-Voice until I showed her how to get to Google Now, and how much better it was (and I remapped her home key to make things even easier).
When Google controls both software and hardware, they can just release THEIR apps without worrying about the third party manufacturer putting their stuff on. While the carrier pricing is what it is, selling them for cheap(er) on the Play store leads more consumer to the product. Honestly, were it not for the Nexus pricing, I would have picked up a Note 3 or be looking into the One Max. I imagine the sales from the GPE HTC One and S4 still go to HTC and Samsung, with a cut going to Google for the cost of the pages. While Google may be eating some cost in the short run by selling the devices at a negative or break even margin, the information they get by people using their services will more than make up for the cost of the device. And if anyone has money to invest in the short term, it's Google.
This is all just an educated guess based on knowing about Google and knowing about different products. If it's true, awesome. If not, then I'd be interested to learn the true reason or logic.