Fortunately, Randall Munroe of XKCD fame has set his mind to the task of answering that question on his What If? site. Firstly, it's worth noting there's no easy way to calculate an answer—but he's given it a good go. First, consider the location of the shoot:
The ISS is expensive, but there have been music videos set against an even more expensive backdrop. At a cost of roughly $400 billion, the US Eisenhower Interstate Highway System is probably the most expensive peacetime public works project in the history of mankind. If we’re including the entire ISS in the cost of Commander Hadfield’s video, any video shot on the American highway system should get the cost of the highway system added to its total. By that measure, the commander’s video would lose to U2’s Last Night on Earth, which was filmed on a section of I-670 in Missouri, and therefore cost more than the ISS and the Moon landing program combined.
A bargain, then! But both the road and the ISS are used for things other than making videos—so what about cost compared to how much time the shoot took?
If you spread out the ISS’s price tag across all the astronaut-hours spent on board, you come up with about $7.5 million per person per day, or roughly $90 per second. That sounds like a lot, but at that rate, the five-and-a-half-minute video only runs about $30,000. Given that the video has probably done more for space industry than millions in public outreach, that’s a good deal.
And certainly not the most expensive music video ever made. Factor in that Chris Hadfield filmed the video himself, only earns in the region of $85 an hour, and is allowed some time off to relax while he's aboard the ISS, and the video seems like an absolute bargain. Check out the full What If? post for more detail—and to find out how much the guitar he played the song on cost to get into space. [What If?]