Who Paid for the Beers?

There was a time when U.S. banks valued the Canadian dollar at $0.90 American, and Canadian banks returned the favor by valuing the U.S. dollar at $0.90 Canadian. This inspired the following puzzle. I’ll give my answer next week.
A man walked into a bar in International Falls, Minn., U.S., and ordered a 10-cent beer (such was the price at the time.) He paid the bartender a U.S. dollar and a got a Canadian dollar in change (for of course both currencies freely circulate in the cosmopolitan community of International Falls.) The man then walked across the border into Canada, ducked into another bar, and ordered a beer. It too cost 10 cents (Canadian). The man paid by giving the bartender the Canadian dollar he’d been given, and got a U.S. dollar in change.
You get the picture. The man then went back to the U.S. side, bought another beer the same way, then returned to the Canadian bar. By the end of the day, he was falling-down drunk, with $1 American in his pocket.
Who really paid for the man’s beers?