$\textbf{Who Paid for the Beer}$

Joe lives in a town along the US-Canada border. One day, both countries' currencies are discounted $10\%$ on the other side of the border. That is, a US dollar is worth $90$ Canadian cents in Canada, and a Canadian dollar is worth $90$ US cents in the US. Joe buys one US dollar's worth of beer in the US. He pays using a ten US dollar bill and receives ten Canadian dollars as exchange. Then, he walks across the border and buys one Canadian dollar's worth of beer. He pays using the ten Canadian dollars he has and receives ten US dollars as exchange. He then walks back to the US side to buy another US dollar's worth of beer. He receives ten Canadian dollars as the exchange before goes to Canada again. After coming back and forth, Joe finally returns to his home and becomes dead drunk. However, he still has ten US dollars in his hand. The question is who has paid for all the beers Joe has consumed?