## Friday, February 29, 2008

### Currencies + alcohol = Profit?!

[Note: I'm starting to think that putting difficulty ratings at the beginning of each puzzle was a mistake--so I'm not going to do it this time!]

U.S.A. and Canada were having an argument. I know! How could possibly be unhappy with the U.S.? But that's what happened in this hypothetical. Tempers flared, and before we knew it, each country took action on the other. Previously, the U.S. and Canadian currency had been on equal terms: one dollar to a dollar. But then the U.S. made it law that every Canadian dollar is now only worth ninety cents in U.S. currency. Canada made it law that every U.S. dollar is now only worth ninety cents in Canadian currency.

Charlie, ever the opportunist, found a way to profit from this. He lives near the border, where there are two bars, one on either side. In the bar in the U.S., he uses a U.S. 10 dollar bill to buy a 1 dollar drink, and receives 10 Canadian dollars of change. He walks across the border to the other bar, and buys a 1 dollar drink with his 10 Canadian dollars. He receives 10 U.S. dollars change. He crosses the border again back to the U.S. bar to buy another drink. This process is repeated until he is drunk silly.

Charlie is obviously profiting from this situation. But who is losing?

This is an open-ended problem, so I will not have a separate solution post like I usually do.

intrinsicallyknotted said...

Let's see…well, the bartenders are not losing directly, since they're still getting the correct price of \$1 (in their own currency) for each \$1 beer they sell. Could they be losing for a different reason, though?

Since the situation is symmetric, I'll focus on the US side of things. The US bartender has Canadian currency in his register, which he might have gotten by charging someone \$1.11 in Canadian dollars for a drink. That transaction doesn't cost him anything. On the other hand, he might have gotten the Canadian currency from an exchanger like a bank.

Usually, a foreign exchange will take a small percentage of the total amount as a fee, but let's assume they don't just to make the problem simpler. If the bartender's wise he'll do it in the US where he can give only \$9US to get \$10 Canadian. This equivalent to giving Charlie \$9 change in US currency, so the bartender still isn't losing. If he were to do the exchange in Canada, he'd have to pay \$11.11US to get \$10 Canadian, so he would be losing.

This is the key, I think. At some point in the process, someone is going to have to exchange US money for Canadian in Canada, and Canadian money for US in the United States. What Charlie is doing is equivalent to the process of buying Canadian money cheap in the US, selling it for more in Canada, and so on, which is why he makes a profit. If he didn't drink the profit each time, he would multiply his money by a factor of 1.11 each time he crossed the border. But somebody is therefore selling Canadian money cheap in the US and buying it for more in Canada, whether it be the currency exchange, the bartenders, other customers, etc.

miller said...

I think there are further possibilities if you think of it more as a real world problem. How would the economy react?

intrinsicallyknotted said...

I'm going to have to play with it for a while. Economics has never been a strong point for me. I will say I don't think this is a good idea in real life!