Alan and Bob each own a bar. Alan's is in very northern New York, and Bob's is just across the border in Canada.

As it turns out, at the beginning of this problem, a Canadian Dollar is worth exactly the same as the U.S. Dollar, and people are quite accustomed to using them interchangeably (including banks).

But, alas, the U.S. Government and the Canadian government get in a spat. So, the U.S. "devalues" the Canadian dollar 10%, so now they will treat it as worth 90 cents (U.S. currency). In retaliation, Canada does the same and "devalues" the U.S. dollar 10%, so they treat it as worth 90 cents (Canadian currency).

Enter Charlie.

Charlie goes to Alan's bar and purchases a 1 dollar drink and pays with a 10 dollar bill (U.S.). He receives, in change, a 10 dollar bill (Canadian). He then walks across the border to Bob's bar and purchases another 1 dollar drink, paying with a 10 dollar bill (Canadian), and he receives, in change, a 10 dollar bill (U.S.).

Charlie proceeds to continue doing this until he finds himself quite intoxicated.

I think it obvious that Charlie is gaining on these transactions. The question is.... WHO (if anyone) is losing out on these transactions?

rerun141's solution seems better than silverknight's. Forget about the fact that Alan and Bob could exchange their foreign currency for their own. If we're talking about what they COULD do with their foreign money, they could make millions crossing the border like chuck and asking for dollars rather than beers. In that sense, A and B lose. But, ignoring opportunity cost, they make what they wanted to make on each drink and don't have to go anywhere.

A and B convert their less valuable foreign currency into their own more valuable (assuming other establishments honor the exchange rate also)currency. Suppose A has 100c and 100a (a value of 190a for him), and the same for B (his value is 190c). Chuck makes 20 crossings, gets 20 drinks and A is out of canadian; he has 200a; B has 200c. Each makes the 10 dollars he wanted for ten drinks.

This solution has the benefit of not importing information not stated in the problem. No country has to print more money. Nobody has to go to the bank. Nobody but chuck has to go anywhere. A and B have foreign currency and use C to exchange it. rerun141 had it right. No one loses on THESE transactions (presumably 'these transactions' means 'the transactions stated in the problem').

Posted by dy on 2004-04-19 17:38:27