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The story is told that when the Republic of Texas was feuding with Mexico, there was a law passed by Texas to the effect that a Mexican silver dollar was worth only 50 cents in Texas; whereupon Mexico passed a law that a Texan silver dollar was worth only 50 cents in Mexico. A citizen of Brownsville, Texas, walked across the bridge over the Rio Grande to Matamoros, Mexico, went into a bar, ordered a 50-cent drink of whisky, paid for it with a Mexican dollar and received a Texan dollar in change. He then walked back to Texas, went into a bar, ordered a drink, paid for it with the Texan dollar, and received a Mexican dollar in change. This pleasant pastime, repeated several times a day, went on all winter. At the end of the time the Texan citizen still had his dollar. Obviously the barkeepers suffered no financial losses; and the question is: Who paid for the drinks?

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  • $\begingroup$ What is actually the puzzle here? $\endgroup$ – xnor Feb 17 '15 at 0:52
  • $\begingroup$ The puzzle is asking for who actually paid for the 50 cent value of the drinks $\endgroup$ – Alexasaurus Feb 17 '15 at 0:53
  • $\begingroup$ The barkeeps should have given change in their local currency to avoid such shenanigans. $\endgroup$ – Engineer Toast Feb 17 '15 at 17:43
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The citizen has performed financial arbitrage against the inconsistent exchange rates offered by the two sides. The citizen purely gained value, and at the two barkeeps lost that much value in total.

Citizen: +2 drinks
Barkeep 1: -1 Texan dollar, +1 Mexican dollar, -1 drink
Barkeep 2: +1 Texan dollar, -1 Mexican dollar, -1 drink

So, one of the barkeeps has lost value, the amount of which will be determined when the exchange rate stabilizes and the value of the currency settles. For example, if the exchange rate settles to 1 Texan dollar equaling 1 Mexican dollar, then both will have lost one drink of value.

But, if it stabilizes to, say,

1 Texan dollar = 1 drink; 1 Mexican dollar = 4 drinks

then we'll have a value change

Citizen: +2 drinks
Barkeep 1: +2 drinks
Barkeep 2: -4 drinks

and one barkeep will have lost and the other gained.

If the barkeeps use their currency to buy goods and services from others, then they will pass on the risk of loss from the currency being misvalued. Like a pyramid scheme, this loss can be passed on indefinitely as people use this currency within their country. But, currency only has value in its purchasing power, so the loss must eventually be realized The loser depends on who is holding it when exchange rates settle and what they settle to.

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  • $\begingroup$ Agreed. I, too, figured the barkeep(s) would be the ones to suffer the loss, but the original post - "Obviously the barkeepers suffered no financial losses;" - discouraged that thought. $\endgroup$ – Bulldogg6404 Feb 17 '15 at 1:09
  • $\begingroup$ The question does not specify which sort of dollar the Texan ended up with; wouldn't his final valuation depend on that (if the exchange rate ends up unequal)? $\endgroup$ – Josh Caswell Feb 17 '15 at 9:01
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I think the beekeepers or their previous customers did pay for his drinks! Whoever had the Texan money in Mexico when the state rated the currency down.

If the Mexican barkeep had 10 Texan Dollars they were worth 10dollars before and then halved their value. So he lost 5dollars.

Another way to look at it, is that he is trading off his coins each with a loss of 50c, because he could use them over in Texas for their full original value, so he would be trading his coins undervalued and thus pay for the drink himself!

One more economical way to look at it is travel expenses, since the customer is traveling just like a trader, buying local currency and selling it somewhere else far away, the 50c can be seen as his cut/profit as a travelling salesman ;-)

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The barkeepers pay.

The devaluation of the other countries currency is purely artificial. Instead of returning change in the foreign currency, the barkeepers could also return change in the local currency, go over the bridge and use their foreign currency to buy wares for the much higher value their foreign currency has there. Should they be forced to give away their foreign currency at the artificially low exchange rate, they are giving it away below the actual value.

In the real world, the barkeepers would refuse to give away any foreign currency they somehow acquired in their own country. They would do all transactions in local currency and spend any foreign currency abroad where it has more purchasing power.

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