Another presumably easy economics question (or rather puzzle)

A puzzle I found in two different collections; economic background:

Back in the days when rates of exchange weren’t floating but fixed by the governments, there are two countries, let’s call them A and B, both of which call their currencies dollar (A$ and B$). Normally, the currencies are freely convertible and remain in parity - A$1 equals B$1, and so both currencies are de facto used parallelly in both countries.

Now A and B get into quarrels; the government of A decides that the B$ will henceforth be worth only 90 A-cents in A. After this rule, the government of B does the same - A$1 = B$0.90 in B.
(one of the collections takes the US and Canada as countries, between which something along this allegedly was the case, but I’m not sure about that, so I stayed with the fictional countries.)

Now some smartass living close to the border goes into an A bar (where the beer costs 10 A-cents - it was in days gone by as I told you), drinks, pays with A$1, and gets the change - 90 A-cents - in B currency: B$1. With this, he crosses the border, orders a beer (price: 10 B-cents), pays with his B$1 and gets the change as A$1.

Now he got two beers and still has the same amount of money as in the beginning. Question: Who paid for the beers?

It’s obviously not the drunkard; it can’t be the bar owners either, because they got paid properly.
One collection said it’s the two state treasuries, period. The other one (sounding more reasonable to me) say it’s everyone living in those two countries because the tours launched an (albeit miniscule, compared to the overall amount of money circulating, but nonetheless) inflationary effect and the value of the A$ as well as the B$ decreased.

You are right, it’s the second one. Fixed exchange rates are backed by the central banks, not treasuries. They fix the value of the currency by accepting domestic currency in exchange for foreign currency. Foreign reserves are part of the balance sheet of central banks. To avoid an ongoing build up of foreign reserves* the central bank (assuming of course that it went along with this crazy scheme) would have to issue liabilities (domestic currency) to match the assets. One way or another this would drive up prices.

*[sub]Otherwise they would be financing the purchase of the country’s assets at a discount.[/sub]

I think that the flaw here is assuming that the countries actually can control the exchange rate. If each country tries to devalue the other’s currency by the same amount, then there’s still parity, so in terms of real value (as opposed to the value the governments are trying to impose), the currencies are still equal. To anyone living near enough to the border to encounter the other currency with any regularity (and you imply that the entirety of both countries see both regularly), both currencies would still have the same spending power. Both bar owners, then, lost out, because they gave the tourist a dollar in change when he was only owed 90 cents.

[completely unqualified opinion-mongering]
Centrally-contolled economies usually have laws against possession of foreign currency for this very reason; they also quite often have laws against carrying the “home” currency out of the country (not that this is necessary, since controlled-exchange currencies usually aren’t worth the paper they’re printed on, outside of the issuing country).

Such economies also have thriving black markets :smiley:
[/completely unqualified opinion-mongering]

Actually there is a problem in the math here – not sure of is intentional or not. The example provided breaks down for the following reason:

So the exchange rate is A/B = 1.11 and B/A = 0.90.

Wrong, the problem is that the patron should get back B$0.90 which is not equal to A$0.90. According to the exchange rate B$0.90 * 0.90 = A$0.81 NOT A$1. The owner of the bar ends up paying this one because he paid the patron B$1.11 in change instead of B$0.90. As stated this is a logic puzzle and has nothing to do with economics.

Please amend the first sentence of the last paragraph to read "Wrong, the problem is that the patron should get back B$0.90 which is not equal to A$1.

The problem, OG, is that in country B, B$0.90 is A$1. The two countries are enforcing by law incompatible exchange rates, where $0.90 of the local currency is ‘worth’ $1.00 of the foreign currency. Buying the beer is just to make it unclear who’s losing money. You could instead have someone just ferrying cash across the border and exchanging it at banks. A$100 is exchanged for about B$110 in country A, where the B currency has been ‘devalued’ by legislatino; then, you take the B$110 into country B and exchange it for A$121, because in B the A currency has been ‘devalued’. Woo-hoo! Free money! Until you try to take too much at once, at which point the customs folks at the border ask you to step aside for a few moments. Or years, maybe. :smiley:

Yes, if I owned a bar on the border, I would only make change in the same currency. I should not give B$1 as change for A$1 because I could easily cross the border and spend the B$1, which would buy me more than A$.90 on my side. But I would still charge B$1.11 for the beer, since I am a patriot.

The desk clerk paid for the beers. Obvious.:cool:

Economists and foreign exchange dealers call this arbitrage - find a currency that is undervalued in one country, buy heaps of it and sell it somewhere that it’s worth more until the Central Bank runs out of money trying to prop it up.

A great way to make money from stupid governments

[Grandpa Simspon]

The Democrats. Because they are in power.

[/Grandpa Simpson]

Slee

The A beer is paid for either by

  • Someone who brought that B$ into the country
  • Someone in A who held that B$ when the currency was devalued.

And similarly for B.

Just ask the Bank of England.