Help! This is driving me mad!

[jadyn]

Northland and Southland were happy neighbours until yesterday, when Northland declared that a Southland dollar was to be worth only 90 Northland cents.

Not to be outdone, Southland declared that a Northland dollar would be worth 90 Southland cents.

I live in Centerville, on the border between the two countries. I go into a Northland store and buy a kazoo, which costs 10 cents. I pay for it with a Northland dollar and receive a Southland dollar as change.

Then I go across the street and enter a Southland store. There I buy a lemon, which also costs 10 cents. I pay for it with a Southland dollar and receive a Northland dollar as change.

When I get home I have my kazoo and lemon, for which it appears I've paid nothing. And each of the merchants has an additional 10 cents in his receipts.

So who paid for the kazoo and lemon?

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Can anyone solve this for me please? Thank you!

[grasscarp]

You have paid. The dollar given back to you in each store will only buy you a further 90 cents worth of stuff in that store. (That is my opinion anyway)

[bathtub]

Evacuate Centerville now is my advice. This could get nasty! ; )

[dr b]

The decrees are contradictory. If one $S is worth $0.90N, then one $N = $1.11S. Likewise if one $N is worth $0.90S, then one $S = $1.11N (where $N and $S are North & South dollars). Clearly both can't be true, regardless of what some government pinhead decrees.

Let's suppose for the sake of argument that the Northlanders are correct, and a $S is actually worth $0.90N. Then the North shopkeeper was correct to give you one $S (worth 90 N cents) in change. You paid 10 "N cents" and the shopkeeper made 10 "N cents" in profit.

Now when you went to the S shop you gave him one $S (worth 90 N cents), he gave you merchandise worth 10 "S cents" (or 9 "N cents") as well as one $N in return. So you paid him 90 N cents and he gave you back $1.09 N (in merchandise and $N). The S shopkeeper is out the money here, as a result of his government decreeing a nonsensical exchange rate. You got a free kazoo and lemon (enjoy!!).

Of course if the situations were reversed, the N shopkeeper would lose.

[dr b]

To perhaps simplify my answer from last night, suppose the N shopkeeper was willing to make change for you without you buying anything. You could give him one $N and he'd be willing to give you 1.11 $S in exchange (since at the official exchange rate $S 1.11 = 1.11x0.90 = $N 1.00).

You could then walk across the street to the S shopkeeper and buy $S 1.11 of his merchandise.

in contrast if you had just walked into the S shop and given him your $N 1, you'd only be able to buy $0.90 S of merchandise, since the S shopkeeper treats a $N as being worth only 90 S cents (at his official exchange rate).

So just by walking across the street to exchange your $N, you've created 21 S cents. This is an arbitrage opportunity caused by the two governments setting inconsistent exchange rates. A black market in exchanging $N and $S would spring up quickly (much as you see in say, Zimbabwe where the official exchange rate bears no relation to reality).