But before I demonstrate my utter lack of knowledge, I'm going to touch on a subject that I at least have some familiarity with -- mathematics. I'm going to share with you a math problem that I cannot solve. It looks something like this:
--- = 111 = ----
B = B' * 1.41
What is the ratio between A and A'?
Elementary algebra would seem to imply the answer should be 1.41:
--- = ----
A * B' = A' * B
A * B' = A' * B' * 1.41 ==> A = A' * 1.41
By itself, I would have expected this problem would be trivial.
However, what perplexes me is that the observed value for the ratio between A and A' is nowhere near 1.41, but rather approximately 1.0.
And here is where I demonstrate my lack of understanding in the field of economics...
The thing that has been puzzling me for years (even before the recent foreign exchange craze) is that the U.S. dollar has experienced fairly consistent inflation for these 13 years while the Japanese Yen has experienced almost none, yet the exchange rate remains the same.
You see, A' / B' is the average value of the Japanese Yen in U.S. dollars for November 2007. And A / B is the average value of the Japanese Yen in U.S. dollars for April 1994. Both ratios just happen to be approximately 111. (Source: Board of Governors of the Federal Reserve System)
The ratio B' / B is the purchasing power of the U.S. dollar in 2007 relative to dollars in 1994. That is, one 1994 dollar (B) is worth 1.41 2007 dollars (B'). (Source: Bureau of Labor Statistics)
The ratio A' / A is the purchasing power of the Japanese Yen in 2007 relative to yen in 1994. It so happens that one Japanese yen buys the same amount in 2007 that it did in 1994. (Source: Japanese Ministry of Internal Affairs and Communications)
How can this be?
How can two currencies can have different inflation rates, but yet maintain the same conversion rate?
I'm no economist, but I cannot help but wonder if the answer lies outside of math and in the realm of human irrationality. Or that the CPI values uses to calculate the purchasing power of a currency are inconsistent and/or flawed. Actually, I know that CPI calculation methods differ amongst countries, but for some reason I expected Japan to have used to the calculation method that U.S. does. I admit I haven't investigated that explanation yet.
Does anyone have a better explanation (preferably one that does not violate basic math principles)? I would love to put this puzzle to rest.