I am trying to learn the meaning of Terms of Trade, but I'm confused. From the wikipedia article, it says that TOT is the ratio of the value of exports over imports, and since for the other country these are reversed the TOT of the other country is the inverse, but I don't understand how that works.
Suppose country X with currency symbol \$ trades with country Y with currency symbol ¥. (I am using an exchange rate of \$1 = ¥5, but it is not relevant.)
We consider two commodities, A and B. Companies buy inputs and sell output either buying wholesale and selling retail, or buying inputs to industry and selling the product of that industry.
Input A can be bought in Y at ¥10. Since in X it costs \$2.20 to buy it, company XA buys 3 million units from the market in Y. Conversely B can be bought in X at $2, but it costs ¥12 in Y, so company YB buys 3 million units from the market in X.
Since country X exports 3M units of A, which in X are valued at \$2.20, the value of its exports is \$6.6M. Since it imports 3M units of B valued at \$2, the value of its imports is $6M and 1.1 is its TOT.
Country Y exports 3M units of B valued at ¥12, imports 3M units of A valued at ¥10 for 1.2 as its TOT.
I don't understand why TOT should be reciprocal when they are 1.1 and 1.2.
EDIT: Maybe I am doing it wrong. What is the meaning of "value" as in the value of exports and value of imports. I assumed it is the cost if someone bought it locally.