# Are Terms of Trade reciprocal?

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.

• First: You are citing a wikipedia page that lacks citations on its own. This makes it almost impossible to verify their claims. reciprocity is mentioned in a section called "2 country economy". With two countries, one countries' exports are the other countries' imports, by definition. So whatever is in the numerator of one country is in the denominator of the other. Do you agree? – Chris tie Feb 1 '17 at 22:44
• I don't agree that it's as simple as switching numerator and denominator. The value of X's exports divided by X's imports values the goods based on what it costs in country X. When we do Y's exports (X's Imports) divided by Y's imports (X's exports) we should value it in the cost in county Y, so it turns out to not be the same. – Marlin Pierce Feb 2 '17 at 13:35
• So which is the TOT for country X? Is it X's exports divided by X's imports which is 1.1 or is it the reciprocal of the calculation for country Y, which is 1/1.2 or 0.8333? – Marlin Pierce Feb 2 '17 at 13:36

Terms of trade is a measure of relative prices, and prices only. There are no quantities involved. As a recent review paper puts it:

"with exceptions that I will note below, most trade economists have defined a country’s terms of trade as the price of its exports divided by the price of its imports, $p_X/p_M$" (p.2).

Therefore, by definition, in a two country model, they are reciprocal. In a model with more countries, there can be differences, as some countries could import or export different goods.

Actually, I don't know which Wikipedia you are looking at, but in the English version, the first line states:

"Terms of trade (TOT) refers to the relative price of exports in terms of imports and is defined as the ratio of export prices to import prices."

For future reference, Wikipedia is an unreliable source. If you are in an educational institution, it is likely you have access to the New Palgrave Dictionary of Economics (the terms of trade article is here). If not, you can google "terms of trade pdf" and hopefully get the slides of a generous professor who is sharing his/her knowledge with the world.

• I don't know how one would aggregate all trade without using a weighted average and considering quantity, but take quantity out of my example, and I still get 1.1 for country X and 1.2 for country Y which are not reciprocal. The only TOT is reciprocal is if you value imports and exports for country X in value in country X, and then value exports and imports for country Y in value in country X. If you use value in country Y for the TOT of county Y, they are not reciprocal and that seems correct where reciprocal seem incorrect. – Marlin Pierce Feb 3 '17 at 21:30
• I gave an example, and got 1.1 vs 1.2 for TOT. Which, if any, are correct? – Marlin Pierce Feb 3 '17 at 21:33
• I will give you a response as soon as I have more time. :) – luchonacho Feb 5 '17 at 13:10