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In the following image, we have U.S. and U.K. producing wheat and cloth in bushels/hour and yards/hour respectively.

In all cases except in case D, given in the figure, trade is possible between U.S. and U.K.

how did we reach this conclusion?

step 1: U.S. can exchange 4W for 1C domestically if she gets any ratio of exchange lesser than 4W/1C say, 3W/1C or 2W/1C or 1W/1C then U.S. shall be willing to exchange wheat for cloth.

step 2: U.K. can exchange 1W for 2C domestically if she gets any ratio of exchange greater than 1C/2W say, 1W/1C then U.K. shall be willing to exchange cloth for wheat.

Conclusively, if the ratio lies between 4W/1C and 1W/2C, both U.S. and U.K. shall be willing to trade.

if we apply this formula in all cases, we can find whether trade is possible or not between the two nations.

My question is whether this method is foolproof?

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closed as off-topic by denesp, 123, Adam Bailey, Theoretical Economist, Kitsune Cavalry Sep 15 '18 at 23:08

This question appears to be off-topic. The users who voted to close gave this specific reason: