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Although I am aware that the example is a simplified one it still raises two questions for me:
1. How did Martha become such a good ironer of shirts?
2. What happens to the Mexicans who were making computers?
Mexicans who were making computers, after some heavy demonstrating and violent strikes to force the government to subsidize domestic computer production and to tax foreign computers, ended up working in the shirt industry and, after a few years (it takes a while to master shirt-making), earning more money than before.
Question 1: Total world production is 31 units: 13 Computers (1 made by Mexico and 12 made by the US) and 18 Shirts (6 made by Mexico and 12 made by the US). +++ Question 2: Total world production is of 36 units: 14 computers produced by the US and 22 Shirts (10 produced by the US and 12 by Mexico). +++ Question 3: Can trade make both countries better off? How many units have to be traded?
This question can´t be answered as we don’t know the trade ratio of the products and the consumption patterns of each country. One argument would be that a higher output of both computers and shirts can make both countries better off, but let’s look deeper. Assuming that producing a computer creates a lot higher value that producing a shirt, the US is much better off trading with Mexico and Mexico is actually worse off than before as the extra output of 12 more shirts is not likely to buy back one computer. This simplified model also neglects different skill levels and machinery /supply chains which are needed to produce a shirt or a computer.
Trade will happen at a rate anywhere between the opportunity cost of a shirt in terms of computers in the USA and the opportunity cost of a computer in terms of shirts in the USA. Thus it will be at any rate between 1 to 6 shirts per computer. The proposed trade ratio of 3 shirts per computer is just 1 of many possible solutions. I think that the answer will have to do with the demand curves for both computers and shirts in the USA and in Mexico. We can't assume that a computer creates higher value than a shirt in this model, it will be the consumers that will decide that, reflected on the purchase price of both items.
It's pretty simple in an abstract way but I could think of several real life issues that my reduce the effect of trade and the shifting of labour. And yet I think this is a elegant principle that is often forgotten and more often ignored by many experts.
Alex does your text book supply some of the equations to compute this? It looks like linear optimization.