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$3.$ Gains from trade

Suppose there exist two imaginary countries, Denali and Sequoia. Their labor forces are each capable of supplying four million hours per week that can be used to produce shorts, almonds, or some combination of the two. The following table shows the amount of shorts or almonds that can be produced by one hour of labor.

$\backslash$table$[[,$Shorts,Almonds$],[$Country$,($Pairs per hour of labor$),($Pounds per hour of labor$)],[$Denali$,12,24],[$Sequoia$,8,32]]$

Suppose that initially Denali uses $1$ million hours of labor per week to produce shorts and $3$ million hours per week to produce almonds, while Sequoia uses $3$ million hours of labor per week to produce shorts and $1$ million hours per week to produce almonds. As a result, Denali produces $12$ million pairs of shorts and $72$ million pounds of almonds, and Sequoia produces $24$ million pairs of shorts and $32$ million pounds of almonds. Assume there are no other countries willing to engage in trade, so$,$ in the absence of trade between these two countries, each country consumes the amount of shorts and almonds it produces.

Denali's opportunity cost of producing $1$ pair of shorts is $$ of almonds, and Sequoia's opportunity cost of producing $1$ pair of shorts is

$$ of almonds. Therefore, $$ has a comparative advantage in the production of shorts, and $$ has a comparative advantage in the production of almonds.

Suppose that each country completely specializes in the production of the good in which it has a comparative advantage, producing only that good. In this case, the country that produces shorts will produce $$ million pairs per week, and the country that produces almonds will produce