Protectionism is often viewed as positive for the country that implements the protectionism but bad globally due to losses of efficiency and miss allocation of resources. Because protections measures are often met with counter protectionist measures countries try to trade freely and fairly for the mutual benefit of all.(adsbygoogle = window.adsbygoogle || []).push({});

I kind of wondered what this might look like as an optimization problem. A good local approximation that might have these characteristics is:

J1=C11 a+ C12 sqrt(ab)

J2=C21 b+ C22 sqrt(ab)

Where “a” is the money spent in country one. “b” is the money spent in country two. Cm,n are constants that may depend on “a” and “b”. Country one wants to optimize J1 and country two wants to optimize J2. The term “sqrt(ab)” represents the productivity gains from trade.

Now if both countries try to keep their own spending in their own country then they lose the productivity gains and the world suffers. The optimization is interesting because if they each try to optimize independently of each other they will not obtain the optimal trade and will be poorer as a result. However, if the trade is disproportional then there is a possibility that they could suffer worse then had their been no trade.

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# Trade as an optimization problem

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