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Trade as an optimization problem

  1. Feb 3, 2009 #1
    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.

    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.
  2. jcsd
  3. Feb 3, 2009 #2


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    Then they're not constants, and you really have the much broader
    J1=f1(a, b)
    J2=f2(a, b).

    I think a useful model for trade would be more of a prisoner's dilemma: if one side implements protectionist measures that side benefits, as long as the other does not retaliate. But both countries lowering barriers makes both better off.
  4. Feb 5, 2009 #3
    Hmmm...sounds interesting.

    Yes if the constants are not really constant then the above expression takes the general form you gave. However, if they are roughly constant over some region then we can estimate the constants. The constants Ck,1 Show the benefit of the money spent locally while Ck,2 show the mutual benefit from each others prosperity. If Ck,2>Ck,1 then trade more trade would be mutually beneficial and if Ck,1>Ck,2 then less trade would be mutually beneficial. While more trade is generally mutually beneficial, if something in the economy changes (say the price of fuel) then a certain amount of rebalancing might be required.

    To estimate the constants one would need to define the objective function. One possible objective function could be really GDP. Also if one could try to take allowance for more subjective costs in the objective function such as environmental degradation or supporting over seas despots.
  5. Feb 5, 2009 #4


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    Ah, now I understand you. I think you can see where my confusion came from...

    Hmm? That doesn't seem to fit your model.
  6. Feb 6, 2009 #5
    Yea your right. I guess I should fix that by making a and b the goods traded instead of the money spent. Although the way I have it now it is still interesting. The way it is now explores the idea of mutual prosperity vs mutual poverty. Are we richer when our neighbors our poor or poorer when our neighbors are rich?
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