Monday, 6 December 2010

Where the Theorem doesn't Apply

I was discussing free trade with a friend a while ago when he said something that struck me as a good example of easy false superiority.


“Comparative advantage only works between rationally self-interested individuals.”


The law of comparative advantage is a very important one, which shows what wide circumstances trade can be useful; even when one party is strictly superior to another. But, as for any theorem in maths, or physics, it’s important to know the scope of the law; the law only holds given some assumptions. Not knowing about comparative advantage makes you ignorant, but to understand it you have to be able to distinguish the cases where it applies from those it doesn’t.

For comparative advantage, these are not that both agents are rational and self-interested (or even rationally self-interested, which I’ve just realised is different). In this case, the domain of the law of comparative advantage is neither a subset nor a superset of the set of rationally self-interested individuals.


For example, it can work with irrational agents; if nothing else, you might be a not-bad approximation of a rational agent. I think it only collapses to the extent that irrational agents don't have a utility function, at which point it becomes ill-defined what exactly constitutes a benefit for an agent without a utility function. You could trade with a paperclip maximiser though.

It can also work between an altruist and an egoist: the altruist might buy food to give to the poor from the egoist, in return for his programming skills, or whatever.

It could also work between two altruists, but if they both knew each other to be perfect altruists it'd look exactly the same as division of labour, so it's not a very interesting case.


And it doesn't always apply with rational self-individuals.

There's the trivial case, where both agents are identical, and there are no returns to scale, so neither has anything to gain from trade.

There's the 'high costs of trade' case, where shipping, communication, etc. are too expensive. I suspect this is the most common one, and highly prevalent in the modern world: if there weren’t transaction costs, there would be no reason for involuntary unemployment.

There would also be no war; if it weren’t for lack of information and so on, the two countries could just work out what the peace treaty would look like, and use that as a basis for negotiation; both gaining, because they don’t actually have to pay the costs of war.

There's the 'diminishing returns to scale' case, rising marginal costs mean we don't want to trade. A special case of this is where you want to do something because you value being the sort of person who can or does do that thing in itself: you might be a better cook than me, but I still cook for myself because I want to be the sort of person who can cook.

There's the 'my ultimate goal is to kill you' case, where I'm not really interested in your ability to make shoes more effectively than me, and the 'I want to turn the world into paperclips, and you're part of the world' case, which are the same case really.

There’s the prisoner’s dilemma for a known (finite) number of iterations, where it’s in my self interest to defect. (Or at least, it is on the normal decision theories. If you run Timeless Decision Theory, you might cooperate)


There's the 'you have no ability to produce anything I value, or destroy anything I value' case, where I have no reason at all to care what you do. If you were in a very distant land, or another universe, or a lot smaller than me, this could follow. Alternatively, if there are more agents that coefficients in my utility function, it could be that there’s no point my trading with some of those agents; there are other agents with whom it would be more profitable for me to trade.

Finally, there’s a lot that’s abstracted away from the impression given by the Law of Comparative Advantage. It shows that there are mutually beneficial trades; but not which one will be enacted. Bargaining, bluffing and negotiation help determine which particular deal is done, and even with friendly deals the strategy of conflict is still important.


So the law of comparative advantage actually has a very different – and perhaps smaller – domain than we might have thought. It does seem it applies for quite a lot of the sort of human activity we care about though, like international trade. Also, it gives a rigorous account of one mechanism whereby two agents can both become better off through trade. But it isn’t magic, and doesn’t solve all problems.

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