Here’s something I don’t get about comparative advantage.
The implied advice, as far as I understand it, is to check which good you have a comparative advantage in producing, and offer that good to the market.
But suppose that there are a lot more goods and a lot more participants in the market.
For any one individual, given fixed prices and supply of everyone else, it sounds like we can formulate the production and trade strategy as a linear programming problem:
We have some maximum amount of time. That’s a linear constraint.
We can allocate time to different tasks.
The output of the tasks are assumed to be linear in time.
The tasks produce different goods.
These goods all have different prices on the market.
We might have some basic needs, like the 10 bananas and 10 coconuts. That’s a constraint.
We might also have desires, like not working, or we might desire some goods. That’s our linear programming objective.
OK. So we can solve this as a linear program.
But… linear programs don’t have some nice closed-form solution. The simplex algorithm can solve them efficiently in practice, but that’s very different from an easy formula like “produce the good with the highest comparative advantage”.
And that’s just solving the problem for one player, assuming the other players have fixed strategies. More generally, we have to anticipate the rest of the market as well. I don’t even know if that can be solved efficiently, via linear programming or some other technique.
Is “produce where you have comparative advantage” really very useful advice for more complex cases?
Wikipedia starts out describing comparative advantage as a law:
The law of comparative advantage describes how, under free trade, an agent will produce more of and consume less of a good for which they have a comparative advantage.[1]
But no precise mathematical law is ever stated, and the law is only justified with examples (specifically, two-player, two-commodity examples). Furthermore, I only ever recall seeing comparative advantage explained with examples, rather than being stated as a theorem. (Although this may be because I never got past econ 101.)
This makes it hard to know what the claimed law even is, precisely. “produce more and consume less”? In comparison to what?
Skeptics of comparative advantage have underlined that its theoretical implications hardly hold when applied to individual commodities or pairs of commodities in a world of multiple commodities.
Although, without citation, so I don’t know where to find the details of these critiques.
It seems like there are two separate claims here, which is “societies tend to produce goods that are their comparative advantage” and “you, an individual, should try to do this.” I’m mostly focused on the second one, and whether it applies to things like the x-risk ecosystem. People have talked as if it did apply. My guess is that insofar as there’s formal math, it’s much less clear and might be dominated by other considerations.
It still feels vaguely like “what is my comparative advantage” within a particular community aimed at a particular task should be a relevant factor.
The very crude algorithm I think I’ve been doing is “look at the list of things I seem particularly good at” (that I might have absolute advantage in), and then look at the things that are in-demand (which, I might plausibly turn out to have comparative advantage at). That at least narrows the search space a bit to “things that are good hypotheses for being my comparative advantage.”
I once had a discussion with Scott G and Eli Tyre about this. We decided that the “real thing” was basically where you should end up in the complicated worker/job optimization problem, and there were more or less two ways to try and approximate it:
Supposing everyone else has already chosen their optimal spot, what still needs doing? What can I best contribute? This is sorta easy, because you just look around at what needs doing, combine this with what you know about how capable you are at contributing, and you get an estimate of how much you’d contribute in each place. Then you go to the place with the highest number. [modulo gut feelings, intrinsic motivation, etc]
Supposing you choose first, how could everyone else move around you to create an optimal configuration? You then go do the thing which implies the best configuration. This seems much harder, but might be necessary for people who provide a lot of value (and therefore what they do has a big influence on what other people should do), particularly in small teams where a near-optimal reaction to your choice is feasible.
In principle, for work done for market, I guess you don’t need to explicitly think about free trade. Rather, by everyone pursing their own interests (“how much money can I make doing this”?) they’ll eventually end up specializing in their comparative advantage anyway. Though, with finite lifetime, you might want to think about it to short-circuit “eventually”.
For stuff not done for market (like dividing up chores), I’d think there’s more value in thinking about it explicitly. That’s because there’s no invisible hand naturally pushing people toward their comparative advantage so you’re more likely to end up doing things inefficiently.
OK. It seems there are results for more than 2 goods, but the results are quite weak:
Thus, if both relative prices are below the relative prices in autarky, we can rule out the possibility that both goods 1 and 2 will be imported—but we cannot rule out the possibility that one of them will be imported. In other words, once we leave the two-good case, we cannot establish detailed predictive relations saying that if the relative price of a traded good exceeds the relative price of that good in autarky, then that good will be exported by the country in question. It follows that any search for a strong theorem along the lines of our first proposition earlier is bound to fail. The most one can hope for is a correlation between the pattern of trade and differences in autarky prices.
Dixit, Avinash; Norman, Victor (1980). Theory of International Trade: A Dual, General Equilibrium Approach. Cambridge: Cambridge University Press. p. 8
Here’s something I don’t get about comparative advantage.
The implied advice, as far as I understand it, is to check which good you have a comparative advantage in producing, and offer that good to the market.
But suppose that there are a lot more goods and a lot more participants in the market.
For any one individual, given fixed prices and supply of everyone else, it sounds like we can formulate the production and trade strategy as a linear programming problem:
We have some maximum amount of time. That’s a linear constraint.
We can allocate time to different tasks.
The output of the tasks are assumed to be linear in time.
The tasks produce different goods.
These goods all have different prices on the market.
We might have some basic needs, like the 10 bananas and 10 coconuts. That’s a constraint.
We might also have desires, like not working, or we might desire some goods. That’s our linear programming objective.
OK. So we can solve this as a linear program.
But… linear programs don’t have some nice closed-form solution. The simplex algorithm can solve them efficiently in practice, but that’s very different from an easy formula like “produce the good with the highest comparative advantage”.
And that’s just solving the problem for one player, assuming the other players have fixed strategies. More generally, we have to anticipate the rest of the market as well. I don’t even know if that can be solved efficiently, via linear programming or some other technique.
Is “produce where you have comparative advantage” really very useful advice for more complex cases?
Wikipedia starts out describing comparative advantage as a law:
But no precise mathematical law is ever stated, and the law is only justified with examples (specifically, two-player, two-commodity examples). Furthermore, I only ever recall seeing comparative advantage explained with examples, rather than being stated as a theorem. (Although this may be because I never got past econ 101.)
This makes it hard to know what the claimed law even is, precisely. “produce more and consume less”? In comparison to what?
One spot on Wikipedia says:
Although, without citation, so I don’t know where to find the details of these critiques.
This actually has been a major question for me.
It seems like there are two separate claims here, which is “societies tend to produce goods that are their comparative advantage” and “you, an individual, should try to do this.” I’m mostly focused on the second one, and whether it applies to things like the x-risk ecosystem. People have talked as if it did apply. My guess is that insofar as there’s formal math, it’s much less clear and might be dominated by other considerations.
It still feels vaguely like “what is my comparative advantage” within a particular community aimed at a particular task should be a relevant factor.
The very crude algorithm I think I’ve been doing is “look at the list of things I seem particularly good at” (that I might have absolute advantage in), and then look at the things that are in-demand (which, I might plausibly turn out to have comparative advantage at). That at least narrows the search space a bit to “things that are good hypotheses for being my comparative advantage.”
I once had a discussion with Scott G and Eli Tyre about this. We decided that the “real thing” was basically where you should end up in the complicated worker/job optimization problem, and there were more or less two ways to try and approximate it:
Supposing everyone else has already chosen their optimal spot, what still needs doing? What can I best contribute? This is sorta easy, because you just look around at what needs doing, combine this with what you know about how capable you are at contributing, and you get an estimate of how much you’d contribute in each place. Then you go to the place with the highest number. [modulo gut feelings, intrinsic motivation, etc]
Supposing you choose first, how could everyone else move around you to create an optimal configuration? You then go do the thing which implies the best configuration. This seems much harder, but might be necessary for people who provide a lot of value (and therefore what they do has a big influence on what other people should do), particularly in small teams where a near-optimal reaction to your choice is feasible.
In principle, for work done for market, I guess you don’t need to explicitly think about free trade. Rather, by everyone pursing their own interests (“how much money can I make doing this”?) they’ll eventually end up specializing in their comparative advantage anyway. Though, with finite lifetime, you might want to think about it to short-circuit “eventually”.
For stuff not done for market (like dividing up chores), I’d think there’s more value in thinking about it explicitly. That’s because there’s no invisible hand naturally pushing people toward their comparative advantage so you’re more likely to end up doing things inefficiently.
OK. It seems there are results for more than 2 goods, but the results are quite weak: