This was helpful, but I'm still somewhat confused. Conspicuously absent from your post is an outright statement of what comparative advantage is -- particularly, what the concept and theorem is supposed to be in the general case with more than two resources and more than two agents.
The question is: who and where do I order to grow bananas, and who and where do I order to build things? To maximize construction, I will want to order people with the largest comparative advantage in banana-growing to specialize in banana-growing, and I will want to order those bananas to be grown on the islands with the largest comparative advantage in banana-growing. (In fact, this is not just relevant to maximization of construction - it applies to pareto-optimal production in general.)
Could you elaborate on this by providing the general statement rather than only the example?
Before reading your post, I had in mind two different uses for the concept:
Your post gave me a third potential application, namely, a criterion for when trade may occur at all. This expanded my understanding of the concept considerably. It's clear that where no comparative advantage exists, no trade makes sense. A country that's bad at producing everything might want to buy stuff from a country that's just 10x better, but to do so they'd at least need a comparative advantage in producing money (which doesn't really make sense; money isn't something you produce). (Or putting it a different way: their money would soon be used up.)
But then you apply the concept of comparative advantage to a case where there isn't any trade at all. What would you give as your general statement of the concept and the theorem you're applying?
I intentionally didn't give the general statement in the post, because I wanted to keep the post non-mathematical, and the general statement is pure math. It's basically just Arrow-Debreu-style microeconomics.
Here's the general version:
The typical assumptions built-in to the models ensure that the greedy algorithm actually achieves the optimal point - e.g. independent production functions, continuous allocation of time/other resources, etc. (We don't necessarily need linear production functions, but concavity is usually assumed.)
Intuitively: the price vector quantifies the trade-off between production of goods in the system as a whole. If e.g. the price of apples is 1, oranges is 2, and bananas is 3, then that means producing 1 more apple costs 1/2 orange or 1/3 banana or (in general) 1/2*x orange and 1/3 * (1-x) bananas. That's opportunity cost in the system as a whole, assuming that a pareto-optimal trade-off is made - i.e. assuming that we produce the additional apple while remaining on the pareto surface. The resources required to produce an additional apple could have been used to produce 1/2*x orange and 1/3 * (1-x) bananas instead, for whatever value of x we want (assuming it's small enough that the linear approximation still holds).
But an individual person, or any particular choice faced, may have different trade-offs than the system as a whole. Maybe I have an opportunity to produce 1 apple at the cost of 1 orange, or 1/4 bananas, or 1*x orange and 1/4*x bananas (so my prices are 1, 1, 4 rather than 1, 2, 3). What's my optimal move? Well, if I devote a fraction x1 of my resources to apples, x2 to oranges , and x3 to bananas, then I'll produce (something proportional to) 1*x1 apples, 1*x2 oranges, and 1/4*x3 bananas, for a total value (proportional to) 1*1*x1 + 1*2*x2 + 1/4*3*x3. In that case, I'll achieve maximum value by devoting as much production as possible to oranges.
In general, assuming the greedy algorithm works, we maximize total value by locally choosing the option with highest (global price)/(local price), where prices capture the opportunity costs of producing one thing rather than something else.
Does that make sense? Happy to give more detail/math on any particular points.
Also, one minor side note, in response to this:
Dynomight's post seems to provide a sufficient counterargument to this, in its example illustrating how with more than 2 players, opening up a trade route may not be a Pareto improvement (may not be a good thing for everyone).
Note that, in that example, the new trade route still allows a pareto improvement in total production of goods. It's "not a pareto improvement" in the sense that fewer goods may be allocated to a particular agent. Thus the standard argument from economics that we should rely on free markets plus wealth transfers: free markets ensure pareto optimal total production of goods, and wealth transfers allow that production to be distributed in such a way that nobody ends up worse off. That's the theory, anyway.
Thus the standard argument from economics that we should rely on free markets plus wealth transfers: free markets ensure pareto optimal total production of goods, and wealth transfers allow that production to be distributed in such a way that nobody ends up worse off. That's the theory, anyway.
Approaching this from a mechanism design standpoint, is there a way to distribute wealth such that this guarantee is actually enforced? It seems challenging!
It's tough, at least if we want the mechanism to be fairly general.
Here's an example of the kind of problem which comes up. We expect richer people to substitute from inferior to superior goods - e.g. as the populace becomes wealthier, they eat a bit less rice and a bit more chicken, or a bit less chicken and a bit more beef. So opening up trade creates a pareto improvement in the production frontier (e.g. holding everything else constant, we can always get more beef), but consumers may move to a new point on that frontier with different things produced.
So far, that's not really a problem for mechanism design - all the goods are still traded on the market, presumably for money, so we can still use monetary income to tell whether someone is better/worse off. The real problem comes when people use extra wealth to substitute toward non-market goods - most notably leisure. If the populace becomes wealthier in real terms, they may decide to work less. But for mechanism design purposes, it's really hard to separate that from new trade putting someone out of business.
Nope. Roughly speaking, pareto-optimality tells us about a gradient, while concavity/convexity tell us about curvature. That said, if we can randomize decisions, then pareto-optimality under expectations implies concavity: if our frontier is convex, we can take a random mix of two points on the frontier in order to get a point whose expected value is a pareto improvement over the frontier.
I think of comparative advantage & specialization as features of production. People producing the things that they have comparative advantage at puts society on the pareto frontier in terms of the amount of each good that is produced.
I haven't been thinking of this as a theorem, but I think it could go something like: there are n people and m goods and person i will produce p*f(i,j) units of good j if they devote p fraction of their time to producing good j, and each person uses 100% of their time producing goods. Then if you want to describe the pareto frontier that maximizes the amount of goods produced, it involves each person producing a good where they have a favorable ratio of how much of that good they can produce vs. how much of other goods-being-produced they can produce.
That seems like a sensible way to set up the no-trade situation. Presumably the connection to trade is via some theorem that trade will result in pareto-optimal situations, therefore making comparative advantage applicable.
But I still wonder what the exact theorem is.
Then if you want to describe the pareto frontier that maximizes the amount of goods produced, it involves each person producing a good where they have a favorable ratio of how much of that good they can produce vs. how much of other goods-being-produced they can produce.
What do you mean by "favorable"? Is there some threshhold?
What do you mean by "involves each person producing"? Does it mean that they'll exclusively produce such goods? Or does it mean they'll produce at least some of such goods?
There is a weaker condition to trade with 10x better economy. If the other economy is 11 times more efficient in one good but only 9 times more efficient in another by offering to be a trade partner they get closer to their good good efficiency on the bad good. Essentially you need a resource they can exploit you for. They don't care if you work a buttload for a penny, but you agree to it if your shambling technique is worse than getting screwed over.
Since the people living inland could not live without it, the salt monopolist could charge quite high prices - a “trade” arguably not so different from threatening inland farmers with death if they did not pay up.
Especially given that you speak of the British and India, it seems like you ignore the political factors that come with the salt. It's no historical accident that Ghandi picked his fight with the British over salt. If salt would all be about comparative advantage it doesn't explain why Ghandi was forbidden from picking up salt by British law.
Since the people living inland could not live without it, the salt monopolist could charge quite high prices - a “trade” arguably not so different from threatening inland farmers with death if they did not pay up.
Farmers have no problem storing unprocessed wheat for longer periods of time without salt. They are not threatened with death. On the individual level they just have to suffer tasteless food which means that they are willing to buy the salt even with salt taxes.
Beyond the individual they can't feed an army because an army that travels around can't carry wheat and process it to feed itself while it's moving. Control over the salt is control over the ability to feed a moving army and if the government has control over the flow of salt the inland farmers can't raise an army to challenge the power of the government.
For more on the role of salt Salt: A World History by Mark Kurlansky was insightful for me.
To be clear, the claim in the OP is not that anything is all about comparative advantage. Comparative advantage is the main factor in pareto-optimal production; allocation (i.e. who gets the gains) is where other factors enter. Comparative advantage was a necessary element for anyone to make any profit from a salt monopoly, but they still had to enforce that monopoly in order to actually capture the gains.
(Also, I don't know why people keep assuming I was talking about British India. The same dynamic was present in many places - e.g. the Chinese government profited from monopolies on iron and salt a millennium earlier.)
+1 to the Kurlansky recommendation - his book on Cod was excellent, and Salt has been on my reading list for a while.
The thing about the British monopol on salt in India is that it's achieved by forbidden certain easy salt production like the one in which Ghandi engaged.
There's artificial scarcity in India and I don't think it makes sense to speak of comparative advantage when it comes to monopoly gains that are achieved by creating artificial starcity.
As far as I understand the Chinese situation the monopoly was a lot more natural in nature. In the Chinese situation it wasn't possible for someone who didn't like the governments control of the salt to walk a bit like Ghandi and pick up own salt from the ground.
I'm also not sure to what extend a goverment raising taxes from it's citizens (what the Chinese did) should be called "making a profit". Would you also call the US income tax "the US government making profits by exploiting comparitive advantage"? I see no reason to use that model over saying that the government raises taxes because of it using coercion.
For the US income tax example: generally speaking, (monetary) income comes from people trading with each other, and that generally wouldn't happen without comparative advantage between the two people trading. No comparative advantage => no trading => no income to tax.
I think part of the confusion is that I am NOT claiming that the people/organizations making a profit have a comparative advantage. People can totally make a profit by seizing that profit from someone else. But without comparative advantage, there's no profit to seize (relative to a world where goods never change hands). If the profit requires goods moving bidirectionally between people, then there must be an underlying comparative advantage.
Now, it's possible to find someone operating in isolation (i.e. collecting their own salt) and seize part of what they're producing. Then comparative advantage won't play a role. (Of course, that'll be hard to enforce - it's not easy to prevent people from producing things for their own consumption in secret.) The key point is that this scenario does not increase the total amount of goods produced relative to everyone operating in isolation. Comparative advantage is about changes in total production, not changes in distribution.
But without comparative advantage, there's no profit to seize (relative to a world where goods never change hands).
Just because there's no profit to seize doesn't mean that goods won't move from one person to the other if the person who wants to use the goods uses coercive force.
While I'm not certain to what extend it's true, from time to time I heard the claim that the British didn't get net profit from colonization. It's possible that they still did it because they believed it would be good for them even when it wasn't profitable.
Just because there's no profit to seize doesn't mean that goods won't move from one person to the other if the person who wants to use the goods uses coercive force.
Right, this is exactly why I talk about goods moving bidirectionally. If someone is just straight-up seizing goods by force, then there's no reason for goods to move back in the other direction. So, if the profit requires goods moving bidirectionally, then that indicates some relative advantage is involved somewhere.
You need to go to another place to loot the place and that usually involves transporting personal, weapons and equipment.
Most wars where there's no net profit but a lot of capital lost include some bidirectional flow of goods.
Baudel is criticizing Ricardo's model of "comparative advantage", which only has two agents, Home and Foreign.
https://en.wikipedia.org/wiki/Comparative_advantage#Ricardian_model
Ricardo criticizes "comparative advantage" specifically for being too simple.
Your supposed explanation of it involves inland farmers, salt miners and English merchants connecting the two. This is indeed more complicated than Ricardo and thus seems to address Baudel's supposed confusion, but it also has nothing to do with Ricardo's model of "comparative advantage".
It simply does not make sense to say that there is an "underlying comparative advantage" between the salt miners and the farmers, since they're not trading with each other, they're each just trading with the merchant.
The merchant has an "absolute advantage" in "transported salt" over the farmers. The salt miners can't offer "transported salt", since they're in the "salt-mine salt" business.
"Salt mine salt" is completely worthless to the farmers, since their farms aren't where the salt mines are.
The English merchant by the act of transport, turns worthless (to the farmers) "salt-mine salt" into valuable "transported salt".
And if the English can force a monopoly over the river, sinking every non-English salt-trader who would turn "salt-mine salt" into "transported salt", this model also involves coercion.
A mercantilist ruins the potential for "comparative advantage" by slapping on import taxes, which is also coercive.
Ricardo assumes a free market, and shows that "comparative advantage" is also specifically the gain only a free market can provide.
Just look how nice Portugal and England are to each other, seamlessly cooperating to maximize wine, cloth and minimize hours spent! Everybody gets richer without any coercion by being nice to each other. It shows that something beautiful would be lost, if England raised import taxes on Portugues wine and how it doesn't serve English interests. And that Portugal would lose by raising import taxes on English cloth, as well.
That's why classical economics is part science, part humanitarian philosophy.
Also the wiki article doesn't mention pareto or pareto-optimal or optimization. So I'm guessing you're confused what "comparative advantage" means, rather than Baudel.
I think what's unrealistic about the principle of comparative advantage, from the perspective of a historian, is its presumption that interactions will be peaceful. If one tribe has more resources, soon it will have a larger population. Once its population has expanded to the limit of its resources, it will almost certainly attempt through conquest to expand to the limit of its neighbors' resources. The idea that the weak can profit from interaction with the strong was considered and dismissed by the "father of history".
The argument johnswentworth has presented is that comparative advantage is still at work, and does not require trade or peace. Comparative advantage is what we would use to make sense of strength; it is also what we would use to describe what the weak have which is worth taking.
You can have comparison in non-peaceful terms; an Ottoman delegation to America commented that we were excellent with guns but had no grasp at all of swordsmanship (this was true, for what it was worth). Any battle inherently results in a comparison of the martial strength of the two sides. But Ricardo's basic idea was that two parties with different comparative advantages could trade peacefully to the benefit of both. Comparative advantage without peaceful trade loses the point of the idea. I suppose you could say that the Aztecs had a comparative advantage over their neighbors in capturing enemies for human sacrifice and cannibalism, but does it make sense to say that their neighbors had a comparative advantage in being captured, murdered, and eaten? If that's an advantage, I'd hate to see a disadvantage.
Removing peaceful trade may lose the point Ricardo wanted to make, but modern economics cares about as much about what point Ricardo wanted to make as modern physics cares about what point Kepler or Newton wanted to make. (The latter, after all, was deeply into numerology, and probably wanted his work to make a point about that.) Comparative advantage itself is the central concept here, and that concept is plenty useful without any peaceful trade.
So where does that concept get us, without peaceful trade?
Suppose we have a simple, two-factor model of the Hundred Years' War. The English have a comparative advantage in archers; the French have a comparative advantage in armored knights. Without peaceful trade, what non-obvious conclusion does comparative advantage lead us toward?
It was obvious, even before the concept of comparative advantage was developed, that English strategy should favor archers and French strategy should favor knights. It was obvious that both sides should attempt wherever possible to fight when circumstances favor their preferred mode of fighting and to avoid battle when circumstances are against them.
What I'm trying to say is that you can look at pretty much anything through pretty much any analytical lens; you could probably attempt to apply the lens of Biblical prophecy to the unification of Japan. Most of those views do not give meaningful insights (I admit that some promote success in humanities graduate programs, which strains the definition of meaningfulness). What insight do you see that can be gained through applying the lens of comparative advantage to a new subject?
P.S. France won.
It sounds like you're still thinking about the "comparative" part of "comparative advantage" as comparing between two people/groups of people, which isn't really the point. Lemme try another example to see if that helps.
In Coherent Decisions Imply Consistent Utilities, Eliezer uses the example of a hospital administrator (named Robert) who is budgeting the hospital's big purchases.
Let's say that Robert has a total budget of $100,000,000 and is faced with a long list of options such as these:
- $100,000 for a new dialysis machine, which will save 3 lives
- $1,000,000 for a liver for Johnny, which will save 1 life
- $10,000 to train the nurses on proper hygiene when inserting central lines, which will save an expected 100 lives
- ...
Now suppose—this is a supposition we'll need for our theorem—that Robert does not care at all about money, not even a tiny bit. Robert only cares about maximizing the total number of lives saved. Furthermore, we suppose for now that Robert cares about every human life equally.
If Robert does save as many lives as possible, given his bounded money, then Robert must behave like somebody assigning some consistent dollar value to saving a human life.
We should be able to look down the long list of options that Robert took and didn't take, and say, e.g., "Oh, Robert took all the options that saved more than 1 life per $500,000 and rejected all options that saved less than 1 life per $500,000; so Robert's behavior is consistent with his spending $500,000 per life."
Alternatively, if we can't view Robert's behavior as being coherent in this sense—if we cannot make up any dollar value of a human life, such that Robert's choices are consistent with that dollar value—then it must be possible to move around the same amount of money, in a way that saves more lives.
This is an example of comparative advantage at work.
In this case, each of the options entails different trade-offs between saving lives and saving money. Comparing e.g. the two options "$100,000 for a new dialysis machine, which will save 3 lives" vs "$1,000,000 for a liver for Johnny, which will save 1 life", the dialysis machine has a relative advantage in saving lives, while the new liver has a relative advantage in saving money. When Robert achieves pareto optimality (i.e. saves the most lives subject to some budget constraint), there will be some "price" - some trade-off between marginal dollars and lives saved. All the options with a relative-advantage-in-saving-lives better than that price will specialize in saving lives (i.e. he'll spend money on those things, thereby saving lives), and all the options with a relative-advantage-in-saving-dollars better than the price will specialize in saving dollars (i.e. he'll "spend lives" by not buying those things, thereby saving money).
Does that much make sense, at least?
I see what you're saying. I would have called that "weighing my options", but if you prefer to call it "comparative advantage" I have no problem.
I'll note that there might not be a coherent price for the optimum decision for various reasons. For example, there might be a very cost-effective idea that requires more than Robert's total budget (so he can't choose it). Alternatively, there might be ideas where the outcome is uncertain and the probability of success is not reasonably estimable, so no marginal price can be computed*.
*He could always assign a probability by the method of rectal extraction, but the computation would not be reliable.
I greatly appreciate this post because my favorite thing in the world is disposing of unnecessary assumptions. The non-coercion assumption that always seems to accompany trade examples is such a one, even aside from ridiculous in general.
On previous post about comparative advantage there was a true distinction between a trade concept and a non-trade concept.
I think there are two concdepts and not making them name collide would be proper. If you are dictator and just a thing done asap you allocate all your best workers that can be allocated to do that and disuse people that do not have a specialization that shines above the usability baseline. If you want to produce as much as possible you migth be tempted to overwork your people to have abundance of items. But in the case that overworking everyone leads to revolt, making the people that would most get angry/suffer from work not do so can be easy source of "peace points". Thus an unfair work allocation where skilled work is utilised more than what would be arrived with equalization of misery can be used. There is less total misery but it is concentrated on fewer individuals.
I think the original critism was that if we assume different conditions then on top of that we can have "voluntary" or "free" trade. But in order to have the conditions we need to have differentation which is often upheld violently against tendency to share and dissolve. Consider that if there were no toll toll on the river people could trade salt at lower prices. Blocking access makes both sides artificially rely on local resources. So a deal that is worse than uncontrolled river but better than complete separation makes sense to accept.
Braudel is probably the most impressive historian I have read. His quantitative estimates of premodern populations and crop yields are exactly the sort of foundation you’d think any understanding of history would be based upon. Yet reading his magnum opus, it became steadily clearer as the books progressed that Braudel was missing some fairly fundamental economic concepts. I couldn’t quite put my finger on what was missing until a section early in book 3:
... these deliberately simple tautologies make more sense to my mind than the so-called ‘irrefutable’ pseudo-theorem of David Ricardo (1817), whose terms are well known: that the relations between two given countries depend on the “comparative costs” obtaining in them at the point of production
Braudel, apparently, is not convinced by the principle of comparative advantage. What is his objection?
The division of labor on a world scale (or on world-economy-scale) cannot be described as a concerted agreement made between equal parties and always open to review… Unequal exchange, the origin of the inequality in the world, and, by the same token, the inequality of the world, the invariable generator of trade, are longstanding realities. In the economic poker game, some people have always held better cards than others…
It seems Braudel is under the impression that comparative advantage is only relevant in the context of “equal” exchange or “free” trade or something along those lines.
If an otherwise impressive economic historian is that deeply confused about comparative advantage, then I expect other people are similarly confused. This post is intended to clarify.
The principle of comparative advantage does not require that trade be “free” or “equal” or anything of the sort. When the Portugese or the British seized monopolies on trade with India in the early modern era, those trades were certainly not free or equal. Yet the monopolists would not have made any profit whatsoever unless there were some underlying comparative advantage.
For example, consider an oversimplified model of the salt trade. People historically needed lots of salt to preserve food, yet many inland areas lack local sources, so salt imports were necessary for survival. Transport by ship was historically orders of magnitude more efficient than overland, so a government in control of a major river could grab a monopoly on the salt trade. Since the people living inland could not live without it, the salt monopolist could charge quite high prices - a “trade” arguably not so different from threatening inland farmers with death if they did not pay up. (An exaggeration, since there were other ways to store food and overland smuggling became viable at high enough prices, but I did say it’s an oversimplified example.)
Notice that, in this example, there is a clear underlying comparative advantage: the inland farmers have a comparative disadvantage in producing salt, while the ultimate salt supplier (a salt mine or salt pan) has a comparative advantage in salt production. If the farmer could produce salt with the same opportunity cost as the salt mine/pan, then the monopolist would have no buyers. If the salt mine/pan had the same opportunity cost for obtaining salt as the farmers, then the monopolist would have no supplier. Absent some underlying comparative advantage between two places, the trade monopolist cannot make any profit.
Another example: suppose I’m a transatlantic slave trader, kidnapping people in Africa and shipping them to slave markets in the Americas. It’s easy to see how the kidnapping part might be profitable, but why was it profitable to move people across the Atlantic? Why not save the transportation costs, and work the same slaves on plantations in Africa rather than plantations in the Americas? Or why not use native American slaves entirely, rather than importing Africans? Ultimately, the profits were because the Americas had a lot lower population density - there was more land, and fewer people to work it. Thus, labor was worth more in the Americas (and that same comparative advantage drove not just the slave trade, but also immigration and automation). Without a comparative advantage, enslaving people might still have been profitable, but there would be no reason to ship them across the Atlantic.
Let’s take it a step further. This argument need not involve any trade at all.
Suppose I’m the dictator of some small archipelago. I have total ownership and control over the country’s main industries (bananas and construction), and there’s an international embargo against trade with my little country, so there’s no trade to worry about either internally or externally. Let’s say I just want to maximize construction output - although I will still need to order some banana-growing in order to keep my construction workers fed.
The question is: who and where do I order to grow bananas, and who and where do I order to build things? To maximize construction, I will want to order people with the largest comparative advantage in banana-growing to specialize in banana-growing, and I will want to order those bananas to be grown on the islands with the largest comparative advantage in banana-growing. (In fact, this is not just relevant to maximization of construction - it applies to pareto-optimal production in general.) There’s no trade; I’m just using comparative advantage to figure out how best to deploy my own resources.
Takeaway: comparative advantage is not a principle of trade, it’s a principle of optimization. Pareto-optimal production means specialization by comparative advantage.