Comparative advantage and when to blow up your island

One important thing I'd include: while adding more people (i.e. more than two) creates the possibility of individuals becoming worse off, it also very quickly removes most of the incentives for strategic negotiation behavior (i.e. hiding information, faking skill, threatening to blow up islands, etc). Even with just a dozen people/islands, multiple people have to form a cartel in order to achieve high price for a particular good, and it only takes one defector to break a cartel.

I believe this is a very important topic, so thank you for addressing it! But making a focus on comparative (as opposed to absolute) advantage at the beginning seems to me like distraction from the main problem, which occurs regardless of whether the advantage is absolute or not.

It is a separate (and very important) fact that mutually beneficial trade can occur in situations where one party doesn't have an absolute advantage at anything. (At least, if we ignore the transaction costs.) Without economical education, people are often unaware of this, but if you take an interest in economics, this will be one of the first things they will teach you.

But another fact is that if we have a situation (or possibility) of mutually beneficial trade -- regardless of how specifically that happened -- and the traded resources are (sufficiently) continuous, then there is actually a whole interval of possible mutually beneficial trades (ZOPA), and it matters a lot at which specific point the trade happens. It matters so much that it actually makes sense to put the entire trade at risk in order to achieve a more profitable point (which is still profitable for your trade partner!). For some reason, this fact is taught much less frequently (at least it seems so to me).

If you understand the concept of relative advantage, but don't understand the concept of ZOPA (and other people know this), what happens is that you get many trade offers that all give you epsilon extra benefit, and at the end of the day you are confused: "If I am participating in so many mutually beneficial trades, why am I not so rich?" Yeah, the technical answer is that your profit margin is low; but the important question is: why?

Even worse, low profit margin may seem like a natural consequence of trading at an efficient market (which again is a concept you do learn in Econ 101). So we get a "valley of bad economical literacy" where you believe that your behavior is optimal, and you even have seemingly solid scientific arguments to prove it, but in fact you are leaving a lot of money on the table. That's because you are an "educated stupid" and whenever you meet a market imperfection [LW · GW], you allow someone else to pick up the banknote from the street. (For the purposes of this article, the market imperfection is that there are two different islands, instead of thousand similar ones.)

I wonder what other similarly important concepts I am unaware of...

EDIT:

The way I used to describe this topic is: Imagine that if you work alone, you can make $100 a day. There is another person who can also make $100 a day working alone. But if you work together, you can make $300 a day. How would you split the money?

Now, the second scenario: If you work alone, you can make $100 a day. Another person approaches you and offers to work together, because that would be more productive; at the end of the day the person will give you $120. Would you accept the offer? You don't know how much money the other person can make alone, and how much money they will keep if you work together; they refuse to tell you. Do you actually need this information in order to make a rational decision? Obviously, $120 is more than $100, therefore...

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?

One spot on Wikipedia says:

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.

Curated. I've read several explanations of comparative advantage over the years, and I found this to be among the most clear and accessible ones that I've read. I also liked the juxtaposition with ZOPA. I found Villiam's followup comment [LW · GW] additionally helpful for solidifying how a couple different economics principles fit together.

The author discusses impossibly perverse behaviors such as blowing up one's island, but forgets to mention the most common anti-competitive practices such as dumping and product tying.

For example, the other guy would price coconuts and bananas well below the Zone of Possible Agreement (dumping), and you would be so glad to buy everything from them -- destroying your industry and increasing his comparative advantage.

Of course, he is not altruist, so, when you are completely dependent, he will raise his prices above the ZOPA -- and you have no option because it would cost you a lot (time and effort) to rebuild your industry and regain your comparative advantage.

If you try to produce bananas, he drops the price of bananas, making profit from coconuts; if you try to produce coconuts, he drops the price of coconuts, making profit from bananas.

When you start to recover one industry (say, coconuts) he could force you to buy coconuts if you want to buy bananas (tying).

And if you ever managed to rebuild both industries, all he had to do was to bring his prices below ZOPA -- and you would have to decide if you still believe in free and unregulated markets, or avoid the same mistake, imposing tariffs and regulation.

---

You can observe this kind of imbalance in the real world: developing countries export iron for $100 per metric ton ($0.05/pound) and buy high value-added products (phones, tablets, computers) for $500/unit.

Developed countries use the profit they make from high value-added products and services to subsidize their farmers, pushing the price down. For instance, wheat costs $188.75/ton ($0.10 per pound).

Without subsidies, the farming industry would be decimated from rich countries, and prices would go up. Of course, there is no such thing as "free market".

Markets need regulation to prevent anticompetitive behavior.

There's no simple simple math to decide what point in the ZOPA we settle on.

Actually, you could model this as a bargaining problem. The only issue that the basic theory models only one resource that is to be distributed among two people, whereas now we have two (coconuts and bananas). This means it requires both of us to be honest about our preferences for how we weight bananas vs coconuts. Given that, bargaining theory requires that we define

A feasibility set $F$, a closed subset of $R^2$ that is often assumed to be convex, the elements of which are interpreted as agreements. $F$ is often assumed to be convex because, for any two feasible outcomes, a convex combination (a weighted average) of them is typically also feasible.

A disagreement, or threat, point $d=(d_1,d_2)$ , where $d_1$ and $d_2$ are the respective payoffs to player 1 and player 2, which they are guaranteed to receive if they cannot come to a mutual agreement.

The disagreement point $(d_1,d_2)$ equals the pair of {coconut plus banana utility for (me,you) according to our honest preferences} we get when we don't trade. The feasibility set consists of all possible pairs of of {coconut plus banana utility for (me,you) according to our honest preferences} when we trade according to any one exchange rate.^[1] So point in the ZOPA corresponds to one point in the space.^[2] Given this, there's a unique mathematical solution that follows from some basic properties.

If both parties accept this, this would solve a part of the problem. Not all, since we are still incentivized to lie about our preferences.

What is the development of this that accounts for the different style of transactions, and for risk?

• Before trade, X minutes yields a banana or a coconut, which allows for keeping marginal gains. In the trade scenario, this is replaced with a lump sum payment at the end of the day. It seems like we should weigh an all-or-nothing transaction differently then incrementally adding bananas.
• Following on this, the risks are different. There's not much in the way of perverse behavior you will encounter working for yourself. Further, even outside of perverse behavior you will now absorb regular risks that affect the trade partner and their island. Sprained ankle; outbreak of rats; hurricane hits them but not you.

The ZOPA issue you raise actually disappears when the trade involves a lot of players, not only two.

Let's say we have N players. The first consequence would be the existence of a unique price. A lot of mechanisms can lead to a unique price, you could spy on your neighbors to see if they get a better deal than you do, or you could just have a price in mind which gets updated each time you get a deal or you don't - If I get a deal, that's suspicious, my price wasn't good enough, I'll update it. If I don't, I was too greedy, I'll update it - In the end, everyone will use the same price.

At this point, everyone will specialize in one good (banana or coconut) based on whether each one values banana/coconut more or less than the market does.

The ZOPA is therefore the ZOPA between the worst banana gatherer and the worst coconut gatherer. The bigger N, the smaller the ZOPA, therefore the smaller the need for perverse behaviors.

There's the other externality of becoming dependent on the bridge existing. Right now supply chains that were working well a year ago collapsed as COVID-19 lead to borders being closed. 

How interesting! And what happens when you introduce naturally fluctuating harvests? It seems that the dweller of the unlucky island has to re-negotiate to progressively worse conditions?

Thinking about this if the diffference in gathering rates is due to gathering skill then learning the gathering technique of the more skilled gatherer would have equal impact to trade as blowing up your island.

If the difference is not learnable and is due to soil and such one would think that the poor island resident would be tempted to relocate to the rich island. Such relocation could go over peacefully or it might cause tensions and border enforcing. But if it goes to enforcement it could go to violence and even threat of violence could be a form of coersion. So already in "We are in our respective islands" we are already in the realm of coersion.

I think another point to keep in mind when thinking of comparative advantage is that it is clearly a necessary condition for trade (or at least seems obvious to me that it is) but not clearly a sufficient condition.

Even in this two good model it seems that one must accept there is an implied third good, everything else (leisure, sleep, something else?) so the analysis of the two goods is a partial equilibrium analysis. If the margins are getting changed there then the general equilibrium has now been disturbed. That will then feed back into the two good relationships.

I think one of the questions then is just what margins or constrains are being relaxed when looking to trade based on the comparative advantage.

For instance, lets assume that the two islands specialize in either coconuts or bananas and then trade at the 1:1 exchange. Production and consumption has not changed. Since they clearly had more minutes in the day to increase output on their own consuming 10 bananas and coconuts a week was optimal. If that level of consumption is not changed due to trade (generally assumed to be the case but lets ask) what happens with the time no longer needed for production?

If the additional available time is now just boredom I would think trade becomes a bit of an annoyance and trade is curtailed. If that is true on one side but on the other they other things they can do with the time a different form of friction emerges, perhaps one side claiming the other is dumping or protectionist.

Concealing information. You are smart. After the bridge appears, you quality realize I might spy on you, and this would harm your negotiation position.

realizing does not have the nature of quality, I suspect it's nature of quickly however is more fitting. Trade these words or my island will blow-up.

What irks me a little is that work is being allocated to be done by people who are bad at that job. If people who were good at the picking did all the picking collecitvely between the two of them there would be only 300 minutes of work. In the specialization arrangement there is a total of 700 minutes of work. I do wonder whether there is any way of finding an activity that takes between 300/2=150 minutes and 600 minutes to make up for the increased workload of the trading partner (say massage them).

On particular it seems weird that the bananas not being picked on the efficient island are then picked on the inefficient island for 3 times as long. It is also strange that one benefits from poor conditions elsewhere to improve their own situation. It also takes incentive away form alleviating the others poor conditions and maybe even have more trade partners with poor conditions or comparative advantages dissimilar to yourself.

In section IV Zopa, this text is repeated twice:

Of course, I’d prefer to pay you fewer bananas! So I’d prefer a rate to the left end of this range. Conversely, it takes you twice as long to make banana as a coconut. You’d be thrilled if I paid you 4 bananas per coconut, but you’d never accept less than 1/2 a banana for one coconut.