Summary: A toy economic model of trading coconuts and bananas demonstrates the idea of comparative advantage. This leaves a range of possible coconut / banana exchange rates. It’s “rational” to do seemingly crazy things to move around the rate within that range.

Economists say that free trade is good because of comparative advantage. But what is “comparative advantage”, and why do we want it? Wikipedia says:

“agents have a comparative advantage over others in producing a particular good if they can produce that good at a lower relative opportunity cost or autarky price”

I’m sure this is helpful to those with the meaning of “autarky” at their fingertips. For the rest of us, an example: Say you live alone on an island.

Each week you gather and eat 10 coconuts and 10 bananas. It takes you five minutes to gather a coconut, and 10 minutes for a banana. Thus, you work 150 minutes per week.

You Need Time to gather one Time You Spend Coconuts 10 5 minutes 50 minutes Bananas 10 10 minutes 100 minutes Total: 150 minutes

Oh, by the way: I live on a nearby island. My dietary needs are the same as yours, but unlike you I’m terrible at everything.

I Need Time to gather one Time I Spend Coconuts 10 60 minutes 600 minutes Bananas 10 30 minutes 300 minutes Total: 900 minutes

Since I’m incompetent, I need to work a lot more than you — six times as much.

Thus, we live our lives until one day a bridge appears between the islands. We are both totally committed to peace. We will not coerce each other, but are otherwise completely selfish. What will happen?

Intuitively, you value bananas more, while I value coconuts more. Thus, it would be natural to exchange my bananas for your coconuts. We agree as follows: Each week, you gather 20 coconuts, and I gather 20 bananas. Then, I trade 10 of my bananas for 10 your coconuts. It’s easy to check that this will make both of us better off.

You Gather Time to gather one Time You Spend Coconuts 20 5 minutes 100 minutes Bananas 0 10 minutes 0 minutes Total: 100 minutes I Gather Time to gather one Time I Spend Coconuts 0 60 minutes 0 minutes Bananas 20 30 minutes 600 Total: 600 minutes

Even though you’re better than me at everything, trading saved us both 1/3 of our effort.

The phrase “comparative advantage” was invented for situations like this: You have an “advantage” at doing everything. But I have a comparative at bananas, because my ratio (banana time) / (coconut time) is lower.

This is why economists like free trade. If different producers have different relative abilities, everyone can benefit from specializing. This is true even if one producer is better at everything.

The real world, of course, is more complex. For example:

We might measure the cost to transport stuff

Coconuts might take longer to find as we gather more of them.

There might be other people on other islands.

We might also gather mangos.

More sophisticated models can deal with these complications with basically the same conclusion.

But even in this toy model, I skipped an important step. How did we decide to trade 10 coconuts for 10 bananas? I might say: “I’ll trade 7 bananas for 10 of coconuts. Take it or leave it!”

Of course, this would be great for me. But it’s easy to check that this is better for you than no trade at all.

You Gather Time to gather one Time You Spend Coconuts 20 5 minutes 100 minutes Bananas 3 10 minutes 30 minutes Total: 130 minutes I Gather Time to gather one Time I Spend Coconuts 0 60 minutes 0 minutes Bananas 17 30 minutes 510 Total: 510 minutes

Now, what possible exchange rates could we arrive at? I’d be thrilled to pay you nearly zero bananas for each coconut. On the other hand, it takes me twice as long to make a coconut as a banana. I’d never agree to pay you three bananas per coconut — it would be “cheaper” for me to just make the coconuts myself.

Thus, I benefit from any trade where I pay you between 0 and 2 bananas for one coconut. These are the only trades I could ever agree to.

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.

Thus, you benefit from any trade where I give you more than 1/2 a banana for a coconut.

You’d like me to pay you as many bananas as possible. So you’d prefer a rate as far to the right as possible.

Now, the big question is: What rate do we agree on? Simple economics does not tell us the answer! In principle, our negotiations could arrive at an “exchange rate” of anywhere between .5 and 2 of your coconuts for 1 of my bananas.

This range of (.5 to 2) is the Zone of Possible Agreement (ZOPA) in negotiation theory.

What this simple logic doesn’t dictate is what point in the ZOPA we eventually agree on. This can lead to strange and perverse behaviors.

[Walking away] Since we are nonviolent, the only “threat” is to refuse to trade. If you know I am “rational” and won’t refuse a beneficial deal, you can be “irrational” and refuse to trade unless we do so at the end of the range that’s favorable to you. Thus, your “irrational” behavior gives you a better outcome than my “rational” behavior.

[Gaining information] Before our first meeting, I construct a telescope and spy on you. When we meet, I claim: “I’ve observed that it takes you 2x as long to make a banana as a coconut. Bananas sure are hard, aren’t they? It actually takes me 1.95x as long to make a banana as a coconut. Because I like you, I’m willing to trade at a rate of .512=1/1.95 bananas per coconut. This does nothing for me, but you have a kind face, and I want to help you. I’m very generous, I know!”

[Concealing information] You are smart. As soon as you hear the bridge is going to appear, you realize that I might spy on you, and that this would hurt your negotiating position. Thus, you construct a privacy wall around your island so I can’t see you.

[Faking skills] You’re a hard-ass. You will walk away unless I agree to an exchange on your end. I’ve tried walking away, but you just wait me out. I always blink before you, and we both know it. What can I do? For a weeks, I secretly gather coconuts in the night. The next time we meet, I bring a huge pile of coconuts. I say “I’ve been practicing, and now it only takes me 1.5x as long to make a coconut as a banana. I know you’re a badass and you want the sweet end of the ZOPA. I admit I can’t beat you, but the ZOPA has shifted.” If you believe me, you need to offer a better deal.

[Blowing up my island] You’re a hard-ass. I only get .501 coconuts for 1 banana. I’ve tried walking away, but we both know you will out-wait me. Because we are non-violent, I can’t coerce you. However, there’s nothing wrong with hurting myself, right? I construct a machine that monitors inter-island commerce. If there is ever a trade that is not 1 coconut for 1 banana, the machine activates a bomb, my island sinks into the ocean forever, and I die. If I try to disable the machine, the bomb activates, my island sinks into the ocean forever, and I die. Even though you don’t care about me, you don’t want me to die because then you’d have to gather your own bananas. When we next meet I say “OK. I can’t out bad-ass you. However, because of this machine, it will forever be against my interest to agree to a non-even trade. There’s no point in you waiting me out now, since I don’t want to sink into the ocean.”