Chapter 3: Interdependence and the Gains from Trade
Chapter 3 builds on the model we developed in Chapter 2 (Production
Possibilities Frontier). The importance of the chapter is to motivate why
trade is so ubiquitous. Every day, consciously or not, we engage in trade
perhaps hundreds of times. I cannot think of anything that I consume that I
do not depend on others to provide. My coffee is from somewhere near the
equator, my orange juice starts in Florida (I guess) and somehow makes it
to my local grocery store - never mind my iPhone, my car, my clothes etc.
This is the interdependence that the book refers to.
Note that in the examples above, the trades I refer to are all organized
through markets where I pay a price for each good. And, to be honest, after
this chapter we will begin thinking about trade (exchange between buyers
and sellers) in these terms. For now, it will be easier to consider a simple
economy. Trade, as I refer to it here, simply means the exchange of goods
between two people. Let’s follow along with the example in the text.
There are 2 people (Frank the farmer and Ruby the rancher) and two goods
(potatoes and meat). Again, like the PPF model, the number of people and
the number of goods is irrelevant to the intuition of the model. This
simplifying assumption only allows us to more easily sketch out the graphs
and see the underlying intuition. Further, there is only 1 resource, they each
have 8 hours per day to work. I will also say that the incentives of each
person is to consume as much as possible - More is better.
The first thing we need to do is depict their respective PPFs. To do so we
need to figure out how many potatoes and meat they can produce. In 8
hours, Frank can produce 8 ounces of meat (each ounce requires 60 minutes
of work) or 32 ounces of potatoes (each ounce requires 15 minutes of work).
Similarly, in 8 hours Ruby can produce 24 ounces of meat (each ounce
requires 20 minutes of work) or 48 ounces of potatoes (each ounce requires
10 minutes of work). For simplicity, I am also going to assume that both
Frank and Ruby can costlessly switch between tasks so that I can depict
their PPFs as linear lines.
Here we have meat on the vertical axis and potatoes on the horizontal. As
explained above, if Frank spends all of his available time producing meat
(potatoes) he would be able to produce 8 (32) ounces. These determine the
endpoints of their PPFs. Because it is linear, I simply connect these
endpoints and call it a PPF. Do the same for Ruby.
Before we move on, let’s say that in isolation (in the absence of
trade/exchange between Frank and Ruby) they each decide to split their
time evenly. These points are depicted on the graphs above. They imply that
Frank will produce and consume 4 meat and 16 potatoes while Ruby
produces and consumes 12 meat and 24 potatoes. By the way, I am
dropping the units (ounces) for the rest of this example.
Since they are each on their PPF we know the outcome is efficient. They are
each consuming all that they are able to given their resources (8 hours).
This is the best they can do, anything outside the PPF is unobtainable.
As suggested by the title of the chapter. The question is whether Frank and
Ruby could be better off if they engaged in trade. It is not entirely obvious
that they can. Ruby is able to produce a lot more meat AND potatoes than
Frank. Why would she engage in trade?
Well, the motivation for trade does not stem from how much you can
produce. Rather, what matters is how much it costs you to produce. Let’s
define two important terms.
Absolute Advantage is the ability to produce a good with fewer inputs.
Here the only input is time and Ruby produces an ounce of meat in 20
minutes versus 60 minutes for Frank. Because we have given each person
the same amount of resources (8 hours), Absolute Advantage is easy to
determine. It just means that Ruby can produce more meat than Frank.
Here we would say that Ruby has the Absolute Advantage is both meat and
potatoes.
Comparative Advantage is the ability to produce a good at a lower
opportunity cost (OC). This is the important concept. The nice thing about
this model is that it makes OC really easy. The OC of meat is simply how
many potatoes you give up to produce the meat. Let’s run through the
example.
Recall chapter 2. The OC is the slope of the PPF - here the slope is 8/32 =
1/4. The only problem is that you need to know which good has the OC of
¼. This isn’t terribly difficult but I have always found the following method
(introduced in chapter 2) easier. The way I determined the OC in chapter 2
was to set up an ‘equation’ using the endpoints of the linear PPF.
For Frank I would say that 8 meat = 32 potatoes and I would ‘solve’:
The OC of 1 meat = 32/8 = 4 potatoes (just ‘divide’ both sides by 8) and
The OC of 1 potato = 8/32 = ¼ meat.
The OCs are always reciprocals of each other. By keeping the OC in sentence
form it is easy to keep track of.
It is worth interpreting these OCs. They mean that every time Frank decides
to produce 1 meat he must give up 4 potatoes - that is, the cost of 1 meat is
4 potatoes. This makes complete sense; an ounce of meat requires 60
minutes while an ounce of potatoes only requires 15 minutes (¼ of 60). On
the other hand, to produce 1 potato he only gives up ¼ meat.
Doing the same for Ruby you should get the following:
The OC of 1 meat = 48/24 = 2 potatoes
The OC of 1 potato = 24/48 = ½ meat
We would say that Ruby has the Comparative Advantage in producing meat.
She produces meat at a lower OC. It only costs her 2 potatoes to produce
meat while it costs Frank 4 potatoes to produce meat. Similarly, we would
say that Frank has the Comparative Advantage in producing potatoes.
Gains from Trade
The gains from trade in this model stem from specializing in one’s
comparative advantage. This is pretty intuitive, it just means that each
person should specialize in the production of the good that they produce at
lower OC.
In this example, Frank would specialize in the production of potatoes and
Ruby would specialize in the production of meat. Now, I should note that the
extent of specialization cannot be completely determined - we don’t know
their preferences. Recall that the purpose of the model is to show that Frank
and Ruby can be better off with trade - again, their incentives are to
increase their consumption. In this sense, all we need to show is that
specialization and trade can increase their consumption.
So, in the beginning we said that, in isolation, they split their time evenly.
This means that we ended up with a total (Frank plus Ruby) of 16 ounces of
meat and 40 ounces of potatoes. In order for trade to benefit both parties
here they must collectively produce more of both goods. This will make the
gains from trade unambiguous - more is better.
Following the text, I will say that Frank completely specializes in potatoes
and produces 32. Ruby shifts some of her effort towards meat and ends up
producing 18 meat and 12 potatoes. Now, this simple economy produces 18
ounces of meat and 44 ounces of potatoes.
I will continue to follow the text here and simply give you the exchange rate
between meat and potatoes - we will discuss this a bit more below. Let’s say
that they agree to exchange 5 meat for 15 potatoes - the implied price of 1
meat is 3 potatoes. This leaves Frank with 5 meat and 17 potatoes and Ruby
with 13 meat and 27 potatoes. See depiction of their PPFs below.
The point is that this specialization and trade allows them each to consume
outside their respective PPFs. Recall that prior to specialization and trade
they each consumed on their PPF (they were doing as best as they could).
Now, suddenly, they are each consuming at a point which was unobtainable.
This motivates some to think about trade as a type of technology - with the
same resources (time) we are able to consume more.
This picture suggests that each person (Frank and Ruby) are both
unambiguously better off. They each are able to consume more of both
goods than they would otherwise.
In the above we set the price of trade at 1 meat for 3 potatoes (it is
equivalent to say that the price of 1 potato is ⅓ meat). While we can’t
determine where this price will end up we can provide a range for it. First,
think about the max price that Frank will pay for meat in terms of potatoes
(since Frank specializes in potatoes he wants to know how many potatoes
each meat will cost him). For Frank, the cost of 1 meat is 4 potatoes so this
is the most he will pay. On the other hand, Ruby specializes in meat and will
be concerned with the price of potatoes in terms of meat. For Ruby the cost
of 1 potato is ½ meat - she will not pay more than this. Turning this around
would suggest 1 meat for 2 potatoes.
Thus, their OCs provide the range of prices at which they can each gain from
trade. Here 1 meat must trade for between 2 and 4 potatoes. In general,
each party to this trade would like to increase the price in terms of their
comparative advantage good. For example, Ruby would like to trade each
meat for 3.5 potatoes - each meat that she produces becomes more
valuable to her.
Another Example
There are 2 people stranded on an island. Their only resource is time (they
each have 10 hours per day). Their only needs are Coconuts and Fish.
Person A can produce 1 coconut/hour or 1 fish/hour
Person B can produce 2 coconuts/hour or 0.5 fish/hour
In the notes here I will sketch out the answer. You should be able to work
through the previous example and replicate the provided answers. If not ask
for help.
1. Sketch out their respective PPFs, put coconuts on the vertical axis.
2. Who has the Absolute Advantage in coconuts (fish)?
3. Assume that in isolation they each split their time evenly. Label this
point on each PPF. How many coconuts and fish does each person
produce and consume?
4. Who has the Comparative Advantage in coconuts (fish)? Show your
work and how you calculated their OCs here.
5. Assume that each person completely specializes in their Comparative
Advantage good. Label this point on each PPF. How many coconuts
and fish does each person produce?
6. Assume that they agree to exchange 4 fish for 8 coconuts. How many
coconuts and fish does each person now consume? Label this point on
each PPF.
You should find that person A consumes 6 fish and 8 coconuts while person
B consumes 4 fish and 12 coconuts after they engage in trade.
Applications of Comparative Advantage
Perhaps the most important application of Comparative Advantage is to
international trade. International trade implies the trade of goods and
services between countries.
Imports are goods produced abroad and consumed domestically
Exports are goods produced domestically and sold abroad
These definitions are fine for now but I would argue that they are overly
simplistic. While the US may import cotton shirts from Vietnam we have to
keep in mind that we may have exported cotton to Vietnam. This trade
basically says that the US can grow cotton more cheaply than Vietnam and
that Vietnam can make this cotton into clothes more cheaply than the US
can (of course we mean firms within these respective countries – and let’s
further ignore that we are really talking about multinational firms whose
owners and workers are distributed across countries).
For now, we will simply say that countries differ in their available resources
and this drives variation in the OC of production. Because countries vary in
their relative OCs there is a basis for trade using the concept of Comparative
Advantage.
For another example, let’s make up a simplified example comparing the US
and Japan and wheat and electronics. Given the size of our economy I
suspect that the US can produce more wheat and electronics than Japan can
(we have an Absolute Advantage in both goods). But, who do you think
produces wheat more cheaply? The US has a ton of good, arable, land while
Japan has very little. The idea is that the US has a Comparative Advantage
in growing wheat while Japan has a Comparative Advantage in electronics.
By engaging in trade with Japan we are both able to consume more. It is as
if our farmers have figured out a way to turn wheat into Sony Playstations
and TVs. This is great for US farmers and US consumers – it is not so great
for US producers of electronics as we will discuss in Chapter 9.
This is the main reason that for an economist free trade is unambiguously
good. Whether the trade is between Frank and Ruby or the US and China is
irrelevant. That said, there are certainly valid concerns with trade which we
discuss later.
How would bowed out PPFs affect Comparative Advantage?
Recall from chapter 2 that a bowed out PPF suggests that as you produce
more and more of a particular good the OC rises. The intuition is that inputs
into production are not perfectly substitutable. For this reason, we will not
observe complete specialization in international trade. Think about how the
OC relates to the price of exchange between goods.