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Comparative Advantage Handout

David Ricardo extended Adam Smith's loose argument about the gains from specialization, using arithmetic to make the logic explicit, and applying it to international trade and not just to the baker trading with the tailor. Let's use Ricardo’s model, a barter economy (that is, no “money”) with 2 countries, 2 goods and 1 factor of production. (Prof. Anderson' trade class develops a more general with 2 factors of production; the resulting 2 x 2 x 2 has 8 moving pieces.) We still learn a lot from a 2 x 2 x 1 model.

Goods: two, " wine" and " cloth" (in "casks" and "bolts")
Countries: two, " England" and "Portugal"
Factors of production: one, " labor" of which each country has 10 units

In order to "solve" the model we need to specify both supply and demand.

Supply: We assume a linear production function: output is directly proportion to labor.
Demand: We assume goods are perfect complements, with equal quantities consumed.

We therefore assume that there are no diminishing returns in production. Again, the qualitative results are the same in more complicated models that permit tradeoffs in both production and in consumption.

Details: Without loss of generality, I use the following arithmetically convenient technologies.

Wine Cloth
England 4 6
Portugal 8 2

Let us begin with a state of autarky: the year is 1587 and the Spanish Armada takes a dim view of British merchant ships in the vicinity of Iberia, and vice-versa. Since the quantity consumed of each good must be the same, we get the following:

Wine Cloth
England: 4 6 p=2/3
  labor 6 4
  output 24 24
  consumption 24 24
===============

↔ autarky

=============

↔ autarky

Portugal: 8 2 p=4
  labor 2 8
  output 16 16
  consumption 16 16

England is more productive than Portugal in cloth production, but fares less well in wine production. Overall, however, their technology gives them a higher standard of living: 24 units of each good instead of 16. Prices also differ systematically: given the opportunity cost of labor, 1.5 casks of wine buys 1 bolt of cloth. However, cloth is more expensive in Portugal – it takes 4 casks to buy 1 bolt of cloth.

Now comes 1588 and the Spanish Armada is no longer a factor. Merchant ships prepare to sail from Liverpool. But what should they carry? Well, wine is cheap in Portugal, so they load up on cloth, and on the return trip fill their holds with wine. Of course this affects local markets, and in due course labor pours out of wine production in England, in the face of “unfair” foreign competition. Why “unfair”? – Portugal is poorer, so their labor is “cheap,” never mind the superior quality of their wine. The Portuguese in turn complain of British imperialism.

That’s politics. We want to look at the economics. What happens? We get labor shifting each direction and goods flowing; that should continue until no further movement is possible, which would be the case if one country is fully specialized in a single good.

Wine Cloth
England 4 6 p=2
  labor 0 10
  output 0 60
  trade +40 -20
  consumption 40 40
↔ trade
Portugal 8 2 p=2
  labor 8 2
  output 64 4
  trade -40 +20
  consumption 24 24

This is one potential solution – the result is not unique but depends on the details of the adjustment mechanism. Reflecting market pressures, we would expect a price between the starting prices, an increase in global production, and a splitting of those gains. That's what happens; both benefit from specialization.

But the story is stronger; it is true even if England is more productive than Portugal in both goods, so that it has an absolute advantage. To see this let's make Portugal really poor, reducing productivity by half.

Wine Cloth
England 4 6
Portugal 4 1

Now in autarky we would have the following, with prices as before:

Wine Cloth
England 4 6 p=2/3
  labor 6 4
  output 24 24
  consumption 24 24
============= ============== ↔ autarky
Portugal 4 1 p=4
  labor 2 8
  output 8 8
  consumption 8 8

If we move to trade we can have the following final result:

Wine Cloth
England 4 6 p=1.6
  labor 2 8
  output 8 48
  trade +25 -15
  consumption 33 33
↔ trade
Portugal 4 1 p=1.6
  labor 10 0
  output 40 0
  trade -25 +15
  consumption 15 15

Our demand condition is satisfied—equal amounts of both goods in each country—and our price condition is met: the price of cloth is higher in England and lower in Portugal. Most important, incomes are still higher in both countries. Indeed, with these numbers income is 20% higher in England and almost double in Portugal. All workers in both countries ultimately benefit from trade. They may complain in the short run, but eventually trade benefits the entire populace.

In sum, the Law of Comparative Advantage states you should:

• specialize in that at which you're comparatively better and

• trade on that basis and that thereby

• both parties benefit.

Extensions:

The impetus for change comes from imports, not exports. It is imports that instill greater competition and drive down prices and enable the reallocation of resources. Exports are only a means to that end, and are not in themselves desirable. After all, why produce goods if you can’t consume them – that’s what happens if a country runs a trade surplus.

K&W look at a Chinese example, but it’s artificial. Instead think about call center services. Many of these are low skill jobs, processing an order or answering simple questions. India or the Philippines have lots of English speakers who face low wages whatever they do, a clear (potential) comparative advantage. The telecommunications hardware and software and management systems that enable such trade are a different story. The US, the EU and Japan earn a healthy income exporting those.

Our model suggests that anything that interferes with trade hurts everyone. Adding politics leads to a puzzle. While they ultimately benefit, on "day one" vineyard workers in England and textile workers in Portugal see their accustomed trades vanish. They naturally tend to fight this, as do British vineyard owners and Portuguese textile magnates, thus offering politicians both votes and money. Historically free trade has been central to prosperity. Indeed, the US economy is prosperous in part because our domestic market constitutes the largest free trade area in the world, cemented in place by Article 1 Section 8 of the US Constitution.

The political puzzle is why protectionist forces don't uniformly prevail on the international front. That is a fascinating story that requires combining economic and political analysis with history. Part of the answer is that leadership matters, and in the past enough politicians (presidents and senators, but not house members) sought successfully to further the larger public interest over narrow, short-term, more local ones. Fortunately that has also been true in many other countries, and a network of international institutions – initially GATT (the General Agreement on Tariffs and Trade) and today the successor WTO (World Trade Organization) – seek to keep the world from retrogressing to the protectionism that prevailed between WWI and WWII. Nevertheless, even if other countries are protectionist, we benefit from unilaterally lowering barriers to trade. The primary losers from protectionist policies are the citizens of the countries doing the protection.

Finally, let us return to pure theory. First, there are non-Ricardian models of trade. We implicitly assumed perfect competition; that requires goods to be homogenous rather than differentiated. But in the real world much of trade is of such differentiated products; Europe both exports and imports cars. Models that incorporate that still show that trade is beneficial. Paul Krugman wrote the key early papers in this area.

Analyzing trade when there are externalities such as polluting activities or exporters with monopoly power is necessary. In such cases, with sufficient cleverness economists can write down a model that will generate almost any result, including that trade is harmful. Such extreme models do not mesh well with real world observations. But as is true in general in economics, market imperfections create room in theory for policy to improve welfare. In such models free trade is never optimal but is nevertheless beneficial. Paul Krugman was also a central figure in developing this literature. In the process he revived the long dormant field of economic geography.

Work both in political economy and in empirical trade theory, however, lead toward the conclusion that in the real world free trade is best. There is irony here: while Jagdish Bhagwati and Paul Krugman became famous within the economics profession for demonstrating the many ways in which market failures (or  markets less than perfectly competitive) lead to distortions that could be in theory improved through policy, both are classic liberals in the British sense (in US political discourse, old-school economic conservatives). While both criticize specific policies, they have on the whole served as eloquent, vocal advocates of less restricted trade.

Empirics

There is a large empirical literature examining the relative cost of capital and labor (or other inputs) and comparing them to trade patterns. One expected outcome from the Ricardian story above is that countries should either export or import, as in large economies diminishing returns and so on are likely less important so incomplete specialization should likewise be less important. However, if we look at US trade, one of our largest exports is of motor vehicles. They are also one of our largest imports. We find the same when we look at vehicle parts & components.

One motivation is product differentiation. BMW’s South Carolina plant is the only place world-wide that makes the X-series crossovers. In contrast, they don’t make sedans (except for the Z4 convertible sports car). Some 70% of BMW Spartanburg’s output is exported – anyone in Germany driving an X-series is driving an import. The logic is that assembly and the related locally-based elements of the supply chain benefit from economies of scale. For a variety of reasons (such as hedging foreign exchange risk), BMW and other producers scatter plants that turn out global products across multiple countries.

A variant is vertical specialization: Korean firms make the screens for the iPhone, others make the radio chip that sends/receives signals to cell towers, others make the antenna, and so on. In practice that means that individual modules of many assembled goods cross borders multiple times. (Some automotive components cross the US-Mexican border 8 times!) Such specialized factories can be in a location for all sorts of random reasons, at least from a Ricardian perspective. At one time such trade was minor. That appears to no longer be the case.

Michael Smitka © 2017