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  #1  
Old Sunday, December 17, 2006
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Default The Theory of Comparative Advantage

Historical Overview


The theory of comparative advantage is perhaps the most important concept in international trade theory. It is also one of the most commonly misunderstood principles. There is a popular story told amongst economists that once when an economics skeptic asked Paul Samuelson (a Nobel laureate in economics) to provide a meaningful and non-trivial result from the economics discipline, Samuelson quickly responded with, "comparative advantage."

The sources of the misunderstandings are easy to identify. First, the principle of comparative advantage is clearly counter-intuitive. Many results from the formal model are contrary to simple logic. Secondly, the theory is easy to confuse with another notion about advantageous trade, known in trade theory as the theory of absolute advantage. The logic behind absolute advantage is quite intuitive. This confusion between these two concepts leads many people to think that they understand comparative advantage when in fact, what they understand is absolute advantage. Finally, the theory of comparative advantage is all too often presented only in its mathematical form. Using numerical examples or diagrammatic representations are extremely useful in demonstrating the basic results and the deeper implications of the theory. However, it is also easy to see the results mathematically, without ever understanding the basic intuition of the theory.

The early logic that free trade could be advantageous for countries was based on the concept of absolute advantages in production. Adam Smith wrote in The Wealth of Nations,

"If a foreign country can supply us with a commodity cheaper than we ourselves can make it, better buy it of them with some part of the produce of our own industry, employed in a way in which we have some advantage. " (Book IV, Section ii, 12)

The idea here is simple and intuitive. If our country can produce some set of goods at lower cost than a foreign country, and if the foreign country can produce some other set of goods at a lower cost than we can produce them, then clearly it would be best for us to trade our relatively cheaper goods for their relatively cheaper goods. In this way both countries may gain from trade.

The original idea of comparative advantage dates to the early part of the 19th century. Although the model describing the theory is commonly referred to as the "Ricardian model", the original description of the idea can be found in an Essay on the External Corn Trade by Robert Torrens in 1815. David Ricardo formalized the idea using a compelling, yet simple, numerical example in his 1817 book titled, On the Principles of Political Economy and Taxation. The idea appeared again in James Mill's Elements of Political Economy in 1821. Finally, the concept became a key feature of international political economy upon the publication of Principles of Political Economy by John Stuart Mill in 1848.


Source: Internationalecon.com
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David Ricardo's Numerical Example


Because the idea of comparative advantage is not immediately intuitive, the best way of presenting it seems to be with an explicit numerical example as provided by David Ricardo. Indeed some variation of Ricardo's example lives on in most international trade textbooks today. (See page 40-5 in this text)

In his example Ricardo imagined two countries, England and Portugal, producing two goods, cloth and wine, using labor as the sole input in production. He assumed that the productivity of labor (i.e., the quantity of output produced per worker) varied between industries and across countries. However, instead of assuming, as Adam Smith did, that England is more productive in producing one good and Portugal is more productive in the other; Ricardo assumed that Portugal was more productive in both goods. Based on Smith's intuition, then, it would seem that trade could not be advantageous, at least for England.

However, Ricardo demonstrated numerically that if England specialized in producing one of the two goods, and if Portugal produced the other, then total world output of both goods could rise! If an appropriate terms of trade (i.e., amount of one good traded for another) were then chosen, both countries could end up with more of both goods after specialization and free trade then they each had before trade. This means that England may nevertheless benefit from free trade even though it is assumed to be technologically inferior to Portugal in the production of everything,.

As it turned out, specialization in any good would not suffice to guarantee the improvement in world output. Only one of the goods would work. Ricardo showed that the specialization good in each country should be that good in which the country had a comparative advantage in production. To identify a country's comparative advantage good requires a comparison of production costs across countries. However, one does not compare the monetary costs of production or even the resource costs (labor needed per unit of output) of production. Instead one must compare the opportunity costs of producing goods across countries.

A country is said to have a comparative advantage in the production of a good (say cloth) if it can produce cloth at a lower opportunity cost than another country. The opportunity cost of cloth production is defined as the amount of wine that must be given up in order to produce one more unit of cloth. Thus England would have the comparative advantage in cloth production relative to Portugal if it must give up less wine to produce another unit of cloth than the amount of wine that Portugal would have to give up to produce another unit of cloth.

All in all, this condition is rather confusing. Suffice it to say, that it is quite possible, indeed likely, that although England may be less productive in producing both goods relative to Portugal, it will nonetheless have a comparative advantage in the production of one of the two goods. Indeed there is only one circumstance in which England would not have a comparative advantage in either good, and in this case Portugal also would not have a comparative advantage in either good. In other words, either each country has the comparative advantage in one of the two goods or neither country has a comparative advantage in anything.

Another way to define comparative advantage is by comparing productivities across industries and countries. Thus suppose, as before, that Portugal is more productive than England in the production of both cloth and wine. If Portugal is twice as productive in cloth production relative to England but three times as productive in wine, then Portugal's comparative advantage is in wine, the good in which its productivity advantage is greatest. Similarly, England's comparative advantage good is cloth, the good in which its productivity disadvantage is least. This implies that to benefit from specialization and free trade, Portugal should specialize and trade the good in which it is "most best" at producing, while England should specialize and trade the good in which it is "least worse" at producing.


Note that trade based on comparative advantage does not contradict Adam Smith's notion of advantageous trade based on absolute advantage. If as in Smith's example, England were more productive in cloth production and Portugal were more productive in wine, then by we would say that England has an absolute advantage in cloth production while Portugal has an absolute advantage in wine. If we calculated comparative advantages, then England would also have the comparative advantage in cloth and Portugal would have the comparative advantage in wine. In this case, gains from trade could be realized if both countries specialized in their comparative, and absolute, advantage goods. Advantageous trade based on comparative advantage, then, covers a larger set of circumstances while still including the case of absolute advantage and hence is a more general theory.
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The Ricardian Model - Assumptions and Results
The modern version of the Ricardian model and its results are typically presented by constructing and analyzing an economic model of an international economy. In its most simple form the model assumes two countries producing two goods using labor as the only factor of production. Goods are assumed homogeneous (identical) across firms and countries. Labor is homogeneous within a country but heterogeneous (non-identical) across countries. Goods can be transported costlessly between countries. Labor can be reallocated costlessly between industries within a country but cannot move between countries. Labor is always fully employed. Production technology differences across industries and across countries and are reflected in labor productivity parameters. The labor and goods markets are assumed to be perfectly competitive in both countries. Firms are assumed to maximize profit while consumers (workers) are assumed to maximize utility. (See page 40-2 for a more complete description)

The primary issue in the analysis of this model is what happens when each country moves from autarky (no trade) to free trade with the other country - in other words what the effects of trade are. The main things we care about are trade's effects on the prices of the goods in each country, the production levels of the goods, employment levels in each industry, the pattern of trade (who exports and who imports what), consumption levels in each country, wages and incomes, and the welfare effects both nationally and individually.

Using the model one can show that, in autarky, each country will produce some of each good. Because of the technology differences, relative prices of the two goods will differ between countries. The price of each country's comparative advantage good will be lower than the price of the same good in the other country. If one country has an absolute advantage in the production of both goods (as assumed by Ricardo) then real wages of workers (i.e., the purchasing power of wages) in that country will be higher in both industries compared to wages in the other country. In other words, workers in the technologically advanced country would enjoy a higher standard of living than in the technologically inferior country. The reason for this is that wages are based on productivity, thus in the country that is more productive, workers get higher wages.

The next step in the analysis is to assume that trade between countries is suddenly liberalized and made free. The initial differences in relative prices of the goods between countries in autarky will stimulate trade between the countries. Since the differences in prices arise directly out of differences in technology between countries, it is the differences in technology that cause trade in the model. Profit-seeking firms in each country's comparative advantage industry would recognize that the price of their good is higher in the other country. Since transportation costs are zero, more profit can be made through export than with sales domestically. Thus each country would export the good in which they have a comparative advantage. Trade flows would increase until the price of each good is equal across countries. In the end, the price of each country's export good (its comparative advantage good) will rise and the price of its import good (its comparative disadvantage good) will fall.

The higher price received for each country's comparative advantage good would lead each country to specialize in that good. To accomplish this, labor would have to move from the comparative disadvantaged industry into the comparative advantage industry. This implies that one industry goes out of business in each country. However, because the model assumes full employment and costless mobility of labor, all of these workers are immediately gainfully employed in the other industry.

One striking result here is that even when one country is technologically superior to the other in both industries, one of these industries would go out of business when opening to free trade. Thus, technological superiority is not enough to guarantee continued production of a good in free trade. A country must have a comparative advantage in production of a good, rather than an absolute advantage, to guarantee continued production in free trade. From the perspective of a less developed country, the developed countries' superior technology need not imply that LDC industries cannot compete in international markets.


Another striking result is that the technologically superior country's comparative advantage industry survives while the same industry disappears in the other country, even though the workers in the other country's industry has lower wages. In other words, low wages in another country in a particular industry is not sufficient information to know which country's industry would perish under free trade. From the perspective of a developed country, freer trade may not result in a domestic industry's decline just because the foreign firms pay their workers lower wages.

The movement to free trade generates an improvement in welfare in both countries both individually and nationally. Specialization and trade will increase the set of consumption possibilities, compared with autarky, and will make possible an increase in consumption of both goods, nationally. These aggregate gains are often described as improvements in production and consumption efficiency. Free trade raises aggregate world production efficiency because more of both goods are likely to be produced with the same number of workers. Free trade also improves aggregate consumption efficiency, which implies that consumers have a more pleasing set of choices and prices available to them.

Real wages (and incomes) of individual workers are also shown to rise in both countries. Thus, every worker can consume more of both goods in free trade compared with autarky. In short, everybody benefits from free trade in both countries. In the Ricardian model trade is truly a win-win situation.
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Defending Against Skeptics:
The True Meaning and Intuition of the Theory of Comparative Advantage


Many people who learn about the theory of comparative advantage quickly convince themselves that its ability to describe the real world is extremely limited, if not non-existent. Although the results follow logically from the assumptions, the assumptions are easily assailed as unrealistic. For example, the model assumes only two countries producing two goods using just one factor of production. There is no capital or land or other resources needed for production. The real world, on the other hand, consists of many countries producing many goods using many factors of production. Each market is assumed to be perfectly competitive, when in reality there are many industries in which firms have market power. Labor productivity is assumed fixed, when in actuality it changes over time, perhaps based on past production levels. Full employment is assumed, when clearly workers cannot be immediately and costlessly moved to other industries. Also, all workers are assumed identical. This means that when a worker is moved from one industry to another, he or she is immediately as productive as every other worker who was previously employed there. Finally, the model assumes that technology differences are the only differences that exist between the countries.

With so many unrealistic assumptions it is difficult for some people to accept the conclusions of the model with any confidence, especially when so many of the results are counterintuitive. Indeed one of the most difficult aspects of economic analysis is how to interpret the conclusions of models. Models are, by their nature, simplifications of the real world and thus all economic models contain unrealistic assumptions. Therefore, to dismiss the results of economic analysis on the basis of unrealistic assumptions means that one must dismiss all insights contained within the entire economics discipline. Surely, this is not practical or realistic. Economic models in general and the Ricardian model in particular do contain insights that most likely carry over to the more complex real world. The following story is meant to explain some of the insights within the theory of comparative advantage by placing the model into a more familiar setting.
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A Gardening Story

Suppose it is early spring and it is time to prepare the family backyard garden for the first planting of the year. The father in the household sets aside one Sunday afternoon to do the job but hopes to complete the job as quickly as possible. Preparation of the garden requires the following tasks. First, the soil must be turned over and broken up using the roto-tiller, then the soil must be raked and smoothed. Finally, seeds must be planted or sowed.

This year the father's seven-year-old son is anxious to help. The question at hand is whether the son should be allowed to help if one's only objective is to complete the task in the shortest amount of time possible.

At first thought, the father is reluctant to accept help. Clearly each task would take the father less time to complete than the time it would take the son. In other words, the father can perform each task more efficiently than the seven-year-old son. The father estimates that it will take him three hours to prepare the garden if he works alone, as shown in the following table.

Task -----------Completion Time (hours)
Roto-Tilling ----------1.0
Raking ----------1.0
Planting ---------1.0
Total -------------3.0



On second thought, the father decides to let his son help according to the following procedure. First the father begins the roto-tilling. Once he has completed half of the garden, the son begins raking the roto-tilled section while the father finishes roto-tilling the rest of the garden plot. After the father finishes roto-tilling he begins planting seeds in the section the son has already raked. Suppose the son rakes slower than the father plants, and that the father completes the sowing process just as the son finishes raking. Note this implies that raking takes the son almost 2 hours compared to one hour for the father. However, because the son's work is done simultaneously with the father's work, it does not add to the total time for the project. Under this plan the time needed to complete the tasks in shown in the following table.

Task --------Completion Time (hours)
Roto-Tilling ----------1.0
Raking & Planting ----1.0
Total-------- 2.0



Notice that the total time needed to prepare the garden has fallen from 3 hours to 2 hours. The garden is prepared in less time with the son's help than it could have been done independently by the father. In other words, it makes sense to employ the son in (garden) production even though the son is less efficient than the dad in every one of the three required tasks. Overall efficiency is enhanced when both resources (the father and son) are fully employed.

This arrangement also clearly benefits both the father and son. The father completes the task in less time and thus winds up with some additional leisure time which the father and son can enjoy together. The son also benefits because he has contributed his skills to a productive activity and will enjoy a sense of accomplishment. Thus both parties benefit from the arrangement.

However, it is important to allocate the tasks correctly between the father and the son. Suppose the father allowed his son to do the roto-tilling instead. In this case the time needed for each task might look as follows.

Task ---------Completion Time (hours)
Roto-Tilling------------ 4.0
Raking ---------1.0
Planting ---------1.0
Total -----------6.0



The time needed for roto-tilling has now jumped to 4 hours because we have included the time spent traveling to and from the hospital and the time spent in the emergency room! Once the father and son return, the father must complete the remaining tasks on his own. Overall efficiency declines in this case compared to the father acting alone.

This highlights the importance of specializing in production of the task in which you have a comparative advantage. Even though the father can complete all three tasks quicker than his son, his relative advantage in roto-tilling greatly exceeds his advantage in raking and planting. One might say that the father is most-best at roto-tilling while he is least-best at raking and planting. On the other hand, the son is least-worse at raking and planting but most-worse at roto-tilling. Finally, because of the sequential nature of the tasks, the son can remain fully employed only if he works on the middle task, namely raking.
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Interpreting the Theory of Comparative Advantage

The garden story offers an intuitive explanation for the theory of comparative advantage and also provides a useful way of interpreting the model results. The usual way of stating the Ricardian model results is to say that countries will specialize in their comparative advantage good and trade them to the other country such that everyone in both countries benefit. Stated this way it is easy to imagine how it would not hold true in the complex real world.

A better way to state the results is as follows. The Ricardian model shows that if we want to maximize total output in the world then,

first, fully employ all resources worldwide;

second, allocate those resources within countries to each country's comparative advantage industries;

and third, allow the countries to trade freely thereafter.

In this way we might raise the wellbeing of all individuals despite differences in relative productivities. In this description, we do not predict that a result will carry over to the complex real world. Instead we carry the logic of comparative advantage to the real world and ask how things would have to look to achieve a certain result (maximum output and benefits). In the end we should not say that the model of comparative advantage tells us anything about what will happen when two countries begin to trade; instead we should say that the theory tells us some things that can happen.
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