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Qurratulain · #2 Sunday, December 17, 2006

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.