Comparative advantage
Comparative advantage in an economic model is the advantage over others in producing a particular good. A good can be produced at a lower relative opportunity cost or autarky price, i.e. at a lower relative marginal cost prior to trade. Comparative advantage describes the economic reality of the gains from trade for individuals, firms, or nations, which arise from differences in their factor endowments or technological progress.
David Ricardo developed the classical theory of comparative advantage in 1817 to explain why countries engage in international trade even when one country's workers are more efficient at producing every single good than workers in other countries. He demonstrated that if two countries capable of producing two commodities engage in the free market, then each country will increase its overall consumption by exporting the good for which it has a comparative advantage while importing the other good, provided that there exist differences in labor productivity between both countries. Widely regarded as one of the most powerful yet counter-intuitive insights in economics, Ricardo's theory implies that comparative advantage rather than absolute advantage is responsible for much of international trade.
Classical theory and David Ricardo's formulation
first alluded to the concept of absolute advantage as the basis for international trade in 1776, in The Wealth of Nations:Writing two decades after Smith in 1808, Robert Torrens articulated a preliminary definition of comparative advantage as the loss from the closing of trade:
In 1814 the anonymously published pamphlet Considerations on the Importation of Foreign Corn featured the earliest recorded formulation of the concept of comparative advantage. Torrens would later publish his work External Corn Trade in 1815 acknowledging this pamphlet author's priority.
In 1817, David Ricardo published what has since become known as the theory of comparative advantage in his book On the Principles of Political Economy and Taxation.
Ricardo's example
In a famous example, Ricardo considers a world economy consisting of two countries, Portugal and England, each producing two goods of identical quality. In Portugal, the a priori more efficient country, it is possible to produce wine and cloth with less labor than it would take to produce the same quantities in England. However, the relative costs or ranking of cost of producing those two goods differ between the countries.| Cloth | Wine | Total | |
| England | 100 | 120 | 220 |
| Portugal | 90 | 80 | 170 |
In this illustration, England could commit 100 hours of labor to produce one unit of cloth, or produce units of wine. Meanwhile, in comparison, Portugal could commit 100 hours of labor to produce units of cloth, or produce units of wine. Portugal possesses an absolute advantage in producing both cloth and wine due to more produced per hour. If the capital and labour were mobile, both wine and cloth should be made in Portugal, with the capital and labour of England removed there. If they were not mobile, as Ricardo believed them to be generally, then England's comparative advantage in producing cloth means that it has an incentive to produce more of that good which is relatively cheaper for them to produce than the other—assuming they have an advantageous opportunity to trade in the marketplace for the other more difficult to produce good.
| Cloth | Wine | Saved | |
| England | 200 | – | 20 |
| Portugal | – | 160 | 10 |
In the absence of trade, England requires 220 hours of work to both produce and consume one unit each of cloth and wine while Portugal requires 170 hours of work to produce and consume the same quantities. England is more efficient at producing cloth than wine, and Portugal is more efficient at producing wine than cloth. So, if each country specializes in the good for which it has a comparative advantage, then the global production of both goods increases, for England can spend 220 labor hours to produce 2.2 units of cloth while Portugal can spend 170 hours to produce 2.125 units of wine. Moreover, if both countries specialize in the above manner and England trades a unit of its cloth for to units of Portugal's wine, then both countries can consume at least a unit each of cloth and wine, with 0 to 0.2 units of cloth and 0 to 0.125 units of wine remaining in each respective country to be consumed or exported. Consequently, both England and Portugal can consume more wine and cloth under free trade than in autarky.
Ricardian model
The Ricardian model is a general equilibrium mathematical model of international trade. Although the idea of the Ricardian model was first presented in the Essay on Profits and then in the Principles by David Ricardo, the first mathematical Ricardian model was published by William Whewell in 1833. The earliest test of the Ricardian model was performed by G. D. A. MacDougall, which was published in The Economic Journal of 1951 and 1952. In the Ricardian model, trade patterns depend on productivity differences.The following is a typical modern interpretation of the classical Ricardian model. In the interest of simplicity, it uses notation and definitions, such as opportunity cost, unavailable to Ricardo.
The world economy consists of two countries, Home and Foreign, which produce wine and cloth. Labor, the only factor of production, is mobile domestically but not internationally; there may be migration between sectors but not between countries. We denote the labor force in Home by, the amount of labor required to produce one unit of wine in Home by, and the amount of labor required to produce one unit of cloth in Home by. The total amount of wine and cloth produced in Home are and respectively. We denote the same variables for Foreign by appending a prime. For instance, is the amount of labor needed to produce a unit of wine in Foreign.
We do not know if Home can produce cloth using fewer hours of work than Foreign. That is, we do not know if. Similarly, we do not know if Home can produce wine using fewer hours of work. However, we assume Home is relatively more productive than Foreign in making in cloth vs. wine:
Equivalently, we may assume that Home has a comparative advantage in cloth in the sense that it has a lower opportunity cost for cloth in terms of wine than Foreign:
In the absence of trade, the relative price of cloth and wine in each country is determined solely by the relative labor cost of the goods. Hence the relative autarky price of cloth is in Home and in Foreign. With free trade, the price of cloth or wine in either country is the world price or.
Instead of considering the world demand for cloth and wine, we are interested in the world relative demand for cloth and wine, which we define as the ratio of the world demand for cloth to the world demand for wine. In general equilibrium, the world relative price will be determined uniquely by the intersection of world relative demand and world relative supply curves.
We assume that the relative demand curve reflects substitution effects and is decreasing with respect to relative price. The behavior of the relative supply curve, however, warrants closer study. Recalling our original assumption that Home has a comparative advantage in cloth, we consider five possibilities for the relative quantity of cloth supplied at a given price.
- If, then Foreign specializes in wine, for the wage in the wine sector is greater than the wage in the cloth sector. However, Home workers are indifferent between working in either sector. As a result, the quantity of cloth supplied can take any value.
- If, then both Home and Foreign specialize in wine, for similar reasons as above, and so the quantity of cloth supplied is zero.
- If, then Home specializes in cloth whereas Foreign specializes in wine. The quantity of cloth supplied is given by the ratio of the world production of cloth to the world production of wine.
- If, then both Home and Foreign specialize in cloth. The quantity of cloth supplied tends to infinity as the quantity of wine supplied approaches zero.
- If, then Home specializes in cloth while Foreign workers are indifferent between sectors. Again, the relative quantity of cloth supplied can take any value.
In autarky, Home faces a production constraint of the form
from which it follows that Home's cloth consumption at the production possibilities frontier is
With free trade, Home produces cloth exclusively, an amount of which it exports in exchange for wine at the prevailing rate. Thus Home's overall consumption is now subject to the constraint
while its cloth consumption at the consumption possibilities frontier is given by
A symmetric argument holds for Foreign. Therefore, by trading and specializing in a good for which it has a comparative advantage, each country can expand its consumption possibilities. Consumers can choose from bundles of wine and cloth that they could not have produced themselves in closed economies.
There is another way to prove the theory of comparative advantage, which requires less assumption than the above-detailed proof, and in particular does not require for the hourly wages to be equal in both industries, nor requires any equilibrium between offer and demand on the market. Such a proof can be extended to situations with many goods and many countries, non constant returns and more than one factor of production.