The theory of comparative advantage is an economic theory about the work gains from trade for individuals, firms, or nations that arise from differences in their factor endowments or technological progress.[1] In an economic model, agents have a comparative advantage over others in producing a particular good if they can produce that good at a lower relative opportunity cost or autarky price, i.e. at a lower relative marginal cost prior to trade.[2] 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.[3] The closely related law or principle of comparative advantage holds that under free trade, an agent will produce more of and consume less of a good for which they have a comparative advantage.[4]

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.[5][6] Widely regarded as one of the most powerful[7] yet counter-intuitive[8] insights in economics, Ricardo's theory implies that comparative advantage rather than absolute advantage is responsible for much of international trade.

## The classical theory

Adam Smith first alluded to the concept of absolute advantage as the basis for international trade 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. The general industry of the country, being always in proportion to the capital which employs it, will not thereby be diminished ... but only left to find out the way in which it can be employed with the greatest advantage."[9]

Writing several decades after Smith in 1808, Robert Torrens articulated a preliminary definition of comparative advantage as the loss from the closing of trade:

"[I]f I wish to know the extent of the advantage, which arises to England, from her giving France a hundred pounds of broad cloth, in exchange for a hundred pounds of lace, I take the quantity of lace which she has acquired by this transaction, and compare it with the quantity which she might, at the same expense of labour and capital, have acquired by manufacturing it at home. The lace that remains, beyond what the labour and capital employed on the cloth, might have fabricated at home, is the amount of the advantage which England derives from the exchange."[10]

David Ricardo

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, which produce 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 of producing those two goods differ between the countries.

Hours of work necessary to produce one unit
Country Cloth Wine
England 100 120
Portugal 90 80

In this illustration, England could commit 100 hours of labor to produce one unit of cloth, or produce ${\displaystyle {\frac {5}{6}}}$ units of wine. Meanwhile, in comparison, Portugal could commit 90 hours of labor to produce one unit of cloth, or produce ${\displaystyle {\frac {9}{8}}}$ units of wine. So, Portugal possesses an absolute advantage in producing cloth due to fewer labor hours, and England has a comparative advantage due to lower opportunity cost.

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 ${\displaystyle {\frac {5}{6}}}$ to ${\displaystyle {\frac {9}{8}}}$ 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.

### The Ricardian model

The Ricardian model is a general equilibrium mathematical model of international trade. Although the idea of Ricardian model was first presented in the Essay on Profits (a single-commodity version) and then in the Principles (a multi-commodity version) by David Ricardo, the first mathematical Ricardian model was published by William Whewell in 1833.[11] The earliest test of Ricardian model was performed by G.D.A MacDougall, which was published in Economic Journal of 1951 and 1952. [12] In Ricardian model, trade patterns depend on productivity differences.

The following is a typical modern interpretation of the classical Ricardian model.[13] 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 ${\displaystyle \textstyle L}$, the amount of labor required to produce one unit of wine in Home by ${\displaystyle \textstyle a_{LW}}$, and the amount of labor required to produce one unit of cloth in Home by ${\displaystyle \textstyle a_{LC}}$. The total amount of wine and cloth produced in Home are ${\displaystyle Q_{W}}$ and ${\displaystyle Q_{C}}$ respectively. We denote the same variables for Foreign by appending a prime. For instance, ${\displaystyle \textstyle a'_{LW}}$ is the amount of labor needed to produce a unit of wine in Foreign.

We don't know if Home is more productive than Foreign in making cloth. That is, if ${\displaystyle a_{LC}. Similarly, we don't know if Home has an absolute advantage in wine. However, we will assume that Home is more relatively productive in cloth than Foreign:

${\displaystyle a_{LC}/a'_{LC}

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:

${\displaystyle a_{LC}/a_{LW}

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 ${\displaystyle a_{LC}/a_{LW}}$ in Home and ${\displaystyle a'_{LC}/a'_{LW}}$ in Foreign. With free trade, the price of cloth or wine in either country is the world price ${\displaystyle P_{C}}$ or${\displaystyle P_{W}}$.

Instead of considering the world demand (or supply) for cloth and wine, we are interested in the world relative demand (or relative supply) for cloth and wine, which we define as the ratio of the world demand (or supply) for cloth to the world demand (or supply) for wine. In general equilibrium, the world relative price ${\displaystyle \textstyle P_{C}/P_{W}}$ will be determined uniquely by the intersection of world relative demand ${\displaystyle \textstyle RD}$ and world relative supply ${\displaystyle \textstyle RS}$ curves.

The demand for cloth relative to wine decreases with the relative price of cloth in terms of wine; the supply ${\displaystyle RS}$ of cloth relative to wine increases with relative price. Two relative demand curves ${\displaystyle RD_{1}}$ and ${\displaystyle RD_{2}}$ are drawn for illustrative purposes.

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 supplied at a given price.

• If ${\displaystyle \textstyle P_{C}/P_{W}=a_{LC}/a_{LW}, then Foreign specializes in wine, for the wage ${\displaystyle P'_{W}/a'_{LW}}$ in the wine sector is greater than the wage ${\displaystyle P'_{C}/a'_{LC}}$ in the cloth sector. However, Home workers are indifferent between working in either sector. As a result, the quantity supplied can take any value.
• If ${\displaystyle \textstyle P_{C}/P_{W}, then both Home and Foreign specialize in wine, for similar reasons as above, and so the quantity supplied is zero.
• If ${\displaystyle \textstyle a_{LC}/a_{LW}, then Home specializes in cloth whereas Foreign specializes in wine. The quantity supplied is given by the ratio ${\displaystyle \textstyle {\frac {L/a_{LC}}{L'/a'_{LW}}}}$ of the world production of cloth to the world production of wine.
• If ${\displaystyle \textstyle a_{LC}/a_{LW}, then both Home and Foreign specialize in cloth. The quantity supplied tends to infinity as the quantity of wine supplied approaches zero.
• If ${\displaystyle \textstyle a_{LC}/a_{LW}, then Home specializes in cloth while Foreign workers are indifferent between sectors. Again, the relative quantity supplied can take any value.
The blue triangle depicts Home's original production (and consumption) possibilities. By trading, Home can also consume bundles in the pink triangle despite facing the same productions possibility frontier.

The relative price is always bounded by the inequality

${\displaystyle a_{LC}/a_{LW}\leq {P_{C}/P_{W}}\leq {a'_{LC}/a'_{LW}}.}$

In autarky, Home faces a production constraint of the form

${\displaystyle a_{LC}Q_{C}+a_{LW}Q_{W}\leq L,}$

from which it follows that Home's cloth consumption at the production possibilities frontier is

${\displaystyle Q_{C}=L/a_{LC}-(a_{LW}/a_{LC})Q_{W}}$.

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

${\displaystyle a_{LC}Q_{C}+a_{LC}(P_{W}/P_{C})Q_{W}\leq L}$

while its cloth consumption at the consumption possibilities frontier is given by

${\displaystyle Q_{C}=L/a_{LC}-(P_{W}/P_{C})Q_{W}\geq L/a_{LC}-(a_{LW}/a_{LC})Q_{W}}$.

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.

Terms of trade is the rate at which one good could be traded for another. If both countries specialize in the good for which they have a comparative advantage then trade, the terms of trade for a good (that benefit both entities) will fall between each entities opportunity costs. In the example above one unit of cloth would trade for between ${\displaystyle {\frac {5}{6}}}$ units of wine and ${\displaystyle {\frac {9}{8}}}$ units of wine.[14]

### Modern theories

Since 1817, economists have attempted to generalize the Ricardian model and derive the principle of comparative advantage in broader settings, most notably in the neoclassical specific factors Ricardo-Viner and factor proportions Heckscher–Ohlin models. Subsequent developments in the new trade theory, motivated in part by the empirical shortcomings of the H–O model and its inability to explain intra-industry trade, have provided an explanation for aspects of trade that are not accounted for by comparative advantage.[15] Nonetheless, economists like Alan Deardorff,[16] Avinash Dixit, Gottfried Haberler, and Victor D. Norman[17] have responded with weaker generalizations of the principle of comparative advantage, in which countries will only tend to export goods for which they have a comparative advantage.

In both Ricardian and H–O models, the comparative advantage concept is formulated for 2 country, 2 commodity case. It can easily be extended to the 2 country, many commodity case or many country, 2 commodity case.[18][19] But in the case with many countries (more than 3 countries) and many commodities (more than 3 commodities), the notion of comparative advantage requires a substantially more complex formulation.[20]

### New theory of international values

Recently, Y. Shiozawa succeeded to construct a theory of international value on the tradition of Ricardo's cost-of-production theory of value.[21] It is based on a wide assumption as follows:

• Many countries
• Many commodities
• Several production techniques for a product in a country
• Durable capital goods with constant efficiency during a predetermined lifetime
• No transportation cost (extendable to positive cost cases)

In a famous comment McKenzie pointed that "A moment's consideration will convince one that Lancashire would be unlikely to produce cotton cloth if the cotton had to be grown in England."[22] However, McKenzie and later researchers could not produce a general theory which includes traded input goods because of the mathematical difficulty.[23] As John Chipman points it, McKenzie found that "introduction of trade in intermediate product necessitates a fundamental alteration in classical analysis."[24] Durable capital goods such as machines and installations are inputs to the productions in the same title as part and ingredients.

In view of the new theory, no physical criterion exists.[25] The competitive patterns are determined by the traders trials to find cheapest products in a world. The search of cheapest product is achieved by world optimal procurement. Thus the new theory explains how the global supply chains are formed.[26]

## Evidence of effects on the economy

Comparative advantage is a theory about the benefits that specialization and trade would bring, rather than a strict prediction about actual behavior. (In practice, governments restrict international trade for a variety of reasons, e.g. North Korea's ideological adherence to Juche.) Nonetheless there is a large amount of empirical work testing the predictions of comparative advantage. The empirical works usually involve testing predictions of a particular model. For example, the Ricardian model predicts that technological differences in countries result in differences in labor productivity. The differences in labor productivity in turn determine the comparative advantages across different countries. Testing the Ricardian model for instance involves looking at the relationship between relative labor productivity and international trade patterns. A country that is relatively efficient in producing shoes tends to export shoes.

### Early tests

Two of the first tests of comparative advantage were by MacDougall (1951, 1952).[27][28] A prediction of a two-country Ricardian comparative advantage model is that countries will export goods where output per worker (i.e. productivity) is higher. That is, we expect a positive relationship between output per worker and number of exports. MacDougall tested this relationship with data from the US and UK, and did indeed find a positive relationship. The statistical test of this positive relationship was replicated[29][30] with new data by Stern (1962) and Balassa (1963).

### More recent evidence

Dosi et al. (1988)[31] conduct a book-length empirical examination that suggests that international trade in manufactured goods is largely driven by differences in national technological competencies.

One critique of the textbook model of comparative advantage is that there are only two goods. The results of the model are robust to this assumption. Dornbusch et al. (1977)[32] generalized the theory to allow for such a large number of goods as to form a smooth continuum. Based in part on these generalizations of the model, Davis (1995)[33] provides a more recent view of the Ricardian approach to explain trade between countries with similar resources.

More recently, Golub and Hsieh (2000)[34] presents modern statistical analysis of the relationship between relative productivity and trade patterns, which finds reasonably strong correlations, and Nunn (2007)[35] finds that countries that have greater enforcement of contracts specialize in goods that require relationship-specific investments.

Taking a broader perspective, there has been work about the benefits of international trade. Zimring & Etkes(2014)[36] finds that the Blockade of the Gaza Strip, which substantially restricted the availability of imports to Gaza, saw labor productivity fall by 20% in three years. Markusen et al. (1994)[37] reports the effects of moving away from autarky to free trade during the Meiji Restoration, with the result that national income increased by up to 65% in 15 years.

## Considerations

### Development economics

The theory of comparative advantage, and the corollary that nations should specialize, is criticized on pragmatic grounds within the import substitution industrialization theory of development economics, on empirical grounds by the Singer–Prebisch thesis which states that terms of trade between primary producers and manufactured goods deteriorate over time, and on theoretical grounds of infant industry and Keynesian economics. In older economic terms, comparative advantage has been opposed by mercantilism and economic nationalism. These argue instead that while a country may initially be comparatively disadvantaged in a given industry (such as Japanese cars in the 1950s), countries should shelter and invest in industries until they become globally competitive. Further, they argue that comparative advantage, as stated, is a static theory – it does not account for the possibility of advantage changing through investment or economic development, and thus does not provide guidance for long-term economic development.

Much has been written since Ricardo as commerce has evolved and cross-border trade has become more complicated. Today trade policy tends to focus more on "competitive advantage" as opposed to "comparative advantage". One of the most in-depth research undertakings on "competitive advantage" was conducted in the 1980s as part of the Reagan administration's Project Socrates to establish the foundation for a technology-based competitive strategy development system that could be used for guiding international trade policy.

### Free mobility of capital in a globalized world

Ricardo explicitly bases his argument on an assumed immobility of capital: " ... if capital freely flowed towards those countries where it could be most profitably employed, there could be no difference in the rate of profit, and no other difference in the real or labor price of commodities, than the additional quantity of labor required to convey them to the various markets where they were to be sold."[38]

He explains why, from his point of view (anno 1817), this is a reasonable assumption: "Experience, however, shows, that the fancied or real insecurity of capital, when not under the immediate control of its owner, together with the natural disinclination which every man has to quit the country of his birth and connexions, and entrust himself with all his habits fixed, to a strange government and new laws, checks the emigration of capital."[38]

## Criticism

Several arguments have been advanced against using comparative advantage as a justification for advocating free trade, and they have gained an audience among economists. For example, James Brander and Barbara Spencer demonstrated how, in a strategic setting where a few firms compete for the world market, export subsidies and import restrictions can keep foreign firms from competing with national firms, increasing welfare in the country implementing these so-called strategic trade policies.[39]

However, the overwhelming consensus of the economics profession remains that while these arguments are theoretically valid under certain assumptions, these assumptions do not usually hold and should not be used to guide trade policy.[40] Gregory Mankiw, chairman of the Harvard Economics Department, has said: ″Few propositions command as much consensus among professional economists as that open world trade increases economic growth and raises living standards.″[41]

Economist James K. Galbraith disputes these claims of the benefit of comparative advantage. He states that "free trade has attained the status of a god" and that ". . . none of the world's most successful trading regions, including Japan, Korea, Taiwan, and now mainland China, reached their current status by adopting neoliberal trading rules." He argues that ". . . comparative advantage is based upon the concept of constant returns: the idea that you can double or triple the output of any good simply by doubling or tripling the inputs. But this is not generally the case. For manufactured products, increasing returns, learning, and technical change are the rule, not the exception; the cost of production falls with experience. With increasing returns, the lowest cost will be incurred by the country that starts earliest and moves fastest on any particular line. Potential competitors have to protect their own industries if they wish them to survive long enough to achieve competitive scale."[42]

Galbraith also contends that "For most other commodities, where land or ecology places limits on the expansion of capacity, the opposite condition - diminishing returns - is the rule. In this situation, there can be no guarantee that an advantage of relative cost will persist once specialization and the resultant expansion of production take place. A classic and tragic example, studied by Erik Reinert, is transitional Mongolia, a vast grassland with a tiny population and no industry that could compete on world markets. To the World Bank, Mongolia seemed a classic case of comparative advantage in animal husbandry, which in Mongolia consisted of vast herds of cattle, camels, sheep, and goats. Opening of industrial markets collapsed domestic industry, while privatization of the herds prompted the herders to increase their size. This led, within just a few years in the early 1990s, to overgrazing and permanent desertification of the subarctic steppe and, with a slightly colder than normal winter, a massive famine in the herds."

"Countries doomed by climate and history to produce bananas, coffee, or cocoa and little else are invariably poor. Why? First, the demand for their products is inelastic: when supply increases worldwide, the price falls, and with it national income. Second, they suffer from diminishing returns. Contrary to Ricardo, it is generally impossible to expand agriculture indefinitely at a constant unit cost: good land and water are in limited supply. Third, a country with just one major cash export will lack a cushion in other products when fashion or technology turns against their specialty. Conversely, diversification pays. Countries with the capacity to diversify across multiple industries are far more likely to weather export demand shocks or insurgent competition from (say) China than those that commit themselves to a single industry or product line. Diversifiers are also better placed to take advantage of new technical opportunities, since by diversification they develop expertise in a range of products and processes."[43]

According to historian Cecil Woodham-Smith, Ireland in the 1800s is an example of the dangers of specialization. When the union with Great Britain was formed in 1800, Irish textile industries protected by tariffs were exposed to world markets where England had a comparative advantage in technology, experience and scale of operation which devastated the Irish industry. Ireland was forced to specialize in the export of grain while the displaced Irish labor was forced into subsistence farming and relying on the potato for survival. When the potato blight occurred the resulting famine killed at least one million Irish in one of the worst famines in European history. As Woodham-Smith would later comment, "the Irish peasant was told to replace the potato by eating his grain, but Trevelyan once again refused to take any steps to curb the export of food from Ireland. 'Do not encourage the idea of prohibiting exports,' he wrote, on September 3, (1846) 'perfect free trade is the right course'."[44]

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38. ^ a b
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