International trade theory is a sub-field of economics which analyzes the patterns of international trade, its origins, and its welfare implications. International trade policy has been highly controversial since the 18th century. International trade theory and economics itself have developed as means to evaluate the effects of trade policies.

Adam Smith's model

Adam Smith describes trade taking place as a result of countries having absolute advantage in production of particular goods, relative to each other. Within Adam Smith's framework, absolute advantage refers to the instance where one country can produce a unit of a good with less labor than another country.

In Book IV of his major work the Wealth of Nations, Adam Smith, discussing gains from trade, provides a literary model for absolute advantage based upon the example of growing grapes from Scotland. He makes the argument that while it is possible to grow grapes and produce wine in Scotland, the investment in the factors of production would cost thirty times more than the cost of purchasing an equal quantity from a foreign country. The minimization of aggregate real costs and efficient resource allocation through trade without strong consideration for comparative costs form the basis of Adam Smith's model of absolute advantage in international trade.

Ricardian model

The Ricardian theory of comparative advantage became a basic constituent of neoclassical trade theory. Any undergraduate course in trade theory includes a presentation of Ricardo's example of a two-commodity, two-country model. For the modern development, see Ricardian trade theory extensions

The Ricardian model focuses on comparative advantage, which arises due to differences in technology or natural resources. The Ricardian model does not directly consider factor endowments, such as the relative amounts of labor and capital within a country.

New interpretation The Ricardian model is often presented as being based on the following assumptions: Labor is the only primary input to production. The relative ratios of labor at which the production of one good can be traded off for another, differ between countries.

This is incomplete, because the Ricardian model can be extended to the situation where many goods can be inputs for a production. See Ricardian trade theory extensions below. Relative ratio of labor input coefficients has a valid meaning only for simple cases such as two-country, many commodity case or many-country, two-commodity case without no intermediate goods.Alan V. Deardorff (2005) Ricardian comparative advantage with intermediate inputs. North American Journal of Economics and Finance 16(1): 11-34.

As for the meanings of four magic numbers, a new interpretation became popular in the 21st century. In 2002, Roy Ruffin pointed the possibility of new reading of Ricardo's explanations.Roy J. Ruffin (2002) David Ricardo's discovery of comparative advantage. History of Political Economy 34: 727-748. Andrea Maneschi made a detailed account in 2004.Andrea Maneschi (2004) The true meaning of David Ricardo's four magic numbers. Journal of International Economics 62(2): 433-443. Now the new interpretation has become almost as established as Ricardo's text, not only for the first third of Chapter 7 but for all descriptions throughout his book concerning international trade.Gilbert Faccarello (2017) A calm investigation into Mr. Ricardo's principles of international trade. Senga et al. (eds.) Ricardo and International Trade. London and New York: Routledge.

Specific factors model

The specific factors model is an extension of the Ricardian model. It was due to Jacob Viner's interest in explaining the migration of workers from the rural to urban areas after the Industrial revolution.

In this model labor mobility among industries is possible while capital is assumed to be immobile in the short run. Thus, this model can be interpreted as a short-run version of the Heckscher-Ohlin model. The "specific factors" name refers to the assumption that in the short run, specific factors of production such as physical capital are not easily transferable between industries. The theory suggests that if there is an increase in the price of a good, the owners of the factor of production specific to that good will profit in real terms.

Heckscher–Ohlin model

In the early 1900s, a theory of international trade was developed by two Swedish economists, Eli Heckscher and Bertil Ohlin. This theory has subsequently become known as the Heckscher–Ohlin model (H–O model). The results of the H–O model are that the pattern of international trade is determined by differences in factor endowments. It predicts that countries will export those goods that make intensive use of locally abundant factors and will import goods that make intensive use of factors that are locally scarce.

The H–O model makes the following core assumptions:

Labor and capital flow freely between sectors equalising factor prices across sectors within a country. The amount of labor and capital in two countries differ (difference in endowments) Technology is the same among countries (a long-term assumption) Tastes are the same upon countries

Stolper-Samuelson theorem According to the Stolper-Samuelson theorem, the export of a product which is a relatively cheap, abundant resource makes this resource more scarce in the domestic market. Thus, the increased demand for the abundant resource leads to an increase in its price and an increase in its income. Simultaneously, the income of the resource used intensively in the import-competing product decreases as its demand falls.

Simply put, this theorem indicates that an increase in the price of a product rises the income earned by resources that are used intensively in its production. Conversely, a decrease in the price of a product reduces the income of the resources that it uses intensively. The abundant resource that have comparative advantage realizes an increase in income, and the scarce resource realizes a decrease in its income regardless of industry. This trade theory concludes that some people will suffer losses from free trade even in the long-term.

Later generalized by economist Ronald Jones, the Magnification Effect describes how, when countries engage in free trade, the real return of a country's relatively abundant factor increases, while the return on its relatively scarce factor decreases. In a capital-abundant country, capital owners are likely to see increased purchasing power, while workers may experience a decline in wages and living standards. The effect is reversed in labor-abundant countries. As trade liberalization causes prices to shift—typically lowering import prices and increasing export demand—resources move toward export-driven industries. This shift intensifies demand for the abundant factor (e.g., capital), increasing its return, while oversupplying the scarce factor (e.g., labor), which leads to lower real wages, reduced purchasing power for workers, and long-term inequality between factor groups.

Empirical Evidence for the Heckscher–Ohlin model In 1953, Wassily Leontief published a study in which he tested the validity of the Heckscher-Ohlin theory. The study showed that the United States was more abundant in capital compared to other countries, therefore the United States would export capital-intensive goods and import labor-intensive goods. Leontief found out that the United States' exports were less capital intensive than its imports. The result became known as Leontief's paradox.

After the appearance of Leontief's paradox, many researchers tried to save the Heckscher-Ohlin theory, either by new methods of measurement, or by new interpretations.

New trade theory

New trade theory tries to explain empirical elements of trade that comparative advantage-based models above have difficulty with. These include the fact that most trade is between countries with similar factor endowment and productivity levels, and the large amount of multinational production (i.e., foreign direct investment) that exists. New trade theories are often based on assumptions such as monopolistic competition and increasing returns to scale. One result of these theories is the home-market effect, which asserts that, if an industry tends to cluster in one location because of returns to scale and if that industry faces high transportation costs, the industry will be located in the country with most of its demand, in order to minimize cost.

"New" new trade theory New trade theory is a theory of international trade inaugurated by Marc Melitz in 2003.Melitz, Marc J. (2003) The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica 71(6): 1695-1725. It discovered that efficiency of firms in a country changes much and those firms engaged in international trade have higher productivity than firms which produce only for domestic market. As it is fitted to big data age, the research produced many follows and the trend is now called New new trade theory in comparison to Paul Krugman's new trade theory.

Gravity model

The Gravity model of trade presents a more empirical analysis of trading patterns. The gravity model, in its basic form, predicts trade based on the distance between countries and the interaction of the countries' economic sizes. The model mimics the Newtonian law of gravity which also considers distance and physical size between two objects. The model has been shown to have significant empirical validity.Akman, 2016. "The facilitating role of visa policies on international trade and foreign direct investment"

Ricardian trade theory extensions According to Eaton and Kortum,Jonathan Eaton and Samuel Kortum (2012) Putting Ricardo to Work. Journal of Economic Perspectives 26(2): 65-89. p.66. in the 21 century, "the Ricardian framework has experienced a revival. Much work in international trade during the last decade has returned to the assumption that countries gain from trade because they have access to different technologies. ... This line of thought has brought Ricardo's theory of comparative advantage back to center stage." The Ricardian trade theory was expanded and generalized multiple times: notably to treat many-country many-product situations and to include intermediate input trade, and choice of production techniques. In Ricardian framework, capital goods (comprising fixed capital) are treated as goods which are produced and consumed in the production.

Another attempt to restore comparative advantage to the center of the stage is the "basic laws of trade". Comparative advantage is the first law in the basic laws of trade. At the international level, the basic laws require real exchange rates for tradables only (RER-T). The basic laws state that if the actual exchange rate is the same as the RER-T, then trade between countries tends to be relatively balanced and gains of trade are optimal for all participating countries.

Many countries, many goods There were three waves of expansions and generalizations.

First phase: Major general results were obtained by McKenzie and Jones. McKenzie was more interested in the patterns of trade specialisiations (including incomplete specializations), whereas Jones was more interested in the patterns of complete specialization, in which the prices moves freely within a certain limited range., section 4. The formula he found is often cited as Jones' inequality, p.508. or Jones' criterion.Golub, S. S. (1995) Comparative and absolute advantage in the Asia-Pacific region (No. 95-09). Federal Reserve Bank of San Francisco. p.4