Palio in Siena, Italy (2000). Horse trainers are specific to the horse industry

Specific Factors Model


          Jacob Viner first examined the specific factors model, which is a variant of the Ricardian model. It was further developed by Paul Samuelson and Ronald Jones. It is also called the Ricardo-Viner model. Michael Mussa (1974) developed the graphical approach to illustrate the main results of this model. In contrast to the Ricardian model, this model includes factors other than labor.

          Thus, there are two types of factors. Labor is the mobile factor that can move between the two sectors. Each of the other two factors is assumed to be specific to a particular industry. That is, the quantity of each specific factor is fixed and cannot move to the other industry. Specific factors cannot move between industries.

Basic Assumptions

          Finland produces ocean cruisers and leather products such as reindeer fur, mink and fox coats. Lapland, the nothern part of Finland, is sparsely inhabited by mostly Indians who hunt these wild animals. This cold climate or forest is a factor specific in the leather goods industry. In the urban areas Finns are also engaged in cruise ship building and Finland exports cruisers to European countries. In addition to well educated workers, the ship building industry requires a large amount of capital, which is specific to that industry in that it cannot be used in the leather goods industry. Finnish workers are mobile between the two industries.


A cruiser in Helsinki, September 5, 2003

The economy produces two goods using two factors of production, capital and labor in a perfectly competitive market. Capital is assumed to be specific to each industry, and is immobile between industries. In the two good model, there are two specific factors, K and T. In this sense, Jones calls it a 2-good, 3-factor model. (K = Kapital, which is capital in German, T = Terra in Latin, meaning land or earth. We do not use L to denote land because it is reserved for labor, and the lower case l looks like "one." It is best to avoid confusing symbols.)

          In a Heckscher-Ohlin model to be studied shortly, both factors, capital and labor, are assumed to be mobile. Recall that in production decisions, some factors are fixed (and hence specific) in the short run, but all factors are variable inputs in the long run. Hence, the HO model is a long-run model, whereas the specific factors model is a short run model in which capital and land inputs are fixed but labor is a variable input in production.

However, all factors are assumed to be fully employed.

Production

  • y1 = F(K,L1)

  • y2 = G(T,L2)

    In contrast to the Ricardian model, labor is the mobile factor between the two industries.

    Resource constraint:

  • L1 + L2 = L

  • π1 = p1y1 - wL1 - rK
    Consider a change in the amount of labor employed, ΔL1.
  • Δπ1 = p1Δy1 - wΔL1 = 0 for a maximum profit (The profit function must reach a peak or a plateau so that a change in profit is zero)

    Divide both sides by ΔL1.

  • p1MPL1 = w

    Alternatively,

  • p1 = w/MPL1 = MC1 (For instance, if the marginal worker produced 2 automobiles and got paid $60,000, marginal cost of the automobile is $30,000).

  • p2 = p2y2 - wL2 - sT (s = land rental, sT = landlords' income)

  • p2MPL2 = w.

  • p1MPL1 = p2MPL2

  • p1/p2 = MRT = MC1/MC2

  • Main Results

    1. No specialization

    Unlike in the Ricardian model, labor is shared between the two industries. Thus, the specific factors model explains why a country produces a product and also imports it. For instance, the US produces but also imports oil from the Middle East.

    2. Nonequalization of Wage

    p2MPL2 = w.

    p*2MP*L2 = w*.

    If labor productivities are the same in the two countries, free trade equalizes wage rates. However, due to diminishing marginal returns, marginal product of labor decreases with employment. In general, MPLi is not equal to MP*Li in any industry. Free trade equalizes output prices, but not wages.

    Allocation of Labor

    Price Effects

    How does a change in the output price affect income distribution?
    An increase in the price of the exportable increases wage.

    An increase in the price of the exportable increases rent.


    More generally,

    3. A price increase benefits the specific factor in that sector.

    An increase in the price of a good increases the rent of the factor specific to that industry.

    For instance, international trade raises the price of the exportable good (foodstuff, such as corn and soybean), which in turn raises the price of the factor stuck in that industry such as land. That is, trade raises land value in the Midwest.

    The US government now endeavors to achieve energy independence, i.e., independence from imported oil. Billions of dollars are now being invested to develop alternative source of energy such as ethanal from corn or switchgrass. This increase in the price of ethanol should increase the land value in the Midwest, because it is a fixed factor there.

    Remark: This implies that a movement toward free trade (FT) increases the price of the exportable (p1), and hence increases the return to the factor (K) specific to that industry.

    An increase in the price of the exportable increases its output. Note that PPF is concave to the origin, unlike that in the Ricardian model..

    The Silkroad

    The Ricardian trade model does not explain the caravan trade along the Silkroad between the two empires, Rome and China (because China have exported not only silk but also many other products, including porcelain wares, to Europe). The Specific Factors Model explains the trade along the Silkroad. Emperor Wu Di (145-87 BC) of Han dynasty (206 BC - 220 AD) built the silkroad, connecting Chang An (Xian today, where Qin Shi Huang-Di's tomb was recently found, making it the most important archeological discovery in the 20th Century) and Europe, though central Asia. However, the Chinese were trading with Europe long before the Silkroad was officially built and expanded by emperor Wu Di. Imported colored glasses were found in China during the Warring States period. Silk was produced by the Liangzhu people who lived around the Yangtze River basin (around Shanghai today).

    Read the legend associated with the Silkroad.

    Rome acquired several glass producing centers in Syria and Egypt. China exported porcelain wares (which were known as china) and silk to Rome and the intervening regions (e.g. India and Persia) and imported gold, textiles, spices, colored glass, precious stones (e.g., Mediterranean corals) and gold and silver from them. Colored transparent glass was especially prized in China. China had been producing liuli (opaque glass) before the Christian era. Rome imported glass wares from Syria and in turn exported them to China. China had specific factors such as weather and land suitable for sericulture. China and the rest were exporting the products which use their specific factors and imported other goods.
    Sericulture in ancient China
    Silk was invented by the Liangzhu people who settled down in Liangzhu (near Shanghai now) about 3000 BC. The Liangzhu people was trading jade artifacts during the Neolithic period (3300-2200 BC) even before their first dynasty, Xia. In the "Arabian Nights," the story of Aladdin, a lazy boy in China, indicates that Arabia was an intervening region on the silk road and Arabia connected China and Africa. Gold, amber, and ivory were prized in China and imported from Africa. Aladdin itself is either Persian or Arabic name, meaning "faithful." The intervening regions also joined the trade on the silk road. China imported cobalt oxide from Persia to make blue and white porcelain ware.

    Persia connected China and the Roman Empire. Chlorite vessels were exported to Mesopotamia.

    Persian King, Cyrus, conquered Babylonia and built a vast empire in 549 BC. (Mesopotamia, the "land between two rivers" straddled three continents and was a lucrative region controlling trade among three continents.) He conquered Assyria and liberated Jews to return to their homeland in 538 BC. Of an estimated 150,000 Jews, a third returns to Jerusalem.

    Who can match Persian artisans' touch? (British Museum)

    Boston Museum of Fine Arts

    King of Elam ruled at Susa (now in Iran). Elam was conquered by the Assyrians later.

     

    Qin Shi Huang Di ("Qin's first emperor" in Chinese) united six countries that divided China in 221 BC. His achievements are:

    *standardized weights and measurements.

    *unified written Chinese language.
    *created Qin currency and retired the currencies of the 6 kingdoms.
    *built roads connecting states which facilitated internal and international trade.
    * started construction of the Great Wall of China

    (His kingdom did not last. His son was not wise.)

    These achievements are similar to those of Romans (after Augustus)

    Romans issued currencies (gold aureus, silver denarius, bronze sestertii)

    Romans built roads (via appia), creating a huge free trade area throuought the Roman Empire. In contrast to Qin, Romans established a good governing system. The idea of senate is derived from the Romans. Western government is derived from the Greco-Roman ideas of democracy and government.