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Ricardian model
This model explains that trade is affected by level of productivity, which is due to differences in technology. The model assumes we have 2 countries, 2 goods and that labor is the only factor of production. The country will choose to produce the good that they have comparative advantage in, and they will further specialize in this good. Since labor can move freely around within the country, wages will adjust over time.
Hecksher-Ohlin model
This model explains that trade is not only affected by productivity and tech, but also what resources are available. This model assumes we have 2 countries, 2 goods (cloth and food) and 2 factors (capital and labor). The model also states that a country has more of one resource than the other. Cloth uses capital while food uses labor. A country will export the goods that use their abundant factors intensively, and import the goods that uses their scarce factors intensively. The owners of the abundant factors will gain, while the owners of the scarce factors will loose. Capital and labor can move freely between industries, wages will adjust over time.
Specific factors model
This explains how trade affects the income distribution in a country. The model assumes we have 2 countries, 2 goods (cloth and food) and three resources (land, labor and capital). The model assumes we are in perfect competition. Labor can move around freely within the country, but land and capital are locked to its sectors. Cloth uses capital and labor, while food uses land and labor. The country decides how many workers they want in each sector. So when we open for trade, the price of one good will rise (cloth for example), meaning the other one will become lower (food). This is because of comparative advantage. This means that owners of cloth will "win" and owners of food will loose. But since labor moves freely, we know that the wages will adjust over time. The model explains how trade benefits a country overall, but can affect some groups in the short run.
Stolper Samuelson
When the price of a good rises, the resources used to make this will gain while the others will loose.