Home and Foreign are two countries we considered in the model who produce only two goods. It is assumed that perfect competition happens in the world trade so that price equals to marginal cost. we note that aj is the unit labor requirement which indicates the constant number of hours of labor required to produce one unit of good j. Then 1/aj is labor productivity. The production possibility frontier (PPF) is introduced to show the maximum amount of a good that can be produces for a fixed amount of resources. In autarky, the relative price of trade is determined by the technological references.
However on the empirical side, one factor implies a linear PPF which leads to complete specialization, that is not true in real trade. In equilibrium, home export supply equalize foreign import demand and therefore the Terms of Trade (ToT) is the price of a country’s exports divided by the price of its imports. The Ricardian trade model considers a way where trade between two countries are balanced and both gain from trade. Since there are some shortcomings of Ricardian model, we introduce the Specific factors model where the economy produces 2 goods across two industries with 3 factors of production.
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The diagram on the above left (autarky labor market equilibrium) shows that the value of marginal product of food and manufactures and point 1 is the labor market equilibrium. Nominal wage is known as w1 on vertical axis and the economy is with full employment. In the graph on above right: slope of PPF=-MPLf/MPLm= -Pm/Pf. Suppose the Home specialize in producing manufactures at a lower opportunity cost than Foreign, i. e. manufactures trade at a higher relative price in world market. Now , with free trade Home shifts PPF towards manufactures, hiring more workers from food industry at a higher wage, but the entire labor is not changed. pic] Although nominal wages in both industries rise, impact of trade on the mobile factor is ambiguous because its real income increases in terms of imported goods and decreases in terms of exported goods. Hence, overall gain of labor depends on how many imports and exports consumed. To conclude, both Ricardian trade model and Specific factors model are motivated by the differences in technologies that create a basis for trade due to comparative advantage. All these differences result in different terms of trade in autarky and motivate international trade. But they have some differences in assumptions and the way of analysis.