Question

The construction of the production possibility curve shown in Figures 13.2 and 13.3 can be used to illustrate three important "theorems" in international trade theory. To get started, notice in Figure 13.2 that the efficiency line \(O_{x}, O_{y}\) is bowed above the main diagonal of the Edgeworth box. This shows that the production of good \(x\) is always "capital intensive" relative to the production of good \(y\). That is, when production is efficient, \(\left(\frac{5}{7}\right)_{x}>\left(\frac{5}{1}\right)\), no matter how much of the goods are produced. Demonstration of the trade theorems assumes that the price ratio, \(p=p_{x} / p_{y}\) is determined in international markets-the domestic economy must adjust to this ratio (in trade jargon, the country under examination is assumed to be "a small country in a large world"). a Factor price equalization theorem: Use Figure 13.4 to show how the international price ratio, \(p\), determines the point in the Edgeworth box at which domestic production will take place. Show how this determines the factor price ratio, \(w / v\). If production functions are the same throughout the world, what will this imply about relative factor prices throughout the world? b. Stolper-Samuelson theorem: An increase in \(p\) will cause the production to move clockwise along the production possibility frontier \(-x\) production will increase and \(y\) production will decrease. Use the Edgeworth box diagram to show that such a move will decrease \(k / l\) in the production of both goods. Explain why this will cause \(w / v\) to decrease. What are the implications of this for the opening of trade relations (which typically increases the price of the good produced intensively with a country's most abundant input). c. Rybczynski theorem: Suppose again that \(p\) is set by external markets and does not change. Show that an increase in \(k\) will increase the output of \(x\) (the capital-intensive good) and reduce the output of \(y\) (the labor-intensive good).

Short answer

Answer: In the context of international trade, the factor price equalization theorem implies that relative factor prices will be equal in all countries if the production functions are the same throughout the world. The Stolper-Samuelson theorem states that an increase in the price of the good produced intensively with a country's most abundant input will benefit the owners of that input and worsen income distribution. The Rybczynski theorem highlights that under constant prices, an increase in the endowment of one factor will lead to an increase in the output of the good that uses that factor intensively, and a decrease in the output of the other good.

Step-by-step solution

Show how the international price ratio determines the point in the Edgeworth box

Given that the price ratio \(p=p_{x}/p_{y}\) is determined in the international market, this means that the domestic economy has to adjust to this ratio. In the Edgeworth box, the slope of the iso-value line is equal to the negative of the price ratio, \(-p\). The point where the domestic production takes place is determined at the point where the iso-value line is tangent to the PPF, i.e., where the slope of the iso-value line is equal to the slope of the PPF.

Explain how this determines the factor price ratio \(w/v\)

When production is efficient, the marginal rate of technical substitution (MRTS) in both goods should be equal to the price ratio \(p\). The MRTS in turn is equal to the ratio of marginal productivities of labor and capital. Therefore, the ratio of factor prices \((w/v)\) will adjust to maintain the equality between the price ratio \(p\) and the MRTS in both goods. If production functions are the same throughout the world, this would imply that relative factor prices will also be the same in all countries. b. Stolper-Samuelson theorem

Explain the effect of an increase in the price ratio \(p\) on the production of goods \(x\) and \(y\)

When the price ratio \(p\) increases, the production will move clockwise along the PPF. This means that the production of good \(x\) (capital-intensive) will increase, and the production of good \(y\) (labor-intensive) will decrease.

Use the Edgeworth box diagram to show the effect on \(k/l\) and explain its implications on \(w/v\)

As production shifts to more good \(x\) and less good \(y\), the capital-labor ratio (\(k/l\)) in both goods will decrease. This is because more capital-intensive good \(x\) is being produced, using more capital relative to labor. As a result, the ratio of marginal products \(MP_{k}/MP_{l}\) will also decrease. Since \(w/v = MP_{k}/MP_{l}\), the factor price ratio \(w/v\) will decrease. This implies that the opening of trade relations, which leads to an increase in the price of the good produced intensively with a country's most abundant input, will benefit the owners of that input and worsen the income distribution. c. Rybczynski theorem

Analyze the effect of an increase in \(k\) on the outputs of goods \(x\) and \(y\)

Suppose that the price ratio \(p\) does not change and is set by external markets. When there is an increase in the capital endowment \(k\), the PPF will expand along the good \(x\) axis, since good \(x\) is capital-intensive. This will lead to an increase in the production of good \(x\) and a decrease in the production of good \(y\). This highlights the Rybczynski theorem, which states that under constant prices, an increase in the endowment of one factor will lead to an increase in the output of the good that uses that factor intensively and a decrease in the output of the other good.