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.

Key concepts

Factor Price Equalization Theorem

The Factor Price Equalization Theorem is a central idea in international trade theory. It proposes that, when two countries engage in free trade of goods produced using similar production technologies, the prices of the production factors, like labor (wages) and capital (interest rates), will tend to equalize between these two nations.

This equalization happens because free trade allows goods produced in one country to be consumed in another without barriers. As countries trade, the prices of goods converge, which, in turn, affects the prices needed to produce them. As the price ratio of two goods in the market is determined internationally, each country's production must adjust to keep the marginal rate of technical substitution (MRTS) aligned with this price ratio, ensuring efficient production.

If every country uses the same production functions, the relative factor prices should end up being the same across the globe. This theory highlights how deeply interconnected global economies are and suggests a leveling force in factor pricing due to international trade.

Stolper-Samuelson Theorem

The Stolper-Samuelson Theorem elaborates on the impact of trade on income distribution within a country. Specifically, it deals with how changes in output prices influence the incomes of production factors.

Consider a situation where the price of a capital-intensive good (good X) increases due to trade. According to this theorem, as the price of this good rises, the output of good X also increases, leading to a greater demand for capital. At the same time, the output of labor-intensive goods (good Y) decreases, lowering the demand for labor.

The Edgeworth box can illustrate this shift, showing how production is reallocated, thus affecting the capital-labor ratio ( (k/l) ). As the demand for capital rises compared to labor, the wage-rent ratio ( (w/v) ) drops, benefiting capital owners but negatively affecting labor wages. This explains why trade may increase the return to a country's abundant factor and reduce the return to its scarce factor, influencing the income distribution within the country.

Rybczynski Theorem

The Rybczynski theorem explores the relationship between resource endowments and production output. It indicates that, holding output prices constant, an increase in one factor of production results in an augmented output of the good utilizing that factor extensively, while reducing the output of the other good.

Imagine a scenario with a constant international price ratio. If a country experiences an increase in its capital stock ( (k) ), the production possibility curve (PPC) shifts outward along the horizontal axis for the capital-intensive good (good X). This shift illustrates the increased capacity to produce more of good X.

While the output of good X (capital-intensive) rises due to an increased capital endowment, the output of good Y (labor-intensive) falls because the additional capital skews the productive resources in favor of the capital-intensive good. Thus, the Rybczynski theorem demonstrates how factor endowments critically shape production patterns in an economy.

Production Possibility Curve (PPC)

The Production Possibility Curve (PPC) is a pivotal concept in economics that illustrates the possible combinations of two goods that a country can produce, given a certain level of resources and technology.

This curve is 'bowed out' or concave to represent increasing opportunity costs – producing more of one good requires sacrificing increasing amounts of the other good. The PPC is subjected to efficient production points, where all resources are fully utilized, and inefficient points within the curve.

In international trade, the PPC helps explain how countries decide on their production mix. The tangent line to the PPC, representing the price ratio in international markets, indicates the most profitable combination of goods a country can produce for trade. The slope of this tangent line is crucial, as it points to the optimal allocation of a nation's finite resources when influenced by international trade prices.

Edgeworth Box

The Edgeworth Box is a fundamental tool in economics that illustrates the distribution of resources between two commodities in a competitive market. This two-dimensional diagram showcases how varying combinations of two goods might be produced, given a fixed total of available resources.

The box depicts two efficiency lines (isoquants) representing the optimal usage of resources for producing the two goods. The lines meet at various points, marking the potential efficient allocations of resources to maximize production.

Inside the Edgeworth Box, the lens-shaped area where the isoquants are tangent to one another demonstrates the potential trade-offs and exchanges between the two goods. For international trade, this diagram aids in visualizing how equilibrium is achieved when a country's production aligns with the international price ratio. This insight is valuable in determining how different endowment levels and factor prices can lead to efficient production and trade.