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 \(O_{s}, O,\) 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, \((\theta)_{x}>(\phi)_{y}\) 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 capitalintensive good) and reduce the output of \(y\) (the laborintensive good).

Short answer

Question: Discuss three important theorems in international trade theory while referring to the production possibility curve and the Edgeworth box. Explain how the international price ratio, factor endowments, and opening trade relations affect factor price ratios and production outputs of goods x and y. Answer: The three important theorems in international trade theory are Factor price equalization theorem, Stolper-Samuelson theorem, and Rybczynski theorem. These theorems help to understand how international price ratio, factor endowments, and trade relations influence factor price ratios and production outputs of goods x and y. The Factor price equalization theorem states that free trade in goods leads to equal factor prices among trading countries, provided that they have the same production functions, technology, and international price ratio. In the Edgeworth box, the domestic production occurs where the international price ratio and the domestic production possibility frontier (PPF) are tangent. This tangent point determines the domestic factor price ratio, which will be equal across countries in an efficient state. The Stolper-Samuelson theorem explains that an increase in the relative price of a good enhances the real rewards to the factor used intensively in its production and reduces the real rewards to the other factor. In the Edgeworth box, an increase in the relative price of good x affects the domestic production, increasing x production and decreasing y production. This movement changes capital-labor ratio and wage-rental ratio, which in turn impacts trade relations. The Rybczynski theorem states that if the international price ratio is constant, an increase in the endowment of one factor of production increases the output of the good that uses that factor intensively and decreases the output of the other good. In the Edgeworth box, an increase in capital endowment shifts the PPF outwards, leading to greater output of the capital-intensive good (x) and lesser output of the labor-intensive good (y).

Step-by-step solution

Set up the problem and understand the concept of the factor price equalization theorem

Factor price equalization (FPE) theorem states that under certain conditions, free trade in goods will equalize the factor prices (wages and returns to capital) among trading countries. This occurs when both countries face the same production functions, technology, and international price ratio \((p=p_x/p_y)\).

Show the effect of the international price ratio on domestic production in the Edgeworth box

In Figure 13.4, the international price ratio \((p)\) determines the slope of the consumption possibility curve. This slope represents the ratio of the marginal rate of substitution \((MRS)\) between goods x and y in an efficient state. Domestic production will occur at the point where the international price ratio and the domestic production possibility frontier (PPF) are tangent.

Determine the factor price ratio \((w/v)\)

The tangent point between the PPF and price ratio line in the Edgeworth box also determines the domestic factor price ratio \((w/v)\). The production functions are the same throughout the world, so this implies that the factor price ratio \((w/v)\) will be equal across countries in the efficient state. b. Stolper-Samuelson theorem

Understand the Stolper-Samuelson theorem

The Stolper-Samuelson theorem states that an increase in the relative price of a good will increase the real rewards to the factor used intensively in its production and will decrease the real rewards to the other factor.

Demonstrate the effect of an increase in \((p)\) on the Edgeworth box

An increase in \((p)\), the relative price of good x, will shift the consumption possibility curve upward and cause the domestic production to move clockwise along the PPF. This leads to an increase in x production and a decrease in y production.

Show the effect on factor endowments and the factor price ratio

The clockwise movement along the PPF decreases the capital-labor \((k/l)\) ratio in both x and y production. This leads to a decrease in \((w/v)\), the wage-rental ratio, since less capital-intensive good y will be produced. This has implications for the opening of trade relations, which usually increases the price of a good produced intensively with a country's most abundant input. c. Rybczynski theorem

Understand the Rybczynski theorem

The Rybczynski theorem states that if the international price ratio, \((p)\), is constant, an increase in the endowment of one factor of production will increase the output of the good that uses that factor intensively and will decrease the output of the other good.

Show the effect of an increase in \((k)\) on the Edgeworth box

If \((p)\) remains constant in external markets, an increase in the endowment of capital \((k)\) will shift the PPF outwards on the x-axis since x is the capital-intensive good.

Analyze the effect on the output of goods x and y

The shift in the PPF due to an increase in \((k)\) will result in an increase in the output of good x (the capital-intensive good) and a decrease in the output of good y (the labor-intensive good) because of the higher availability of capital in the economy.

Key concepts

Factor Price Equalization Theorem

Understanding the Factor Price Equalization (FPE) Theorem is pivotal when exploring the nuances of international trade. This theorem posits a fascinating outcome of open global markets: the equalization of factor prices—essentially the costs of labor and capital—across nations engaging in free trade. Imagine it this way: two countries share the stage of global trade, employing similar technologies and exhibiting identical production functions. They are faced with a given set of international prices for goods produced and, voilà, wages and returns on capital tend to align.

Delving into the specifics, consider the Edgeworth box diagram. It's akin to a map that shows us at which exact point our domestic production activities decide to drop anchor, contingent on the international price ratio. Translate this to everyday terms: if the price of what you produce (relative to what you consume) is fixed on a global scale, it tells you how much of each good you should produce and, consequently, what your local prices for labor and capital ought to be. In essence, when conditions are right, a factory worker in one corner of the world should earn a similar wage to a worker in another, providing an even economic playing field fostered by international trade.

Now let's remember the drill-down details: the location in the Edgeworth box where production stabilizes also subtly hints at the ratio of wages to capital returns within a country. If this portrays a global uniformity, the theorem suggests that factor prices will harmonize across borders, painting a picture of international economic interdependence and consistency.

Stolper-Samuelson Theorem

Navigating through the Stolper-Samuelson theorem offers a lens to assess the direct impact of trade on incomes within a country. This theorem frames a scenario where an uptick in the price of a certain product engorges the pay packet of the resource predominantly used in its production; contrariwise, it mitigates the earnings tied to other resources.

Let's draw this out with the Edgeworth box. When the price ratio climbs, the box guides us to see that production veers towards the capital-intensive good. This isn't merely a shift in what we produce; it rewrites the story for how much capital and labor we use in both goods. Visually, it's a movement along the production possibility frontier, clocking in at a more capital-intense mix.

What ensues is a tangible change in the capital-to-labor ratio in both industries, which has a ripple effect on wages and rental rates of capital. In the grand tapestry of trade, this theorem illustrates the ebb and flow of a nation’s resource compensation when doors open to international trade. Specifically, it forecasts the burgeon of reward for the most abundant and hence cheaper factor, painting a picture of dynamic income redistribution as the global marketplace stretches its limbs.

Rybczynski Theorem

Turning the spotlight on the Rybczynski theorem, we unearth another dimension of international trade impact. When the winds of trade are steady—that is, the international price ratio for goods remains unshaken—an interesting phenomenon unfolds as we adjust the quantity of production factors, such as capital or labor.

Envision a scenario where a country suddenly finds itself with a surplus of capital, but the going rate for goods on the world stage doesn't waver. The Rybczynski theorem paints the picture: the bounty of capital naturally bolsters the production of the capital-gorging good, but here’s the kicker—it simultaneously stifles the output of the labor-lovin' good. The gears of the economy shift, captured elegantly within the boundaries of the Edgeworth box diagram. It's like a production see-saw; capital up, capital-intensive goods up, and labor-intensive goods down.

What this dance of supply and demand choreographs is a pivotal transition in a country's economic structure triggered by an imbalance in the factors of production, with no price provocations required. It's a testament to the organic relationship between a country's resources and its production menu, underscored by the immutable laws of supply and demand.

Production Possibility Frontier

The concept of the production possibility frontier (PPF) is fundamental to understanding trade-offs in an economy's production choices. Picture a graph where every possible combination of two goods that can be produced with a fixed set of resources is plotted. The boundary of this graph, the PPF, defines the limits of production efficiency.

A move along the PPF showcases a trade-off—you churn out more butter, you get less guns, assuming those are the two goods in question. It's the art of sacrifice; you can't have it all, and you must decide what takes priority given the resources at hand. This frontier also mirrors the health of the economy: if we peek at a PPF that's expanding, it whispers tales of economic growth, technological innovation, or an influx of resources.

The PPF's shape—a bow, in traditional textbooks—communicates how these trade-offs evolve. A straight line implies constant opportunity costs, while our usual curved line indicates that as you produce more of one good, you cough up ever more significant quantities of the other to keep production humming. Economies live and die on these principles, dictating what they produce, how they grow, and the way they interact with the vast, sprawling marketplace of international trade.

Edgeworth Box Diagram

The Edgeworth box diagram is a wonderous device, a square or rectangular tool that allows economists to peer into the heart of resource distribution and efficiency. Imagine a box where each point symbolizes a different allocation of resources between two goods. Dueling indifference curves for two consumers (or two goods) can be sketched within this box, unveiling the configurations where both can be better off or at least as happy as before—an economist's dream of an efficient allocation.

Oftentimes, it’s used hand-in-hand with the PPF to reveal the inner mechanics of production and consumption decisions—the dance of economics. Adjustments in this box mirror an economy's response to changes in technology, preferences, or resource availability. An increase in resources shifts the box, while a technological advancement may steepen or flatten the curve of production feasibility. Ultimately, it's a tool that crystallizes the axiom that economies are a delicate balance of what we have, what we want, and what we can make of it—a guide to the efficient use of the finite breadcrumbs of resources we've been doled out on this planetary table.