Econ 355 International Trade 2012-13 Professor Matilde Bomba
Econ 355 International Trade2012 13professor Matilde Bombardiniprobl
This assignment requires an in-depth analysis of the Heckscher-Ohlin-Samuelson (HOS) model applied to two goods—Computers and Textiles—and the impact of trade on factor prices and income distribution. The tasks include explaining the behavior of marginal products, deriving relationships between wages and factor intensities, analyzing relative factor usage and prices, and understanding the effects of trade and factor endowment differences through the Stolper-Samuelson and Rybczynski theorems. The questions also involve evaluating statements about international trade theory in terms of factor prices and income distribution effects, especially considering a country like the US opening to trade with China and experiencing changes due to immigration.
Paper For Above instruction
The Heckscher-Ohlin-Samuelson (HOS) model offers a fundamental framework for understanding how comparative advantage arises from differences in factor endowments across countries. In this context, the production functions for two goods—Computers (C) and Textiles (T)—are expressed using varying proportions of skilled labor (S) and unskilled labor (U). These functions are essential for analyzing how factor usage varies with changes in relative prices and wages, underpinning the entire trade analysis.
Initially, considering the marginal products of skilled and unskilled workers in each sector, it becomes evident that the marginal product of skilled workers (MPSC and MPST) is increasing with the amount of unskilled labor used (U S) and decreasing with the amount of skilled labor (U S). This is because the production functions involve fractional powers that reflect diminishing or increasing returns to scale at different levels of input. For example, in the computer sector, MPSC = (2/3) (UC/SC)^(1/3), indicating that as the ratio of unskilled to skilled workers increases, the marginal product of skilled workers also increases, reflecting an increasing marginal productivity owing to the convexity of the function. Conversely, the marginal product of unskilled workers diminishes as U S increases because the partial derivatives indicate diminishing returns at higher U S ratios, consistent with typical diminishing marginal productivity in decreasingly resource-constrained sectors.
Furthermore, the relationship between wages and factor intensities can be derived by considering the relative prices of goods and their relative factor usages. With wages denoted as wS for skilled workers and wU for unskilled workers, and prices as pC and pT for Computers and Textiles respectively, the ratios of the marginal products lead to specific relationships. In the computer industry, the ratio of skilled to unskilled inputs, SC/UC, is proportional to the ratio of wages, specifically: SC/UC = 2 × (wU/wS). Similarly, in the textile industry, ST/UT = (1/2) × (wU/wS). These relationships reveal how wages influence the input ratios employed in each sector.
The comparative analysis indicates that textiles are more “unskilled-labor intensive” than computers, as evidenced by the fact that the ratio of unskilled to skilled labor (ST/UT) in textiles is higher relative to the computer sector's ratio (SC/UC). This means textiles rely more heavily on unskilled labor, reflecting a factor intensity that favors the unskilled workforce. Graphically, when plotting the relationships between relative wages and input ratios, the two sectors display distinct slopes, with textiles showing a steeper relationship, confirming its unskilled-labor intensity.
The relationship between goods prices and factor prices extends further, with the relative price of textiles to computers (pT/pC) related to the ratio of wages via pT/pC = 3√(wU/wS). Graphing this alongside the input ratio relationships provides a visual picture of how changes in relative factor prices influence the relative costs and outputs of each sector.
In the scenario of an autarkic country like the US, characterized by an abundance of skilled labor, and with the initial relative price of textiles to computers (pT/pC) set at 1, the relative wages (wU/wS) and factor usage ratios align accordingly. Under autarky, the balance of factor endowments and prices results in particular levels of wages and input ratios that equate the relative prices and factor costs within the domestic economy.
When the US opens trade with China, an unskilled-labor-abundant economy, the relative prices shift—the price of computers rises relative to textiles, with pT/pC falling to 1/8. This change occurs because the US, now engaging in trade, specializes according to its comparative advantage, exporting the good that intensively uses the abundant factor. Consequently, the relative price increase of computers (a skilled-labor-intensive good) can be explained through comparative advantage and factor price equalization mechanisms asserted by the Stolper-Samuelson theorem. The US gains from trade by exporting computers, benefiting skilled workers through higher wages, while unskilled workers face wage reductions—illustrating income redistribution inherent in trade.
Under trade, the new equilibrium shows adjustments in wages: the relative wage (wU/wS) improves for skilled workers and deteriorates for unskilled workers, who experience decreased real wages. The relative factor usage also shifts, with sectors specializing further according to comparative advantage. The Stolper-Samuelson theorem predicts these changes, emphasizing that trade benefits the abundant factor in each country, leading to increased returns for that factor and potential income inequality within nations.
If a large influx of unskilled immigrants suddenly occurs in the US while maintaining the relative price at pT/pC = 1/8, the model indicates significant impacts following the Rybczynski theorem. The abundance of unskilled labor prompts a reallocation of resources, increasing the production of unskilled-labor-intensive goods (textiles) and decreasing the production of skilled-labor-intensive goods (computers). Simultaneously, the real wages of unskilled workers decline due to increased supply, while the wages of skilled workers may remain unchanged or even increase in relative terms, depending on the elasticity of substitution between factors. This reflects the dynamic adjustment process within a country’s production structure in response to changing factor endowments.
Addressing true/false questions derived from the HOS and Stolper-Samuelson theories offers further insights. First, the relative price of capital-intensive goods tends to decline in capital-abundant countries when trading with labor-abundant nations, aligning with the factor-price equalization mechanism. Second, factor prices tend to converge across countries when trade flows increase, although absolute convergence may take longer or be incomplete due to market frictions. Third, in small open economies, unskilled immigration generally depresses wages of unskilled workers since increased supply lowers marginal productivity. Fourth, trade can improve individual welfare in the short run but may cause long-term disparities, especially if income distribution is uneven. Fifth, the rise in the skill premium in the US correlates with the increasing relative prices of skill-intensive goods, consistent with the HOS model. Lastly, the theory assumes technological differences are fundamental, but empirical evidence suggests that factor endowments are primary drivers of trade patterns globally.