Suppose There Are Two Products: Clothing And Soda Products

Suppose That There Are Two Products Clothing and Soda Producing the PPF

This assignment explores the concepts of production possibility frontiers (PPFs), comparative advantage, and international trade using two products—clothing and soda—produced by Brazil and the United States. The objective is to analyze the potential benefits of trade, determine which country has the comparative advantage, and examine the effects of trade on output, consumer welfare, and factor prices.

Production Possibility Frontiers for Brazil and the United States

The production possibilities frontier (PPF) illustrates the maximum combinations of clothing and soda each country can produce given their resources and technology. For Brazil, the data indicates annual production of 100,000 units of clothing and 50,000 cans of soda. For the United States, the respective figures are 65,000 units of clothing and 250,000 cans of soda. Assuming no change in costs and constant technology, the PPFs are linear and can be graphically represented by the trade-offs between the two goods.

Brazil’s PPF is bounded by the points (100,000 clothing, 0 soda) and (0 clothing, 50,000 soda). The slope — representing the marginal rate of transformation (MRT) — indicates how many units of soda must be forgone to produce one additional unit of clothing. Likewise, the U.S. PPF is defined by the points (65,000 clothing, 0 soda) and (0 clothing, 250,000 soda). These lines depict Brazil’s and the U.S.'s maximum production capacity under their resource constraints.

The Location of Current Production Points and Marginal Transformation Rate

Given that both countries produce specific quantities without trade—45,000 units of clothing and 150,000 cans of soda in the U.S., and 75,000 units of clothing and 30,000 cans of soda in Brazil—these points lie within each country’s PPFs, indicating that they are not fully utilizing their potential. The marginal transformation rate (MTR) in each country measures the opportunity cost of shifting production from one good to another. It is calculated as the ratio of the quantities sacrificed of one good to the gain in another along the PPF.

For Brazil, the MTR of clothing in terms of soda is calculated as the change in soda over the change in clothing: \(\frac{50,000 - 30,000}{0 - 75,000} = \frac{20,000}{-75,000} = -0.267\). The negative sign signifies that producing additional clothing costs approximately 0.267 cans of soda per unit of clothing. For the U.S., the MTR is \(\frac{250,000 - 150,000}{0 - 45,000} = \frac{100,000}{-45,000} = -2.222\). This means the U.S. sacrifices about 2.222 cans of soda to produce one additional unit of clothing.

Should Countries Specialize and Trade? Identifying Comparative Advantage

Trade becomes beneficial when countries specialize based on their comparative advantage—the ability to produce a good at a lower opportunity cost. In analyzing the opportunity costs, Brazil's cost of producing clothing is approximately 0.267 soda per unit, whereas the U.S.'s is roughly 2.222 soda per unit. Conversely, Brazil sacrifices fewer units of soda to produce clothing, indicating that Brazil has a comparative advantage in clothing production. In contrast, the U.S. has a lower opportunity cost for soda because it sacrifices fewer units of clothing per can of soda (calculated as the reciprocal of the MTR).

Therefore, Brazil should specialize in clothing, and the U.S. should specialize in soda, trading to maximize efficiency. When both countries specialize, total output increases because they are operating on their respective PPFs, utilizing resources more efficiently. For instance, Brazil could focus on clothing production, reaching 100,000 units, and the U.S. could focus on soda, producing 250,000 cans, thus expanding global output compared to the autarkic levels.

Trade Terms and Consumer Welfare

The proposed terms of trade are 1 can of soda for 5 units of clothing. This rate lies between the countries’ opportunity costs: Brazil values clothing at about 0.267 soda and the U.S. at 2.222 soda, so trading at 5 units of clothing per can of soda benefits both. Brazilian consumers gain more clothing than they would domestically, and U.S. consumers benefit from more soda, leading to higher overall welfare in both countries.

Trade allows consumers access to a broader mix of goods at lower prices, which increases consumption possibilities. Empirically, consumers in both nations are better off when trade occurs because it expands market choices, lowers prices, and promotes efficiency. Importantly, the gains from trade can lead to income redistribution within countries and potentially reduce poverty, especially in Brazil and other developing countries, by opening access to global markets and technology (Krugman, 2014).

Labor-Intensive Goods, Factor Abundance, and Development

The classification of goods as labor- or capital-intensive depends on the primary input used in their production. Clothing is generally labor-intensive, relying heavily on unskilled or low-skilled labor, whereas soda production may be less labor-dependent or require capital-intensive machinery. Brazil, characterized by abundant unskilled labor, is considered a labor-abundant country, while the U.S., with more capital and advanced technology, is capital-abundant.

Trade can help reduce poverty in Brazil and other developing countries by enabling them to specialize in labor-intensive industries, access higher-income markets, and promote industrial development. Over time, differences in product and factor prices tend to diminish as trade broadens, capital flows, wages adjust, and technological spillovers occur. According to the Heckscher-Ohlin model (SOBEL, 2017), factor-price equalization results from free trade, reducing disparities between countries and fostering economic convergence.

Conclusion

This analysis has highlighted the importance of comparative advantage in determining optimal specialization and trade. Brazil’s comparative advantage in clothing and the U.S.’s in soda demonstrate how international trade can enhance global efficiency and consumer welfare. Trade not only increases total output but also shifts income and resources, creating opportunities for developing countries to alleviate poverty through industrialization and integration into global markets. The eventual equalization of product and factor prices underscores the dynamic effects of trade liberalization, promoting economic growth and development worldwide.

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