Question

If the United States could produce five automobiles instead of one ton of food (that is, the opportunity cost of producing one ton of food is five automobiles) and maximum food production is five million tons, then the maximum automobile production is twenty-five million. Given that on the international market ten automobiles can be exchanged for one ton of food, compare the production possibilities frontier with the trading possibilities frontier.

Short answer

In conclusion, the United States has a comparative advantage in automobile production as the slope of the trading possibilities frontier (TPF) is steeper than the production possibilities frontier (PPF). The steeper slope of the TPF (\(F = \frac{A}{10}\)) indicates that trading automobiles for food in the international market has a lower opportunity cost than producing food domestically (PPF: \(F + \frac{A}{5} = 5,000,000\)). By engaging in trade, the United States can achieve a higher level of consumption of both goods than what would be possible without trade.

Step-by-step solution

Find the Production Possibilities Frontier (PPF)

To find the PPF, we need to use the given opportunity cost of producing one ton of food and the maximum production quantities of food and automobiles. We know that the opportunity cost of producing one ton of food is five automobiles and the maximum food production is five million tons. So, when the country is producing no food, it can produce 25 million automobiles. As a result, the PPF equation can be written as: \(F + \frac{A}{5} = 5,000,000\), where F is food production (in tons) and A is automobile production.

Find the Trading Possibilities Frontier (TPF)

To find the TPF, we need to use the given exchange ratio in the international market. We know that 10 automobiles can be exchanged for 1 ton of food. So for each automobile, the country can get \( \frac{1}{10} \) tons of food. The TPF equation can be written as: \(F = \frac{A}{10}\)

Compare the PPF and TPF

Now that we have the equations for both the PPF and TPF, we can compare them to understand the relative advantage of trade. The PPF equation is: \(F + \frac{A}{5} = 5,000,000\) The TPF equation is: \(F = \frac{A}{10}\) We can see that the slope of the PPF is -5, which represents the opportunity cost of producing one ton of food (5 automobiles), while the slope of the TPF is -10, which represents the exchange rate of trading automobiles for food in the international market. The steeper slope of the TPF indicates that it is more advantageous to trade automobiles for food, as it reduces the overall opportunity cost than producing it domestically. In conclusion, the United States has comparative advantage in automobile production and can benefit from trading automobiles for food in the international market. This allows the country to achieve a higher level of consumption of both goods than what would be possible in the absence of trade.

Key concepts

Understanding Opportunity Cost

When making decisions in economics, we often must choose between different options, each with its own set of costs and benefits. Opportunity cost refers to the value of the best alternative that is given up when a particular choice is made. It's a fundamental concept that highlights the potential cost associated with not choosing the next best alternative.

For example, in the exercise, the opportunity cost of producing one ton of food is five automobiles. This means that when the United States chooses to produce one ton of food, it foregoes the opportunity to produce five automobiles. Understanding opportunity cost helps us to analyze the trade-offs involved in production and allocation of resources. It's crucial for determining the most efficient use of scarce resources to achieve the maximum output or satisfaction.

Trading Possibilities Frontier Explained

The Trading Possibilities Frontier (TPF) represents the maximum amount of goods a country can obtain by exchanging its own goods in the international market, given fixed trade rates. Unlike the Production Possibilities Frontier (PPF), which depicts the maximum feasible production outputs, the TPF gives us insight into the benefits of international trade and how it can expand a country's consumption possibilities.

Using our textbook exercise as an example, the TPF shows that for each automobile, the United States can obtain 0.1 tons of food in the international market. This opens up the possibility for the country to obtain more food while exporting fewer automobiles than if it were to rely solely on domestic production. The TPF is particularly useful for understanding how trade can allow a country to surpass its own production limitations and benefit from the principle of comparative advantage.

Comparative Advantage and Its Role

The principle of comparative advantage is a cornerstone of international trade theory. It states that even if one country is more efficient at producing all goods than another country, both can still benefit from trade if they specialize in producing the goods for which they have a relative efficiency advantage.

In the context of our exercise, although the TPF shows a favorable trade rate, the United States has a comparative advantage in automobile production because it can produce them at a lower opportunity cost relative to food. By specializing in automobile production and trading for food, the United States can consume at a point beyond its own PPF, effectively achieving a higher standard of living for its citizens. Comparative advantage encourages countries to specialize and engage in trade, leveraging their strengths for mutual gain.

The Impact of International Trade

The effects of international trade extend beyond simple import and export of goods. International trade can alter a country's production decisions and consumption possibilities. By exchanging goods and services with other countries, nations can focus on producing goods where they hold a comparative advantage and then trade for other goods they need or want.

In our exercise scenario, the United States can greatly benefit from international trade by exporting automobiles and importing food. This not only optimizes its resource usage but also boosts overall economic welfare. The interplay of opportunity cost, comparative advantage, and trade rates shapes a country's position in global trade, and understanding this dynamic is essential for the development of sound economic policies and strategies.