Worked Problem: It’s Not Magic

In the third book of the bestselling Inheritance Cycle fantasy series by Christopher Paolini, the hero, Eragon, extracts gold from the earth using magic. Eragon learned from his mentor, Oromis, that the earth contains minute particles of nearly every element. While these elements are too expensive to mine, they can be extracted by magic.

In the real world, these elements, called rare earths, aren’t extracted by magic but by Chinese companies. Rare earths are important for the operation of lasers, cell phones, computer hard drives, and many of the appliances we use daily. But they are also scattered about in small amounts, making them very difficult and expensive to mine. China currently controls about 95% of the world’s production of rare earths.

Meanwhile, the United States is the largest producer of chicken in the world. Fortunately, the United States and China can trade with each other. But what if China refused to export rare earths, forcing the United States to find ways to extract these rare earths on its own? What if China stopped importing chicken and reverted to self-production?

Now suppose that China and the United States can produce either chicken or rare earths—a hypothetical example based on an actual trading pattern. Assume that the production possibilities for rare earths and chicken are as follows:

Calculate the opportunity cost of rare earths and chicken for both countries. Does the United States have a comparative advantage in producing rare earths? Suppose China wishes to consume 64 billion pounds of chicken and 12 thousand tons of rare earths. Show this point on a graph of the production possibilities. Is this possible without trade?

Calculate the opportunity cost of rare earths and chicken for both countries.

Review the section “Comparative Advantage and Gains from Trade” on pages 33–36.

The production possibility frontiers for both countries are straight lines, which implies a constant opportunity cost of chicken in terms of rare earths. The slope of China’s production possibility frontier is − (the slope is defined as the change in the y-variable—rare earths—divided by the change in the x-variable—chicken—which in this case is − = − ), and the slope of the production possibility frontier for the United States is − . Thus, the opportunity cost for China of producing 1 thousand tons of rare earths is 4 billion pounds of chicken, and the opportunity cost for the United States of producing 1 thousand tons of rare earths is 10 billion pounds of chicken. Likewise, the opportunity cost for China of producing 1 billion pounds of chicken is of a thousand tons of rare earths (250 tons), and the opportunity cost for the United States of producing 1 billion pounds of chicken is of a thousand tons (100 tons) of rare earths.

45

Does China have a comparative advantage at producing chicken?

Review the section “Comparative Advantage and Gains from Trade” on pages 33–36.

A country has a comparative advantage in the production of a good if the opportunity cost of production is lower for that country than for another country. In this case, the opportunity cost of producing 1 billion pounds of chicken is of a thousand tons of rare earths (250 tons) for China and of a thousand tons (100 tons) of rare earths for the United States. Since is less than , the United States, not China, has a comparative advantage in the production of chicken.

Suppose China wishes to consume 64 billion pounds of chicken and 12 thousand tons of rare earths. Show this point on a graph of the production possibilities. Is this possible without trade?

Once again, review the section “Comparative Advantage and Gains from Trade” on pages 33–36, and especially Figure 2-5.

As shown on the following graph, China’s consumption of 64 billion pounds of chicken and 12 thousand tons of rare earths, demonstrated at point B, is outside the production possibility frontier without trade. If China consumed 64 billion pounds of chicken, without trade, it could consume only 4 thousand tons of rare earths, shown at point A. Thus, without trade, this level of consumption of both goods would be impossible.