But Albania's economy, unlike China's, is not often in the headlines. That is not only because China has such a dynamic economy, but also because it has the world's largest population. Multiplying a middling per capita income by more than 1.3 billion "capita" yields a big number. The combination of a large population and a medium income gives it economic power, and also political power.
Similarly, we consider the US the number-one incumbent power not just because it is rich. If per capita income were the criterion by which to judge, Monaco, Qatar, Luxembourg, Brunei, Liechtenstein, Kuwait, Norway, and Singapore would all rank ahead of the US. (For the purposes of this comparison, it does not matter much whether one uses market exchange rates or PPP rates.) If you are shopping for citizenship, you might want to consider one of those countries.
Read MoreChina wealth gap may be far worse than official estimates
But we do not consider Monaco, Brunei, and Liechtenstein to be among the world's "leading economic powers," because they are so small. What makes the US the world's leading economic power is the combination of its large population and high per capita income.
It is this combination that explains the widespread fascination with how China's economic size or power compares to America's, and especially with the question of whether the challenger has now displaced the long-reigning champion. But PPP exchange rates are not the best tool to use to answer that question.