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Clearly Alicia is better than Boris at making either type of vessel. She has the absolute advantage in making bowls and also the absolute advantage in making mugs. However, she is only a little faster than Boris at making bowls (150 per day versus 130), whereas she is almost twice as fast at Boris at making mugs (120 per day versus 65).
So Boris is more competitive with Alicia at making bowls than he is at making mugs. We describe this fact by saying that Boris has a comparative advantage in making bowls, even though Alicia has an absolute advantage. Where mugs are concerned, Alicia has both a comparative and an absolute advantage, because she is not only faster than Boris but faster by a bigger margin than with bowls. (Whenever there are two goods and two producers, a comparative advantage for one producer in making one good implies a comparative advantage for the other producer in making the other good.)
The reason this is important is that if a situation arises where Alicia and Boris each have to choose whether to make bowls or mugs, Alicia’s opportunity cost will be lower for mugs, but Boris’s will be lower for bowls. Here’s the math: Because Alicia can make either 150 bowls or 120 mugs in a day, the time she spends on 1 mug could have been spent making 1.25 bowls (\(150/120 = 5/4 = 1.25\)). In short, for Alicia the opportunity cost of 1 mug is 1.25 bowls. Conversely, the opportunity cost for Alicia of 1 bowl is 4/5 = 0.8 of a mug (\(120/150 = 4/5 = 0.8\)).
As for Boris, because he can make twice as many bowls in a day as he can mugs, for him the opportunity cost of 1 mug is 2 bowls, and the opportunity cost of 1 bowl is 1/2 = 0.5 of a mug. The opportunity cost in bowls of 1 mug is therefore lower for Alicia (1.25 bowls compared to 2 bowls for Boris), but the opportunity cost in mugs of 1 bowl is lower for Boris (0.5 of a mug compared to 0.8 of a mug for Alicia). So when we say that Boris has a comparative advantage in making bowls, we’re saying that the opportunity cost of making bowls is lower for him than it is for Alicia.
Note that the slope of each production possibilities frontier is the negative of the opportunity cost, measured in mugs per bowl. For Alicia, the slope is \(–120/150 = –0.8\). For Boris, the slope is \(–65/130 = –0.5\).
