Can people lack a comparative advantage and a comparative disadvantage?

Question

Source: Question 9b, p 61, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw
= Question 8b in Principles of Microeconomics, 4 Ed, 2008

9. Are the following statements true or false? Explain in each case.
b. “Certain very talented people have a comparative advantage in everything they do.”

Answer: b. False; it is not true that some people have a comparative advantage in everything they do. In fact, no one can have a comparative advantage in everything. Comparative advantage reflects the opportunity cost of one good or activity in terms of another. If you have a comparative advantage in one thing, you must have a comparative disadvantage in the other thing.

Abbreviate comparative advantage as CA. Mankiw's question above motivates the titled one.

E.g., suppose in a 3-person economy: person A's CA is cooking and person B's foraging, yet person C does nothing.

Answer 1

Comparative advantage doesn't work like that.

If person A's CA is cooking, person C has a comparative advantage in foraging. With B, C has a comparative advantage in cooking.

It's not possible to have a comparative advantage or comparative disadvantage in everything: If you were better at everything than someone else, you would have an absolute advantage. As soon as two people have different skills for anything, they have a comparative advantage of some kind.

It is possible for two people to have no comparative advantage/disadvantages whatsoever: If both people are exactly equal at everything they can do, then there is no comparative advantage or disadvantage between them at all.

Answer 2

In the three person economy, if all three people are equally good at cooking and foraging then they have neither absolute nor comparative advantages. But that's unlikely to be an economically important situation in a real economy with many jobs to do and many forms of skill and ability.

Answer 3

You might be confusing comparative advantage with absolute advantage. Comparative advantage is focused on opportunity costs. You are assuming that person A is good at cooking, B is good at foraging, and C is a good-for-nothing. However, no matter how lousy C is at both the skills, he still possesses them. So in this comparison, take a look at the following scenario:

Assume there are only two skills to be discussed.

A can cook 3 pots of rice per hour OR forage 2 rabbits per hour.

B can cook 2 pots of rice per hour OR forage 3 rabbits per hour.

C can cook 1 pot of rice per hour OR forage 1 rabbit per hour.

In the A and C comparison, A must give up cooking 3 pots of rice per hour in order to forage 2 rabbits for that hour. To make it easier to compare, A must give up cooking 3/2 pots of rice to forage 1 rabbit per hour.

On the other hand, C only needs to give up cooking 1 pot of rice to forage 1 rabbit per hour. So from this, you see that C actually has comparative advantage in foraging compared to A. Note that A is still better than C at foraging (absolute advantage), but he must give up cooking more pots of rice, thus the comparative advantage. Whether or not C actually wants to do any work, it is non-relevant.

In the B and C comparison, B must give up foraging 3 rabbits in order to cook 2 pots of rice per hour. Simplified, B must give up foraging 3/2 rabbits in order to cook 1 pot of rice per hour.

Person C on the other hand, only gives up foraging 1 rabbit to cook 1 pot of rice per hour... and now you see where we are going with this.

I hope this answers your question!