When I teach comparative advantage to my students, I point out that that the improvement in the skill of one person redounds to the benefit even of those whose skills (or, more generally, productivity) remain unchanged.
Suppose at first that if Tom spends all of his time fishing he can catch 50 fish each month; if, instead, he spends all of his time gathering bananas he can gather 50 bananas each month.
Suppose also that if Sue spends all her time fishing she can catch 200 fish each month; if, instead, she spends all of her time gathering bananas she can gather 100 bananas each month.
In this simple example, Tom has a comparative advantage in banana-gathering and Sue has a comparative advantage in fishing. The reason is that the cost to Tom of producing one banana is one fish, while the cost to Sue of producing one banana is two fish. (And the cost to Sue of producing one fish is 1/2 a banana while the cost to Tom of producing one fish is one banana.)
So both Tom and Sue can become wealthier if Tom specializes in banana-gathering, Sue specializes in fishing, and then each trades part of his or her output for part of the output of the other.
Note that Sue is willing to pay Tom up to 2 fish for each banana that she buys from him. The reason is that to produce her own bananas would cost Sue a minimum of 2 fish for each banana that she produces. Because Tom’s cost of producing each banana is one fish, gains from trade are possible.
Now let Sue’s skill as a fisherwoman improve (which, as Adam Smith pointed out, likely happens when workers specialize). Suppose that Sue’s skill as fisherwoman improve so much that she can now, were she to devote all of her worktime to fishing, produce 300 fish per month — 100 more fish than she was able to produce before her fishing skills improved.
Let’s assume also that there’s no change in Sue’s banana-gathering skills, and no change in any of Tom’s skills.
Two facts are interesting to note about Sue’s improved skill at fishing:
First, becoming a better fisherwoman makes Sue a worse banana-gatherer. It’s not that the number of bananas she can gather per month has fallen; it hasn’t. It’s that Sue’s cost of gathering bananas has risen. Sue’s ability to catch more fish per month means that any given amount of time that she spends gathering bananas obliges her now to sacrifice more fish than she sacrificed in the past when gathering bananas. The better she becomes at fishing, the more costly becomes any bananas that she might gather.
Second, Sue’s improved fishing skills — by raising her her cost of gathering bananas — also increases Tom’s efficiency of gathering bananas relative to that of Sue. Before Sue’s fishing skills improved, Tom could produce bananas at half the cost of Sue (one fish per banana for Tom; two fish per banana for Sue). Now, because Sue is a better fisherwoman than before, Tom’s can produce bananas at one-third the cost of Sue (one fish per banana for Tom; three fish for Sue).
Sue’s acquisition of more fishing skills at least potentially benefits also Tom. Before Sue’s skill-enhancement, the most she would have paid for one of Tom’s bananas was two fish; now, being a better fisherwoman, the most Sue will now pay for one of Tom’s bananas is higher, at three fish.
Reflecting on these truths about comparative advantage recalls to mind Wilhelm von Humboldt‘s observation about one of the great benefits of commerce:
It is through a social union, therefore, based on the internal wants and capacities of its members, that each is enabled to participate in the rich collective resources of all the others [The Limits of State Action, p. 11].
[This Humboldt book's title is also sometimes translated as The Sphere and Duties of Government, and is available on line here.]