Comparative Advantage vs Absolute Advantage:
Between any two productive entities, be they people, or nations, there will likely be differences in their ability to produce something. For example, between two people, it is quite likely that while both can cook and clean, one might be able to cook more (better) in an hour vs the other person, and likewise for cleaning.
If an entity can produce more than another, with the given resources, then that entity has a greater productivity, and thus an absolute advantage over the other entity.
Now comes the real deal. If only one good had to be produced in the economy, then clearly the nation that produces more should continue producing as much as it can. However, the fact is that nations require/desire/want/need more than one good. And they need at least 2 goods, even when their resources are in limited supply. The limitation of resources implies that resources now need to be allocated to different production centers. Every time a nation chooses to direct resources towards the production of one good, it takes away the resources from production of the other good.
Thus, every production process has an opportunity cost associated with it. A nation that can produce a good at a lower opportunity cost has a comparative advantage in that good.
Clearly, a nation should produce more of a good for which its opportunity cost is lower. It's decision to specialize completely, giving up fully on producing the other good, or choosing to split production between the two goods then will be based on comparing the opportunity costs between the two producers at each point.
Once the combined production of two goods increases, a trade can be arranged so that both nations get both goods. Who gets what, and how much? Terms of trade are decided based on opportunity costs.
No nation will buy something from another nation, if it can produce the same good cheaper, at a lower opportunity cost than the other nation. Trade only makes sense economically if there are cost differences....opportunity cost differences!
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