I think of comparative advantage & specialization as features of production. People producing the things that they have comparative advantage at puts society on the pareto frontier in terms of the amount of each good that is produced.
I haven’t been thinking of this as a theorem, but I think it could go something like: there are n people and m goods and person i will produce p*f(i,j) units of good j if they devote p fraction of their time to producing good j, and each person uses 100% of their time producing goods. Then if you want to describe the pareto frontier that maximizes the amount of goods produced, it involves each person producing a good where they have a favorable ratio of how much of that good they can produce vs. how much of other goods-being-produced they can produce.
That seems like a sensible way to set up the no-trade situation. Presumably the connection to trade is via some theorem that trade will result in pareto-optimal situations, therefore making comparative advantage applicable.
But I still wonder what the exact theorem is.
Then if you want to describe the pareto frontier that maximizes the amount of goods produced, it involves each person producing a good where they have a favorable ratio of how much of that good they can produce vs. how much of other goods-being-produced they can produce.
What do you mean by “favorable”? Is there some threshhold?
What do you mean by “involves each person producing”? Does it mean that they’ll exclusively produce such goods? Or does it mean they’ll produce at least some of such goods?
I think of comparative advantage & specialization as features of production. People producing the things that they have comparative advantage at puts society on the pareto frontier in terms of the amount of each good that is produced.
I haven’t been thinking of this as a theorem, but I think it could go something like: there are n people and m goods and person i will produce p*f(i,j) units of good j if they devote p fraction of their time to producing good j, and each person uses 100% of their time producing goods. Then if you want to describe the pareto frontier that maximizes the amount of goods produced, it involves each person producing a good where they have a favorable ratio of how much of that good they can produce vs. how much of other goods-being-produced they can produce.
That seems like a sensible way to set up the no-trade situation. Presumably the connection to trade is via some theorem that trade will result in pareto-optimal situations, therefore making comparative advantage applicable.
But I still wonder what the exact theorem is.
What do you mean by “favorable”? Is there some threshhold?
What do you mean by “involves each person producing”? Does it mean that they’ll exclusively produce such goods? Or does it mean they’ll produce at least some of such goods?