Aggregate efficient production and division of labour

Question

How to resolve the following seeming contradiction? Mas-Colell, Whinston, Green p. 148 Prop. 5.E.1 says that the efficient aggregate (coordinated) production is just the sum of individually optimal productions. But Adam Smith argued that division of labour allows more efficient production than the sum of individual productions.

Of course Adam Smith's argument is informal, so it is not clear what assumptions differ from Mas-Colell. It could be that Smith envisioned production units with market power, externalities or some other inefficiency and the inefficiency somehow disappears with aggregation.

Answer 1

I would say, it is more Proposition $5.\text{F}.1$ on page 150, in combination with $5.\text{E}.1$ that leads to, as the authors write discussing the two,

"...if a collection of firms each independently maximizes profits with respect to the same fixed price vector $p >>0$, then the aggregate production is socially efficient. That is, there is no other production plan for the economy as a whole that could produce more output using no additional inputs."

Note that no assumption of identical suppliers is made here, or any other restrictive assumption about technology or the production set. The crucial assumption is the "price-taking" behavior assumed for all firms. Or, "no-market-power". Or, "all firms are equal": doesn't Perfect Competition sound a lot like the market version of Communism (not Socialism)?

P.S.: Externalities could also create issues here, of course.