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What is the relationship between Adam Smith's theorem on the division of labor being limited by the extent of the market and his pin factory example? Are they each touching upon a different aspect of the division of labor? Is there any synergy or connection between the two or are they unrelated aspects?

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The example of pin manufactory is not related to the theory that division of labor is limited by the extent of the market.

Smith used the example of pin factory to demonstrate that division of labor increased output. Smith (WoN Book I Ch I) even explicitly says so, right after the first two paragraphs where he talks only about the "greatest improvements in the productive powers of labour" which he argues have "been the effects of the division of labour," he immediately follows with To take an example,...", and then he follows with the description of pin manufactory.

He does not return to this example in Chapter III, where he talks about the extent of the market being the limiting factor of division of labor. The non-exhaustive examples he gives to support this theory are; porters, smiths, carpenters, masons, even nail makers, but there is no mention of the pin factory anymore. He also focuses on how these professions are differently specialized in villages (small markets) and cities (more extensive markets) but again there is no mention of the pin factory anymore.

The pin factory in the Chapter I does not even properly illustrate the concept division of labor being limited by extent of the market, rather its an example of nearly perfect division of labor where every small task is performed by separate specialist.

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