Velorien comments on Harry Potter and the Methods of Rationality discussion thread, July 2014, chapter 102 - Less Wrong Discussion
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Don't forget potions. You could easily make use of muggle civilisation's amazing mass production ability by having them automate every step but the ones that need magical power. The magic drain from potion creation is minimal, so one or a few wizards could effortlessly power a production line.
Muggles also happen to be very good at large-scale farming, which could easily be applied to the production of magical ingredients, even rare ones.
Add in wizards' ability to cast permanent enchantments at no cost, and their vast array of utility spells (Vanishing Charms alone would be a godsend for any factory), and you have undreamt-of mass production potential.
Small population sizes aren't an issue when you have two worlds' worth of force multipliers.