[AnIrishDuck]

I didn't understand your argument at first; after you clarified I believe you are correct (with the corrections mentioned). My comment was intended to fix some flaws in your argument that rendered it incomplete, not incorrect.

I believe the constant MC assumption is dangerous though. MC is rarely fixed in microeconomics. It is almost always assumed to be an approximately linear function of quantity. Thus, increasing production will always increase MC. You'll need to hire more workers, pay more overtime, buy more expensive supplies, whatever (in the short run; in the long run firms expand production and the supply curve shifts). The assumption that MC won't change is almost always incorrect, and the MC changes affects whether the argument is valid or not.

Sorry if I'm sounding pedantic, just pointing out what my econ prof would've said to me about this argument.

EDIT: and I'm not trying to imply that you don't know any of this, just that it may benefit readers who have less economics exposure.