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I understand that the Average Total Cost is equivalent to demand in a zero profiting monopoly or monopolistically competitive firm in order for there to be zero profits (when ATC = P at a given quantity), but why is ATC tangent to demand instead of intersecting demand at a point when ATC is downward sloping?

See: ATC Intersecting Demand while Tangent on the Left (why is this correct?) ATC Intersecting Demand while Downward Sloping on the Right (why is this wrong?)

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A profit maximiser will aim to seek to maximise the difference between total revenue and total cost, providing this is non-negative

  1. If there is a point at which this is positive, then this is equivalent to a point at which average total cost is below the demand curve, for example slightly to the right of $Q^*$ in your second diagram. At this point the firm will be making a profit, contrary to your assumption of zero profit. So your second diagram does not illustrate the zero-profit case

  2. Alternatively, if the demand curve is always strictly below the average total cost curve then all situations lead to a loss, so not a zero profit

  3. That leaves the case where the demand curve touches the average total cost curve but does not cross it, as in your first diagram. At this point there is zero profit and no opportunity to increase it. If the curves are smooth enough, you might describe this as the average total cost being tangent to demand

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