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The marginal revenue is defined (at least in my Econ 101 course) as $\Delta TR/\Delta Q$. However, say I am examining a town with $10,000$ people, and at a nonzero certain price, $10,000$ people demand a product. Decreasing the price decreases total revenue since there is no change in quantity, but what happens to marginal revenue? It seems to be ill defined in this case.

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Revenue and marginal revenue are defined as a function of $Q$, not of the price. If $Q=10000$ is the maximal demand (assuming consumers have unit demand), then an additional unit produced will be left unsold, so total revenue becomes constant and marginal revenue drops to zero at $Q=10000$.

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  • $\begingroup$ If the change in $Q$ is zero, but the total revenue is still changing then expression above, which is essentially just a derivative without limit, could not possibly be zero. $\endgroup$
    – Chris
    Commented Apr 28, 2023 at 14:13
  • $\begingroup$ @Chris If you produce one more unit, then the change in $Q$ is not zero, it is $1$. $\endgroup$
    – VARulle
    Commented Apr 29, 2023 at 15:21
  • $\begingroup$ My point is that the total revenue is changing but the production is not $\endgroup$
    – Chris
    Commented Apr 29, 2023 at 18:22
  • $\begingroup$ @Chris But $\Delta TR$ and $\Delta Q$ are not changes induced by an exogenous price change. Rather, the change in revenue is induced by the exogenous change in $Q$. $\endgroup$
    – VARulle
    Commented Apr 29, 2023 at 18:41

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