# What happens to marginal revenue when quantity does not change?

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.

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 $$Q=10000$$.
• 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. Commented Apr 28, 2023 at 14:13
• @Chris If you produce one more unit, then the change in $Q$ is not zero, it is $1$. Commented Apr 29, 2023 at 15:21
• @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 $Q$. Commented Apr 29, 2023 at 18:41