Chamberlin showed that monopolistic competition inherently leads firms to operate with unused plant capacity in the long run.
In monopolistic competition each firm has a downward-sloping demand curve.
The only quantity that can be sustained in the long term is a quantity that yields the firm zero profit. This is where Price = Average Cost. We would find and analyze this equilibrium quantity.
Chamberlin assumed the cost function contigent on quantity $c(Q)$ is convex — in fact, he would assume something stronger: average cost $c(Q)/Q$ is convex and U-shaped. (NOTE: $c(Q)$ convex $\not\to c(Q)/Q$, think $c(Q) = Q^{3/2}$.)
Now the equilibrium quantity is where the average cost curve tangent with demand curve: $Q^*$ such that $D(Q^*) = c(Q^*)/Q^*$.
We also define the max production quantity $Q^{**}$ where it minimize average cost curve.
We know that $Q^*< Q^{**}$. Therefore monopolistic competition would lead firms to operate with excess capacity, in the long run at ‘zero-profit equilibrium’ under convex production cost.