A general notion of market perfect contestability is introduced. It coincid
es with the definition given by Baumol ei al. under Bertrand competition, b
ut is compatible with Cournot competition as well as monopolistic competiti
on. Using this notion, we illustrate the fact that the number of active fir
ms in free-entry equilibrium may be largely indeterminate and different lev
els of positive profits may in many cases be sustained. This is shown to be
true, in spite of market perfect contestability, under either Cournot comp
etition or product differentiation. Examples are given for both cases. Appr
opriate conditions of increasing returns are required. JEL Classification N
umbers: D5, D43.