When Does Procompetitive Entry Imply Excessive Entry?

The Dixit-Stiglitz model of monopolistic competition with symmetric CES demand system with gross substitutes is widely used as a building block across many applied general equilibrium fields. Two of its remarkable features are the invariance of the markup rate and the optimality of the free-entry equilibrium. Of course, neither of these two features is robust. Departure from CES makes entry either procompetitive or anticompetitive (i.e., the markup rate either goes down or goes up as more firms enter). Departure from CES also makes entry either excessive or insufficient. But how is the condition for procompetitive vs. anticompetitive entry related to that for excessive vs. insufficient entry? To investigate this question, we extend the Dixit-Stiglitz monopolistic competition model to three classes of homothetic demand systems, which are mutually exclusive except that each of them contains CES as a knife-edge case. In all three classes, we show, among others, that entry is excessive (insufficient) when it is globally procompetitive (anticompetitive) and that, in the presence of the choke price, entry is procompetitive and excessive at least for a sufficiently large market size.