Differentiable comparative statics with payoff functions not differentiable everywhere

In this note we consider Cournot oligopoly. Due to the consideration of sev eral consumers and/or technologies, the profit function is not differentiab le everywhere. We show that Cournot equilibrium never occurs in outputs whe re profit functions are not-differentiable. This result validates the proce dure of differentiating profit functions to perform comparative statics in models where profit functions are not differentiable everywhere. (C) 2001 E lsevier Science B.V. All rights reserved.