In this paper we provide necessary and sufficient conditions for the existence of a Cournot equilibrium when demand is rho-linear and firms are identical and produce under constant returns to scale. We focus on inelastic and convex demand which yields non concave profit functions. We show that equilibrium is unique and stable and yields well-behaved comparative statics. The model is able to generate huge welfare losses and non-downward sloping Laffer curves. We also study where a tax reform which substitutes specific by ad valorem taxation is not welfare-improving. In an Appendix we generalize our results on existence uniqueness and comparative statics to more general inverse demand functions.