The most fundamental proposition about growth and competition is that there is a tradeoff between static welfare and long-term growth. This paper reconsiders this basic proposition in an increasing product variety endogenous growth model with competitive markets for old innovative products and for a traditional good. We shed light on some implications of monopolistic distortions which tend to be ignored by standard models. First, no growth may be better than some growth, since modest positive growth potentially requires sizeable static welfare losses. Second, the economy may converge to a steady state with zero growth, even though another (saddle-point stable) steady state with positive growth exists if the initial share of cheap competitive markets is sufficiently high, as this implies a relatively low demand for expensive innovative goods. Third, such a no-growth trap may happen in a world economy made up of several countries engaged in free trade with each other. The policy implications are that growth-enhancing policies may be misguided and that quick deregulation as well as quick trade liberalization can lead to stagnation in the long term.