We analyze the implications of innovation and social interactions on economic growth in a stylized endogenous growth model with heterogeneous research firms. A large number of research firms decide whether to innovate or not, by taking into account what competitors (i.e., other firms) do. This is due to the fact that their profits partly depend on an externality related to the share of firms which actively engage in research activities. Such a share of innovative firms also determines the evolution of technology in the macroeconomy, which ultimately drives economic growth. We show that when the externality effect is strong enough multiple BGP equilibria may exist. In such a framework, the economy may face a low growth trap suggesting that it may end up in a situation of slow long-run growth; however, such an outcome may be fully solved by government intervention. We also show that whenever multiple BGP exist, they are metastable meaning that the economy may cyclically fluctuate between the low and high BGP as a result of shocks affecting the individual behavior of research firms.