We analyze the long-run growth effects of automation in the canonical overlapping generations framework. While automation implies constant returns to capital within this model class (even in the absence of technological progress), we show that it does not have the potential to lead to positive long-growth. The reason is that automation suppresses wages, which are the only source of investment because of the demographic structure of the overlapping generations model. This result stands in sharp contrast to the effects of automation in the representative agent setting, where positive long-run growth is feasible because agents can invest out of their wage income and out of their asset income. We also analyze the effects of a robot tax that has featured prominently in the policy debate on automation and show that it could raise the capital stock and per capita output at the steady state. However, the robot tax cannot induce a takeoff toward positive long-run growth.