The implications of automation for economic growth and the labor share

We introduce automation into a standard model of capital accumulation and show that (i) there is the possibility of perpetual growth, even in the absence of technological progress; (ii) the long-run economic growth rate declines with population growth, which is consistent with the available empirical evidence; (iii) there is a unique share of savings diverted to automation that maximizes long-run growth; (iv) the labor share declines with automation to an extent that fits to the observed pattern over the last decades.