The implications of automation for economic growth and the labor share of income

We introduce automation into the standard Solovian 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 the long-run growth rate of the economy; (iv) the labor share declines with automation to an extent that fits to the observed pattern.