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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; and (iv) automation explains around 14% of the observed decline of the labor share over the last decades in the United States.
Klaus Prettner (Thu,) studied this question.