Robotic versus traditional capital complementarity and economic growth in the era of full automation

How will the widespread deployment of automation technologies such as industrial robots and artificial intelligence (AI) affect long-run economic performance? To address this question, we develop a model of economic growth for a fully automated economy in which output is produced with only two forms of capital: "traditional capital" (assembly lines, machines, etc.) and "robotic capital" (industrial robots, AI, etc.). In our setting, human labor is no longer competitive, and the central questions become how investment should be allocated across the two types of capital and how the degree of substitutability between them affects long-term economic growth. Using a two-level nested CES production structure (with no further assumptions), we characterize the competitive balanced growth path and the range of feasible long-run growth rates that a fully automated economy can attain. We show that the case of full automation can be consistent with the growth expectations of techno-optimists and the dynamics of economic growth along a balanced growth path depend on preference parameters, depreciation, and the degree of substitutability between robotic and traditional capital in both production and investment decisions. Our framework contributes to the debate on the economic consequences of automation and the extent to which this future is shaped by the underlying forces that determine the accumulation of traditional capital versus robotic capital.