The Autonomy Paradox: AI, Runaway Monopolization, and the Optimal Taxation of Capital

This paper develops a dynamic equilibrium model to analyze the economic consequences of self-improving, autonomous capital - i.e. AI. This new kind of capital makes a new, radical economic growth framework necessary which bears significant implications. I postulate a paradigm shift where the classical principal-agent problem is driven away wich engenders several consequences. The agent´s incentive and participation constraint vanish due to fierce competition with a new, super productive autonomous capital. Thus the agent´s effort is only determined by a new constraint - the \textbf{survival constraint}. If the economic AI productivity surpasses that of humans, agents drop out of the market. Former principals become now agents producing goods with autonomous capital. Due to potential non diminishing returns to scale at a certain point these new agents can not compete with even larger companys. A \textbf{runaway to monopolization} takes place. Hence the theoretical model features endogenous growth driven by capital accumulation with potentially non-diminishing returns, leading to runaway monopolization where large firms grow faster than small ones. This concentration, coupled with the erosion of labor's marginal product due to more and more productive autonomous capital, threatens to spur mass unemployment below a socially-defined survival consumption level. I characterize the government's problem of designing an \textbf{optimal profit tax} that redistributes income to ensure survival, while internalizing the tax's negative effect on investments and thus long-run growth. Using full dynamic optimization and numerical methods calibrated to OECD data, I derive the optimal tax path and identify precise technological conditions for runaway monopolization. The framework provides a unified basis for antitrust, redistribution, and growth policy in the age of AI, with extensions addressing political economy, international tax competition and robustness. JEL Codes: D21, D25, E24, E62, O33, O41