The Future of Work and Capital: Analyzing AGI in a CES Production Model

The integration of Artificial General Intelligence (AGI) into economic production represents a transformative shift with profound implications for labor markets, income distribution, and technological growth. This study extends the Constant Elasticity of Substitution (CES) production function to incorporate AGI-driven labor and capital alongside traditional inputs, providing a comprehensive framework for analyzing AGI's economic impact. Four key models emerge from this framework. First, we examine the substitution and complementarity between AGI labor and human labor, identifying conditions under which AGI augments or displaces human workers. Second, we analyze how AGI capital accumulation influences wage structures and income distribution, highlighting potential disruptions to labor-based earnings. Third, we explore long-run equilibrium dynamics, demonstrating how an economy dominated by AGI capital may lead to the collapse of human wages and necessitate redistributive mechanisms. Finally, we assess the impact of AGI on total factor productivity, showing that technological growth depends on whether AGI serves as a complement to or a substitute for human labor. Our findings underscore the urgent need for policy interventions to ensure economic stability and equitable wealth distribution in an AGI-driven economy. Without appropriate regulatory measures, rising inequality and weakened aggregate demand could lead to economic stagnation despite technological advancements. Moreover this research suggests a renegoation of the Social Contract.