Exploring the conditions for sustainability with open-ended innovation

Can sustained open-ended technological progress preserve natural resources in a finite planet? We address this question on the basis of a stylized model with genuine open-ended technological innovation, where an innovation event corresponds to a random draw of a technology in the space of the parameters that define how it impacts the environment and how it interacts with the population. Technological innovation is endogenous because an innovation may invade if it satisfies constraints which depend on the state of the environment and of the population. We find that open-ended innovation leads either to a sustainable future where global population saturates and the environment is preserved, or to exploding population and a vanishing environment. What drives the transition between these two phases is not the level of environmental impact of technologies, but rather the demographic effects of technologies and labor productivity. Low demographic impact and high labor productivity (as in several western countries today) result in a Schumpeterian dynamics where new "greener" technologies displace older ones, thereby reducing the overall environmental impact. In this scenario, global population saturates to a finite value, imposing strong selective pressure on technological innovation. When technologies contribute significantly to demographic growth and/or labor productivity is low, technological innovation runs unrestrained, population grows unbounded, while the environment collapses. As such, our model captures subtle feedback effects between technological progress, demography and sustainability that rationalize and align with empirical observations of a demographic transition and the environmental Kuznets curve, without deriving it from profit maximization based on individual incentives.