Exploring the conditions for sustainability with open-ended innovation

TL;DR

The paper investigates whether sustained open-ended technological progress can be compatible with resource conservation on a finite Earth by introducing a stylized, genuinely open-ended innovation process that endogenously couples technology, demography, and environment. Technologies invade or fail to invade based on a threshold that depends on current population and environmental state, with innovation draws characterized by labor productivity $q$ and environmental impact $d$. A key finding is a phase transition: for low $q$ the system exhibits Schumpeterian dynamics that drives sustainable outcomes (finite population and recovery of $E$), while for higher $q$ the ecosystem is progressively depleted and population grows without bound. Crucially, the transition is driven by $q$ (labor-productivity-related inefficiency) rather than $d$ (environmental impact), and the model reproduces demographic-transition and environmental Kuznets curve-like behavior without assuming profit-maximizing incentives, highlighting the role of collective governance in steering sustainable open-ended innovation.

Abstract

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.

Figures (4)

• Figure 1: Illustrative sketch of the main variables of the model: $E$ (environment), $N$ (population), and $s_t$ (technology scale), all measured in the same units, and the parameters governing their interactions.
• Figure 2: Results of numerical simulations of the model with $T=10^4, 10^5$ and $10^6$ technologies, $N_0=100$ constant and $E_0=10$. $\theta_t$ and $\gamma_t$ are independently drawn from exponential distributions with mean $1/2$. Top left: $E$ as a function of $q$. Top middle: convergence of $E$ to $E_0$. Top right: $E$ as a function of $d$ (with $q=0.5$). Bottom left: $N$ as a function of $q$ (inset: $N/T$ as a function of $q$). Bottom middle: $n_s/T^{2/3}$ vs $q$. Bottom right: $\tau$ as a function of $q$. All quantities plotted as a function of $q$ are obtained from the same set of simulations, with fixed $d = 0.1$.
• Figure 3: Demographic transition under decreasing efficiency $q(T)$. Results of numerical simulations of the model taking $q(T)=q_0+\frac{x}{1+(T/T_0)^y}$ (red curve in the first plot on the left), with $x=0.50$, $y=2$, $T_0=5\times 10^4$, and $q_0=0.45$. The subsequent recovery of the environment resembles the environmental Kuznets curve grossman1995economic.
• Figure 4: Comparison of asymptotic solutions and simulation results for $\tau$ and $e$ as functions of $q$, with $T=10^6$. All other parameters are consistent with those used in the figures in the main text. The region between dashed lines corresponds to the critical region, with width $q_c \pm \delta q$, with $\delta q = T^{-\nu}$.