Accelerating growth is key to outrun technological black balls---caps numerous existential hazards.

Secondly, note that this existential risk Kuznets curve appears in the transition dynamics of the optimal allocation. Considering that existential risk mitigation is a global public good, it is unlikely resources are allocated to safety optimally in the real world. As such, this should not be taken to be a prediction of what a particular country with a particular set of institutions will do with regard to existential risk.

Nevertheless, there are a number of reasons why we might still be interested in the transition dynamics under the (impatient) optimal allocation. For one, since there are very long timescales involved here, it is very hard to know (and thus model) what government and societal institutions will evolve to deal with existential risk. However, the ideal these institutions will likely aim at is the optimal allocation. The optimal allocation might thus be a rough proxy for the real-world allocation.

Moreover, the (impatient) optimal allocation represents what I would call the “democratic possibilities frontier” or the “impatient public possibilities frontier.” Those who are principally concerned about the long-run future of humanity and advocate for a zero rate of pure time preference might want us to spend as much as possible on safety in order to avoid existential catastrophe and enable human flourishing millions of years into the future. Indeed, even in the Hamiltonian of the optimal allocation, the relative value of life ˜vt is a discounted term; the lower your discount rate ρ, the more you would want to spend on safety. However, the broader public is not so patient. As the empirical evidence cited earlier shows, people tend to have a (relatively large) positive rate of pure time preference; the public is impatient. Even perfectly designed institutions that take into account existential risk externalities will ultimately be constrained by the degree to which society actually cares about the future—they will be constrained by an impatient public. The existential risk Kuznets curve illustrates the implications of this impatience. On the one hand, this impatience results in a period of initially rising levels of risk. For example, this might mean that the arguably rising level of existential risk of the past century is not necessarily a market failure, but may well be part of the optimal path given positive pure time preference. On the other hand, rising standards of living lead even the most impatient public to start caring more about safety and averting an existential catastrophe. This leads workers and scientists to be shifted to the safety sector, eventually causing the hazard rate δ to exponentially decline. Even if people are impatient, if you make them well off enough, they will start caring about existential risk.

Seeing the arguably rising levels of existential risk in the past century, some might call for an end to economic growth. Yet this existential risk Kuznets curve indicates that stopping economic growth would be deleterious: it would simply freeze the hazard rate at a high level, leading to a fatal catastrophe sooner or later. Economic growth enables even an impatient public with a high rate of pure time preference to start caring about life, thus ultimately reducing risk and even leading to positive M ∞.

Some prominent thinkers have previously posited that humanity is passing through a unique period with an elevated risk of technological catastrophe. Sagan (1994) calls this the “time of perils.” Parfit (2011, p. 616), concurs:

We live during the hinge of history. Given the scientific and technological discoveries of the last two centuries, the world has never changed as fast. We shall soon have even greater powers to transform, not only our surroundings, but ourselves and our successors. If we act wisely in the next few centuries, humanity will survive its most dangerous and decisive period. Our descendants could, if necessary, go elsewhere, spreading through this galaxy.

This existential risk Kuznets curve provides theoretical evidence that grounds the intuition that we are living in a “time of perils.” We may be economically advanced enough to have created the means for our permanent destruction, but not economically advanced enough to care enough about decreasing this existential risk.

This “time of perils” has profound implications. For instance, those alive today who care about preserving the long-term future of humanity may have extraordinary altruistic leverage. By working to reduce existential risk now (increasing the resources dedicated to safety), they can reduce the area under the “hump” of the hazard rate δ. This in turn increases M∞, unlocking tremendous value. Moreover, since so few resources are dedicated to safety at the moment, there are likely very high marginal value opportunities available to work on safety. This is a unique situation. Suppose existential risk did not decline to zero exponentially: then M∞ = 0 regardless—the existential risk curve would never bend—so reducing risk now would not change the probability of a long and flourishing future of humanity. And if existential risk did not initially increase, it would never be such a substantial challenge and there wouldn’t be such high marginal value opportunities to work on reducing it.