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Climate policy is often described by economists as an intertemporal consumption trade-off: consume all you want today and face climate damages in the future, or sacrifice consumption today to implement costly climate policies that will bring future benefits through avoided climate damages. If one assumes enduring technological progress, a society that is more averse to intertemporal inequalities should postpone climate policies and let future, richer generations pay more. Growing evidence however suggests that the trade-off is more complex: abrupt, extreme, irreversible changes to the climate may cause discontinuities to socio-economic systems, possibly leading to a sharp decline of human population and consumption per capita. In this paper, we show that, when accounting for a very small risk of catastrophic climate change, it is optimal to pursue stringent climate policies to postpone the catastrophe. Our results conform with the well-known conclusion that tight carbon budgets are preferred when aversion towards inequalities between generations is low. However, by contrast with previous studies, we show that stringent policies are also optimal when inequality aversion is high. The non-monotonicity of the influence of inequality aversion is due to the fact that, for a given investment in abatement, a higher inequality aversion gives a smaller weight to avoided future non-catastrophic damages, but a larger weight to the catastrophic outcome. We also explore the role of population ethics, and show that the size of the optimal carbon budget decreases with the social preference for large populations, although this parameter plays almost no role at extreme levels of inequality aversion. Our result demonstrates that views from opposite sides of the ethical spectrum in terms of inequality aversion converge in terms of climate policy recommendations, warranting immediate climate action. [ABSTRACT FROM AUTHOR]