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• Optimal climate change mitigation mostly focused representative agent framework. • Incomplete insurance markets adds realism and new mechanism for welfare. • Poorer households prefer stronger mitigation policies even absent redistribution. • Redistribution provides extra insurance. • Representative agent framework likely to underestimate welfare impacts of mitigation. Policy makers concerned with setting optimal values for carbon instruments to address climate change externalities often employ integrated assessment models (IAMs). In the past, these tools have relied on representative agent assumptions or other restrictive behaviour and welfare aggregations. However, there is an important trend in the economics of climate change towards including a greater degree of heterogeneity. In the face of global inequality and significant vulnerability of asset poor households, we relax the complete markets assumption and introduce a realistic degree of global household inequality. In contrast to the representative agent framework, we find that a household's position on the global wealth distribution predicts the identity of their most-preferred carbon price. Specifically, poor agents prefer strong public action against climate change to mitigate the risk for which they are implicitly more vulnerable. We find that the carbon tax fills the role of insurance, reducing the volatility of future welfare. It is this role that drives the wedge between rich and poor households' policy preferences, even in the absence of redistribution. Taking into account the risk channel, we derive an optimal tax value four times larger than standard estimates from representative agent models. [ABSTRACT FROM AUTHOR]