The social cost of carbon is a central metric for optimal carbon prices. Previous literature shows that inequality significantly influences the social cost of carbon, but mostly omits heterogeneity below the national level. We present an optimal taxation model of the social cost of carbon that accounts for inequality between and within countries. We find that climate and distributional policy can generally not be separated. If only one country does not compensate low-income households for

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... portionate damages, the social cost of carbon tends to increase globally. Optimal carbon prices remain roughly unchanged if national redistribution leaves inequality between households unaffected by climate change and if the utility of households is approximately logarithmic in consumption.