We estimate an EASI demand system with nonlinear Engel curves, a labour supply schedule, and an income tax schedule from German household data. We combine this with a model of households’ and firms’ carbon emissions to obtain a micro-based simulation model of the German economy. The policy of pricing carbon and rebating the revenue as lump-sum climate dividends curbs emissions and offsets some of the adverse effects on the equity of regressive carbon taxes. If the government is permitted to also reform the income tax system, it never lowers income tax revenue, but makes the tax slightly less progressive in a budgetary-neutral fashion while simultaneously increasing the optimal carbon tax and climate dividend. Carbon tax and climate dividends rise with inequality aversion and carbon is priced consistently below the Pigouvian rate except if inequality aversion is high enough. We decompose the effects on welfare into efficiency, equity, and emission components for different degrees of inequality coefficient and climate damages. Income tax reform is preferred over climate dividends when raising carbon taxes if inequality aversion is low and vice versa.