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This paper studies the impact of the progressivity of income and inheritance tax on wealth inequality in France. By switching to a proportional tax system for each type of tax, we find that income-tax progressivity is more effective than inheritance-tax progressivity in reducing wealth inequality. Income-tax progressivity reduces income risk. The precautionary saving of the wealthiest agents decreases and wealth inequality narrows. Inheritance-tax progressivity does not modify income risk significantly. We also show that inheritance-tax progressivity – unlike income-tax progressivity – is inefficient for reducing income inequality.