We use a heterogeneous agents overlapping generations (OLG) model to quantitatively assess the impact of a reform in which a personal income tax with increasing marginal tax rates is replaced by a flat tax possibly complemented with a deduction. The value of the flat tax rate is set in order to balance the government budget and accordingly it increases with the value of the deduction. The model is calibrated and simulated for Italy. For low values of the deduction, aggregate labor supply increases, though this aggregate effect masks a completely different impact on the intensive and the extensive margin of labor supply: in particular, the activity rate is reduced by the introduction of a flat tax. As to inequality, it rises and this increase can be mitigated by using an higher value of the tax deduction, which however dampens down the positive effect of a flat tax on economic performance. Finally, the effect of a flat tax on social welfare crucially depends on the degree of inequality aversion embedded in the social welfare function and on the Frisch elasticity of labor supply.