How to explain rising income and wealth inequality? We build an original heterogeneous- agent model with three key features: (i) an explicit link between firm’s market power and top income shares, (ii) a granular representation of the tax and transfer system, and (iii) three assets with endogenous portfolio decisions. Using France as an illustration, we look at how changes in markups, taxes, factor productivity, and asset prices affect inequality dynamics over the 1984-2018 period. Rising markups account for the bulk of rising income inequality. Wealth inequality dynamics result mostly from changes in saving rate inequality but only in response to the exogenous changes in taxation and markups. Our results point to the critical importance of endogenous saving decisions in response to exogenous shocks as a key driver of wealth inequality.