We analyze how tariff design incentivizes households to invest in residential photovoltaic and battery storage systems, and explore selected electricity sector effects. To this end, we develop an open-source electricity sector model that explicitly features prosumage agents and apply it to German 2030 scenarios. Results show that lower feed-in tariffs substantially reduce investments in residential photovoltaics, yet optimal battery sizing and self-generation are relatively robust. With increasing fixed parts of retail tariffs and, accordingly, lower volumetric retail rates for grid consumption, households have lower incentives for self-consumption. As a consequence, optimal battery capacities and self-generation are smaller, and households contribute more to non-energy power sector costs. A cap on hourly feed-in by households may relieve distribution grid stress without compromising PV expansion or prosumage models for households. When choosing tariff designs, policy makers should not aim to (dis-)incentivize prosumage as such, but balance effects on renewable capacity expansion and system cost contribution.