We analyze how tariff design incentivizes households to invest in residential photovoltaic and battery systems, and explore selected power sector effects. To this end, we apply an open-source power system model featuring prosumage agents to German 2030 scenarios. Results show that lower feed-in tariffs substantially reduce investments in photovoltaics, yet optimal battery sizing and self-generation are relatively robust. With increasing fixed parts of retail tariffs, optimal battery capacities and self-generation are smaller, and households contribute more to non-energy power sector costs. 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.