The European Commission calls for more small-scale renewable energy producers to actively participate in the energy value chain. In this study, we model an illustrative peer-to-peer (P2P) market with tariffs based on the reservation prices of market participants under the German levy regime. The study is conducted by modeling representative residential buildings with home energy management systems, modulating heat pumps, and photovoltaics, in combination with electrical and thermal storage systems. The resulting mixed-integer linear program is solved over the course of a year, using a rolling horizon approach with a time resolution of one hour. By analyzing the cost- and discomfort-minimizing behavior of the market participants, we evaluate the current levy regime and propose two additional designs. We find that in the current case, a P2P market is not economically viable. Based on feed-in tariffs (FiT) and levies no agreeable market price can be found. With no FiT or reduced levies, all participants benefit from the P2P market. The market split—where each household sources their energy from—is altered only little by the specific details of the market design when staying in the agreeable price range. As prosumagers do not consume on the P2P market, they benefit only marginally from the reduced levies—consumers are most affected. Adjusting the regime could be a measure to rebalance the distribution of renewable energy benefits towards consumers in order to foster social cohesion. Our input data and the model written in the Julia JuMP programming language are available in an open-source format.