Arrovian theorems for economic domains. The case where there are simultaneously private and public goods

We prove that Arrow's theorem and, with quasi-transitive social preferences, a version of Mas-Colell and Sonnenschein's theorem, hold when there are simultaneously private and public goods, and the individuals are supposed to have selfish, continuous, convex and strictly increasing preferences. We first prove the results in an abstract general setting, and show that the above-mentioned economic domain is a model for this setting.