Extended supplement to "Insurance and inequality with persistent private information"

This supplement contains auxiliary technical results and proofs omitted from Bloedel, Krishna, and Leukhina (2025) (henceforth BKL) and its Supplemental Appendix (henceforth SA). First, Section I proves parts (a)–(c) and (e)–(f) of Theorem 3 from Appendix B.1 of BKL. (Part (d) of Theorem 3 is proved in SA-E.1 of BKL.) Second, Section J proves Proposition 3.2 from Section 3.3 of BKL and Lemma B.2 from Appendix B.2 of BKL. Finally, Section K proves supporting facts for Properties (a)–(e) from Section 5.2 of BKL. Throughout, we follow the numbering and labeling conventions from BKL and its SA.