Non-Exclusive Insurance with Free Entry: A Pedagogical Note

We consider the Rothschild-Stiglitz model of insurance but without the exclusivity constraint. It turns out that there always exists a unique equilibrium, in which the reliable and unreliable consumers take out a primary insurance up to its quantity limit, and the unreliable take out further secondary insurance at a higher premium. We provide a simple proof of this result (extended to multiple types of consumers) with the hope that it may be pedagogically useful.