Competitive insurance markets with unbounded cost

• 成果类型: Article
• 署名作者: Levy, Yehuda John; Veiga, Andre
• 署名单位: University of Glasgow; Imperial College London
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2021.105198
• 发表日期: 2021
• 关键词: Adverse selection; asymmetric information; insurance; Equilibrium existence

摘要

Azevedo and Gottlieb (2017) (AG) define a notion of equilibrium that always exists in the Rothschild and Stiglitz (1976) (RS) model of competitive insurance markets, provided costs are bounded. However, equilibrium predictions are fragile: introducing an infinitesimal mass of high-cost individuals discretely increases all prices and reduces coverage for all individuals. We study sensitivity w.r.t. cost bounds by considering sequences of economies with increasing upper bounds of cost, and determining whether their equilibria converge. We present sufficient conditions under which AG equilibrium exists when cost is unbounded. For simple insurance markets, we derive a necessary and sufficient condition for existence: surplus from insurance increases faster than linearly with expected cost. This condition is empirically common. If the condition fails, a higher bound on cost results in market unraveling: all prices diverge and, in the limit, an AG equilibrium does not exist. We use these results to show that the equilibrium for an insurance market with an unbounded continuum of types is characterized by a simple differential equation. We also provide examples of non-existence for a (single-product) market for lemons with unbounded cost. (C) 2021 Elsevier Inc. All rights reserved.