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Competitive insurance markets with unbounded cost

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Title: Competitive insurance markets with unbounded cost
Authors: Veiga, A
Levy, Y
Item Type: Journal Article
Abstract: 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.
Issue Date: Mar-2021
Date of Acceptance: 12-Jan-2021
URI: http://hdl.handle.net/10044/1/85843
DOI: 10.1016/j.jet.2021.105198
ISSN: 0022-0531
Publisher: Elsevier
Start Page: 1
End Page: 36
Journal / Book Title: Journal of Economic Theory
Volume: 192
Copyright Statement: © 2021 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: 1401 Economic Theory
1499 Other Economics
Economic Theory
Publication Status: Published
Online Publication Date: 2021-01-20
Appears in Collections:Imperial College Business School

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