Competitive insurance markets with unbounded cost

Levy, Y. J. and Veiga, A. (2021) Competitive insurance markets with unbounded cost. Journal of Economic Theory, 192, 105198. (doi: 10.1016/j.jet.2021.105198)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Levy, Dr John
Authors: Levy, Y. J., and Veiga, A.
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Journal of Economic Theory
Publisher:Elsevier
ISSN:0022-0531
ISSN (Online):1095-7235
Published Online:20 January 2021
Copyright Holders:Copyright © 2021 Elsevier Inc.
First Published:First published in Journal of Economic Theory 192: 105198
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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