Competitive Insurance Markets with Unbounded Cost

69 Pages Posted: 24 Mar 2020

See all articles by Andre Veiga

Andre Veiga

Imperial College London

Yehuda Levy

Nuffield College and Department of Economics, University of Oxford

Date Written: February 27, 2020


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 sensitive to assumptions made about the upper bound of cost: introducing an infinitesimal mass of high cost individuals discretely increases all equilibrium prices and reduces coverage for all individuals. We measure model sensitivity to these assumptions by considering sequences of economies with increasing upper bounds of cost, and determining whether the sequence of their equilibria converges. We present sufficient conditions under which AG equilibrium exists when cost is unbounded. For simple insurance markets, we derive a condition which is necessary and sufficient for existence: surplus from insurance must increase faster than linearly with expected cost. This condition is empirically common. If this condition does not hold, a wider range of costs results in market unraveling because all prices increase without bound 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 characterised by a simple differential equation. We also provide examples of non- existence for lemons markets (where a single insurance product is available) with unbounded cost.

Keywords: Adverse Selection, Asymmetric Information, Insurance, Equilibrium Existence

JEL Classification: C62, G22, I13, D82

Suggested Citation

Veiga, Andre and Levy, Yehuda, Competitive Insurance Markets with Unbounded Cost (February 27, 2020). Available at SSRN: or

Andre Veiga (Contact Author)

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

Yehuda Levy

Nuffield College and Department of Economics, University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

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