In this paper we extend the Diamond and Dybvig (1983) model of intermediation to study further the conditions under which bank runs can occur and to consider how private parties might adjust to the existence of bank-run equilibria. We provide weaker necessary conditions for runs. We then characterize how banks respond to the possibility of runs in their design of deposit contracts and investment decisions. Banks might choose to offer contracts that prevent runs, but under some conditions the (second) best contracts will involve accepting some risk of runs in order to achieve higher expected returns from their investments.
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Cooper et al. (1998) studied this question.
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