In this paper we extend the Diamond and Dybvig (1983) model of interme
diation to study further the conditions under which bank runs can occu
r 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 migh
t choose to offer contracts that prevent runs, but under some conditio
ns the (second) best contracts will involve accepting some risk of run
s in order to achieve higher expected returns from their investments.
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