The proposition establishes that one of our main results, that market-driven incentives
can lead banks to hold more capital than is socially optimal, continues to hold even for
the case where deposits are not insured. Moreover, it holds under similar conditions as
before: when the opportunity cost of deposits is low relative to the cost of bank capital.
The intuition is similar to that in the previous section, in that the market solution does not
fully internalize all the costs and benefits associated with holding capital. Specifically, when
there is an excess supply of funds banks need to adjust their offers to attract borrowers, and
end up competing their return away. However, the trade-off between the benefit of increased
monitoring and the cost of capital is not the same for borrowers as it is for the society.
From a social welfare perspective, requiring that banks hold large amounts of capital has a
large negative impact on bank profits when capital is relatively costly, and this reduction in
profits may more than offset any gains to borrowers from increased monitoring. Borrowers,
of course, do not fully internalize this effect, and may demand a higher level of capital than
what is socially optimal.
It is also worth pointing out that, unlike the case with deposit insurance, banks may now
wish to hold some capital even when funding is in short supply and borrowers must compete
for funding. The following proposition formalizes this result.
Proposition 8 When there is an excess demand for credit (N<M), banks will hold a
positive amount of capital (i.e., k>0)forrD sufficiently large.
Proof: See the appendix. □
The intuition for this result is as follows. When the deposit rate is constant, banks
have no incentive to hold any capital since capital is a costly form of financing. In the
absence of deposit insurance, however, capital signals a commitment to monitor on the part
of the bank. Depositors recognize this greater incentive to monitor by banks and reduce the
interest payment they demand on their deposits. Banks may therefore have an incentive to
hold capital as a way of reducing their cost of funding, and this incentive is greatest when the
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