project, minus an adjustment to account for the borrower’s reservation value (rL = R — rB).
Banks exert monitoring effort q = min { R-rD , 1} and earn positive expected profits (Π > 0).
Proof: See the appendix. □
The intuition behind Proposition 1 is simple. When there is an excess supply of profitable
lending opportunities, banks will retain all the surplus from investment projects as borrowers
compete away their own returns in order to attract funds. Since equity is more costly to
banks, they choose to finance themselves entirely with deposits. Banks benefit from a high
loan rate in two ways. First, a high loan rate provides them with a large return, all things
equal. Second, a high loan rate also give banks greater incentives to monitor. Loan rates
and capital are indeed two alternative ways to provide banks with monitoring incentives,
but they differ in their impact. Raising capital entails a direct cost only for banks, whereas
increasing loan rates has a negative impact only for borrowers. Banks therefore offer to lend
at the highest rate that borrowers’ are willing to accept.
Given banks’ desire to minimize their holdings of capital, there may be scope for capital
regulation in this context. Due to limited liability, banks do not internalize the full cost
of default, and simply choose their level of capital and loan prices so as to maximize their
expected profits. By contrast, a regulator interested in maximizing social welfare, which
includes the cost borne by the deposit insurance fund, would solve the following problem:
max SW = Π + CS — (1 — q)(1 — k)rD
k
= qR — (1 — k)rD — krE — cq2 (7)
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