choice of capital from a social welfare perspective when we assume that there is an excess
supply of funds, and rates are set as part of a market solution to maximize the return to
borrowers. In other words, a regulator would solve the following problem.
max SW = Π + CS - (1 - q)(1 - k)rD
k
= qR - (1 - k)rD - krE - cq2 (9)
subject to
rL - (1 - k)rD
q = mini------2------, 1∫;
rL =argmaxCS = q(R - r)
r
0 ≤ k≤1.
Again, we focus here on the case of an interior solution, and leave the other cases, which are
qualitatively similar, to the appendix.
Proposition 5 Assume that R < 2c2rEr-rD . When there is an excess supply of funds, cap-
ital regulation that maximizes social welfare requires banks to hold capital equal to kreg =
min n RrD+rD r8c(rE rD), 1O, which is less than 1 for R < 8c(rE-D)
Equilibrium monitoring is q = R-(1-C g)rD < 1.
and equal to 1 otherwise.
Proof: See the appendix, which contains a full characterization of the equilibrium. □
While the interest rate on the loan is determined in a competitive market setting and not
subject to regulatory interference, a regulator may want to impose a capital requirement for
banks in order to ensure they have sufficient incentives to monitor. In contrast to Proposition
2, now the regulator is more likely to require that banks hold a positive amount of capital, and
this amount is greater than in the case where bank funds are in short supply. The reason
is that the market sets a lower loan rate when borrowers obtain the surplus than when
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